SPY/SPX Expected Move + Session Levels📊 Expected Move + Session Levels (SPY / SPX)
Plots the day's expected move band plus the key session levels — automatic, refreshed daily before the open, nothing to enter or maintain.
🔹 Draws: Expected Move High/Low (the one-standard-deviation daily range implied by options pricing, anchored at the prior close), Prior Day High/Low, and Overnight High/Low (from the ES futures overnight session, rescaled to your chart). Optional shaded band and info table.
⚙️ Settings: every level toggles on/off individually; colors, line width, and label size are adjustable. The overnight source, session window, and IV index can be changed, and setting Horizon to 5 with VIX approximates the weekly move. Best on intraday timeframes.
⚠️ Note: the expected move is a statistical estimate, not a boundary — price is expected to close inside the band roughly two days out of three, and beyond it roughly one in three. Treat the edges as context, not walls; the market will go where it chooses. All levels are built from CBOE volatility indices, daily session data, and CME ES futures. Informational only, not trading advice. Indikator
Expected Move BandsEvery options desk opens the week with the same question: how far is this thing supposed to travel by Friday? The answer's already priced. Implied vol is the market's own estimate of the coming move, and you can read it straight off the chart instead of running the math in your head.
This draws that estimate as bands around price. It anchors to the open of each week (or month, your call) and holds the bands flat across the period, the way a desk marks its expected range Monday morning and watches price work inside it.
The teal band is one standard deviation. If the market's vol read is right, price closes inside it about two times out of three. The wider band is two sigma, the tail. When price breaks the one-sigma band and holds out there, that's range expansion, the move getting repriced while it happens. Usually worth a look.
IV comes from VIX on equities and Deribit DVOL on crypto, picked automatically. If neither is on the chart it falls back to a Parkinson range estimate and tags it "(est)" so you know what you're looking at. The dashboard shows the live IV, the expected move in points and percent, and the exact levels. Labels print the prices on the chart. Alerts fire when price closes outside one sigma or tags two.
I trade options and size around the implied move all the time. Am I selling the edge of the band or inside it, is price respecting the range or busting it. That read comes first. Selling a strike outside the expected move is a different bet than selling one inside it, and most people never check.
Expected Move Bands tell you the range the market is pricing. My Vol Premium Gauge tells you whether you're paid enough to sell it. Run them together.
Auto-detects crypto vs equity. Works on any timeframe at or below your anchor.
Free to use, open source. Follow for more vol and options tools.
Cheers,
Ivan Labrie. Indikator
Price Volatility Divergence with Reliability ScoringPrice–Volatility Divergence with Reliability Scoring
Normally, rising price comes with falling implied volatility — fear drains out of a rally. When price pushes to a new high while fear is also rising (or falls to a new low while fear falls), that disagreement is an anomaly worth flagging. This script builds a "fear" oscillator from an implied-volatility index, marks where it diverges from price, and — the original part — scores in real time whether those divergences have actually been worth trading on your symbol, and which direction is carrying the edge.
Why these components are combined (and how they work together). Three pieces form one pipeline, not three separate signals:
An implied-volatility "fear" series — chosen as raw level, term-slope (vol minus its own trend), or variance-risk-premium (implied minus realized). It's z-scored and negated so price-up/fear-up reads as an ordinary bearish divergence on the line.
Confirmed-pivot divergence between that fear series and price — regular and hidden, with an optional triple-pivot mode.
A binomial-proportion confidence test that asks, for each divergence class, whether the expected move followed more often than a same-zone baseline.
Part 2 only fires where price and fear disagree; part 3 decides whether that disagreement has historically mattered here, per direction. Remove any one and the script can't answer its question — "is this fear divergence worth trading, and which way?"
How to read it. The verdict panel translates the statistics: green = these divergences have beaten a same-spot baseline here; red = they've lost to it (skip, or try another fear measure/timeframe); amber = not established yet; grey = still gathering data. "Best signal" names the direction with the strongest measured edge so you know which side to favour. "Reward : risk" is the average best vs worst move after a signal, in ATR. Optional key-info and per-class tables (off by default) show the full breakdown.
Important — this is a proxy, not literal skew. True option skew needs the full per-strike implied-volatility surface, which charts don't expose. This uses a charted VIX / term-structure proxy, stated plainly so you know exactly what you're reading.
Universal. Needs a price source (the chart) and an implied-volatility index, both set in inputs. Defaults target NIFTY futures with India VIX; change the volatility symbol to VIX, VSTOXX, etc. for other markets.
Outputs for other scripts. Generic EXP_* values (oscillator, signal, probability, edge, edge lower-bound, sample count, regime, implied-vol level, fear percentile) are published to the Data Window for use via input.source().
Concept credits. Implied-volatility index construction — CBOE methodology. Variance-risk-premium — academic options literature. Binomial score confidence interval — E. B. Wilson. Trend-efficiency regime measure — P. Kaufman.
Disclaimer. For research and education only. Not financial advice, not a recommendation, not a guarantee of future results. All figures are in-sample and past-only. Markets carry risk — do your own research and manage your own risk. Indikator
IV Rank & Percentile XVI (S&P/ASX200 VIX)Most IV Rank and IV Percentile indicators on TradingView are built for the US VIX. This one is built specifically for XVI — the S&P/ASX 200 VIX (A-VIX) — so Australian index traders, and anyone trading XJO options, finally get the same volatility context without borrowing a US proxy. It reads straight off the published XVI value, so there's no option-chain reconstruction or estimation involved.
The core idea:
XVI is the ASX's "fear number" — the implied volatility of the XJO, the market's estimate of how much it's about to move over the next 30 days. The problem is that a raw XVI value is meaningless on its own. Is 16 high? Low? You can't know without context. This indicator's whole job is to give that context by answering one question: compared to its own recent history, is volatility currently rich, normal, or cheap?
The two ways it measures that:
IV Rank is the simple one. It looks at the highest and lowest XVI over your lookback window (a year by default) and asks where today sits on that line. XVI at its yearly low reads 0. At its yearly high, 100. Halfway between, 50. That's it — it's just "where in the range are we."
IV Percentile asks a slightly different question: of all the days in the window, what percentage had a lower XVI than today? If it reads 70, then vol is higher than it was on 70% of the past year's days. The reason this one's usually better is that IV Rank gets distorted by a single spike — one brief crash sets a sky-high "yearly high," and then every reading afterward looks artificially low against it for a whole year. Percentile doesn't have that problem because it counts days, so one freak day is just one day. That's why the regime label runs off Percentile by default.
The regime label:
This translates those 0–100 numbers into a single word so you don't have to interpret them each time. You set two thresholds — default 80 and 20. Above 80 it reads HIGH (vol is richer than most of the past year). Below 20, LOW (vol is cheap). Anything between, NORMAL. The thresholds are yours to move: if you think 80 is too strict and want it flagging "high" earlier, drop it to 70. The cutoffs define what you consider rich versus cheap. You can also switch whether the label reads off Percentile or Rank.
Live updating:
The ranking history is built from daily XVI closes (you want to rank against a year of daily data, not intraday noise), but the current reading floats live against that history. As XVI moves through the session, IV Rank, IV Percentile, and the regime word update with it rather than waiting for the daily close.
Settings:
Volatility index — defaults to ASX:XVI. Can be pointed at another volatility index if you want to reuse the tool elsewhere.
History timeframe — the bar size the ranking history is measured on. Daily is standard.
Lookback — how far back it ranks. 252 ≈ one year. Drop it to 90 or 60 for a tighter, more recent read; the long-window and short-window answers genuinely differ when the past year contains a stale spike, so comparing the two is useful.
Regime read from / High threshold / Low threshold — choose whether the label is driven by Percentile or Rank, and set the two cutoffs.
Display — plot the Percentile line on or off, and position the readout table in any corner.
Reading it:
The pane plots IV Rank (aqua) and IV Percentile (orange) on a 0–100 scale, with dashed guide lines at your high and low thresholds and a dotted midline at 50. The corner table shows the live XVI level alongside both readings and the current regime.
A note on the data: because XVI is a calculated index rather than a traded instrument, your reading is only as live as your XVI data feed. On delayed feeds it updates with that delay, which is still perfectly adequate for volatility-regime context.
This script is a volatility-context tool, not a trading system. It tells you where implied volatility sits relative to its own history; it does not generate buy or sell signals, and nothing here is financial advice. Indikator
Variance Risk Premium OscillatorVariance Risk Premium Oscillator
What it does
The Variance Risk Premium Oscillator measures the gap between implied volatility (a volatility index such as India VIX) and realized volatility, scaled in standard-deviation (σ) units. That gap — the variance risk premium (VRP) — tells you whether option protection is currently rich (expensive, complacent) or cheap (underpriced, stressed). A vol-of-vol read is shown alongside as an instability gauge.
Why this is different (and original)
Most volatility tools on charts forecast or display realized volatility (ATR, standard-deviation bands, historical-vol plots). This one reads something different: the price of volatility insurance. Decades of research show implied volatility systematically exceeds the volatility that is subsequently realized, so the premium is, on average, positive — investors pay up for protection. When that premium stretches unusually high, protection is expensive and the crowd is complacent; when it collapses or turns negative, fear is being paid for and volatility is cheap. Presenting this premium as a clean, self-normalizing mean-reversion oscillator with a built-in edge test is what makes it original — it is not a realized-vol band and not a VIX plot.
How it works
Realized volatility = annualized standard deviation of log-returns over the chosen window.
Implied volatility = the volatility index you point it at.
VRP = Implied − Realized.
The VRP series is z-scored over the normalization window into the σ oscillator. Vol-of-vol (the standard deviation of the implied index) is tracked separately as an instability read in the dashboard.
How to use it
Above the upper (red) band = vol RICH / complacency — protection expensive.
Below the lower (green) band = vol CHEAP / stress — protection underpriced.
Turns out of an extreme (triangles) are the mean-reversion events: a turn up from the cheap zone often coincides with stress easing; a turn down from the rich zone with complacency ending.
Read the EDGE row. The harness checks whether, after a cheap-zone turn, price actually rallied (and after a rich-zone turn, faded) by ≥ k×ATR within the horizon, versus the unconditional Base %. EDGE = Hit − Base. If it is near zero on your market, the mean-reversion read is not paying there.
Settings guide
01 · Data & Volatility — implied-vol symbol, realized-vol length, annualization (252 for daily; bars-per-year for intraday), vol-of-vol length, universal price source.
02 · Normalization — z-score window, output smoothing.
03 · Calibration — horizon, favourable-move threshold (×ATR), base-rate window.
04 · Bands — stretch and extreme σ bands; divergence pivot.
05 · Display & Theme — visual style, regime tint, dashboard, colors.
Non-repaint
The implied-vol index is requested with lookahead_off and settles on its bar's close — no future leak.
Concept credit
Variance risk premium and its return predictability — Bakshi & Kapadia (2003); Carr & Wu (2009); Bollerslev, Tauchen & Zhou (2009); Coval & Shumway (2001).
Disclaimer
For research and education only. Not financial advice, not a recommendation, and not a guarantee of future results. A stretched premium does not guarantee reversion — regimes can stay rich or cheap for long stretches. All statistics are in-sample, close-to-close, and exclude costs. Do your own research and manage your own risk. Indikator
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Synthetic IV Rank [UAlgo]Synthetic IV Rank is a volatility analysis indicator that creates a practical proxy for IV Rank when direct options implied volatility data is not available. Instead of reading an options chain, the script estimates a synthetic volatility series from price action using a Yang Zhang style historical volatility model, then normalizes that value into a 0 to 100 rank across a user defined lookback window.
This makes the tool especially useful for traders who want an IV Rank style workflow on instruments or markets where true implied volatility is unavailable, limited, or inconsistent. The indicator can be used on stocks, indices, forex, commodities, and crypto, with a dedicated Crypto Mode for annualization based on 365 days.
The script is built as a separate pane indicator and focuses on clear regime awareness. It plots a smooth IV Rank line, adds visual threshold references for high and low volatility zones, and shows a live status label on the most recent bar with both the current rank and the raw synthetic volatility value. The overall design makes it suitable for fast regime checks, mean reversion context, premium selling style filters, and volatility expansion monitoring.
Important note: This is a synthetic IV Rank approximation based on historical price volatility. It is not a substitute for true options implied volatility from an options chain.
🔹 Features
🔸 1) Synthetic IV Rank Using a Yang Zhang Style Volatility Model
The indicator estimates volatility from price data using a Yang Zhang style framework, then converts that estimate into an IV Rank style percentile scale. This gives users an IV Rank like signal even when broker feeds do not provide options implied volatility.
🔸 2) Engine Based Design with Structured Inputs
The script uses a custom VolatilityEngine type to organize the core calculation parameters:
hv_length for volatility estimation length
lookback_length for IV Rank normalization window
annual_factor for market specific annualization
This structure makes the logic easier to maintain and extend.
🔸 3) Stock and Crypto Annualization Modes
The engine supports two annualization conventions through a simple input toggle:
252 day convention for traditional markets
365 day convention for crypto markets
This is a practical detail because the same raw volatility process can produce different annualized values depending on the asset class.
🔸 4) Robust IV Rank Normalization with Safe Fallback
The script computes IV Rank by comparing the current synthetic volatility value against the lowest and highest values over the selected lookback period. If the range collapses to zero, the script safely assigns a neutral rank of 50 instead of causing a division issue.
This improves reliability in flat or low variance periods.
🔸 5) Clear Regime Visualization
The indicator includes a strong visual layout designed for quick interpretation:
A main IV Rank line
A mid reference line at 50
High and low threshold markers at 80 and 20
Gradient fills that visually emphasize extreme zones
This helps users recognize volatility regime shifts at a glance.
🔸 6) Dynamic Last Bar Status Labels
On the latest bar, the script prints a compact status label that shows:
Current IV Rank value
Regime label such as EXTREME FEAR, COMPLACENCY, or NEUTRAL
It also adds a secondary information label showing the raw Yang Zhang synthetic volatility percentage. This gives both normalized context and raw measurement at the same time.
🔸 7) Practical Regime Classification
The script uses simple but effective thresholds for regime tagging:
Above 80 signals elevated volatility conditions
Below 20 signals compressed volatility conditions
Between 20 and 80 is treated as neutral
These thresholds align with common IV Rank style interpretation used in discretionary and systematic workflows.
🔹 Calculations
1) Engine Initialization
On the first bar, the script initializes the custom volatility engine and stores:
The Yang Zhang calculation length
The IV Rank lookback window
The annualization factor based on asset class mode
If Crypto Mode is enabled, the annual factor uses the square root of 365. Otherwise it uses the square root of 252.
2) Synthetic Volatility Source Series
The indicator computes a Yang Zhang style historical volatility estimate from OHLC data. The model combines multiple variance components so it can capture more market behavior than a simple close to close volatility series.
The script calculates:
A first variance component labeled as overnight in the comments
An open to close variance component
A Rogers Satchell style intraday variance component from high, low, open, and close relationships
3) First Variance Component (Commented as Overnight)
In the current implementation, the first component is built from the logarithmic return of close / close , and its rolling variance is measured over the user defined length.
This is important to note because the code comments describe an overnight style component, while the actual formula uses consecutive closes in the current version.
4) Open to Close Variance Component
The script computes the logarithmic open to close return log(close / open) and then applies a rolling variance over the selected length. This measures intrabar movement relative to the bar open.
5) Rogers Satchell Intraday Variance Component
To improve intraday variance estimation, the script calculates a Rogers Satchell style daily variance term using four logarithmic relationships derived from high, low, open, and close. It then smooths this with a rolling simple average across the same volatility length.
This component is useful because it incorporates more intrabar range information than a simple close based measure.
6) Yang Zhang Weighting Factor
The script computes a weighting coefficient k that depends on the volatility length. This weight balances the contribution of the open to close variance and the Rogers Satchell component in the final combined variance.
The implementation follows the standard Yang Zhang style weighting formula shown in the script comments.
7) Combined Synthetic Volatility and Annualization
After computing the variance components, the script combines them into a single Yang Zhang style variance estimate, takes the square root to obtain volatility, and annualizes the result with the engine annual factor. The final synthetic volatility value is expressed as a percentage.
In practical terms, this output is the raw volatility series that the script later converts into Synthetic IV Rank.
8) IV Rank Calculation
The IV Rank logic measures where the current synthetic volatility sits relative to its historical range over the selected lookback:
It finds the lowest synthetic volatility in the lookback window
It finds the highest synthetic volatility in the lookback window
It scales the current value to a 0 to 100 rank
If the lookback range is flat, the script assigns 50.0 as a neutral fallback.
This normalization step is what makes the output behave like an IV Rank style regime indicator rather than a raw volatility plot.
9) Regime State Classification
On the latest bar, the script assigns a text state from the current IV Rank:
EXTREME FEAR when rank is above 80
COMPLACENCY when rank is below 20
NEUTRAL otherwise
The label color also changes with the state, which improves visual scanning.
10) Visual Layer Logic
The visualization includes:
A plotted IV Rank line
Hidden boundary plots for fill anchors
Visible threshold markers at 80 and 20
A midpoint reference line at 50
Gradient fills for high volatility and low volatility zones
The fill logic visually intensifies as the IV Rank moves deeper into an extreme zone, helping users identify volatility compression and expansion phases quickly.
11) What This Indicator Represents in Practice
This script is best understood as a normalized historical volatility regime tool designed to mimic the workflow of IV Rank when direct implied volatility data is not available. It is excellent for context filtering and regime awareness, but it should not be interpreted as a true options market implied volatility feed. Indikator
Implied Volatility RangeThe Implied Volatility Range is a forward-looking tool that transforms option market data into probability ranges for future prices. Based on the lognormal distribution of asset prices assumed in modern option pricing models, it converts the implied volatility curve into a volatility cone with dynamic labels that show the market’s expectations for the price distribution at a specific point in time. At the selected future date, it displays projected price levels and their percentage change from today’s close across 1, 2, and 3 standard deviation (σ) ranges:
1σ range = ~68.2% probability the price will remain within this range.
2σ range = ~95.4% probability the price will remain within this range.
3σ range = ~99.7% probability the price will remain within this range.
What makes this indicator especially useful is its ability to incorporate implied volatility skew. When only ATM IV (%) is entered, the indicator displays the standard Black–Scholes lognormal distribution. By adding High IV (%) and Low IV (%) values tied to strikes above and below the current price, the indicator interpolates between these inputs to approximate the implied volatility skew. This adjustment produces a market-implied probability distribution that indicates whether the option market is leaning bullish or bearish, based on the data entered in the menu:
ATM IV (%) = Implied volatility at the current spot price (at-the-money).
High IV (%) = Implied volatility at a strike above the current spot price.
High Strike = Strike price corresponding to the High IV input (OTM call).
Low IV (%) = Implied volatility at a strike below the current spot price.
Low Strike = Strike price corresponding to the Low IV input (OTM put).
Expiration (Day, Month, Year) = Option expiration date for the projection.
Once these inputs are entered, the indicator calculates implied probability ranges and, if both High IV and Low IV values are provided, adjusts for skew to approximate the option market’s distribution. If no implied volatility data is supplied, the indicator defaults to a lognormal distribution based on historical volatility, using past realized volatility over the same forward horizon. This keeps the tool functional even without implied volatility inputs, though in that case the output represents only an approximation of ATM IV, not the actual market view.
In summary, the Implied Volatility Range is a powerful tool that translates implied volatility inputs into a clear and practical estimate of the market’s expectations for future prices. It allows traders to visualize the probability of price ranges while also highlighting directional bias, a dimension often difficult to interpret from traditional implied volatility charts. It should be emphasized, however, that this tool reflects only the market’s expectations at a specific point in time, which may change as new information and trading activity reshape implied volatility. Indikator
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Asay (1982) Margined Futures Option Pricing Model [Loxx]Asay (1982) Margined Futures Option Pricing Model is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options on Futures where premium is fully margined. This means the Risk-free Rate, dividend, and cost to carry are all zero. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDvol, Speed
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The Black-Scholes-Merton model can be "generalized" by incorporating a cost-of-carry rate b. This model can be used to price European options on stocks, stocks paying a continuous dividend yield, options on futures , and currency options:
c = S * e^((b - r) * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^((b - r) * T) * N(-d1)
where
d1 = (log(S / X) + (b + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
b = r ... gives the Black and Scholes (1973) stock option model.
b = r — q ... gives the Merton (1973) stock option model with continuous dividend yield q.
b = 0 ... gives the Black (1976) futures option model.
b = 0 and r = 0 ... gives the Asay (1982) margined futures option model. <== this is the one used for this indicator!
b = r — rf ... gives the Garman and Kohlhagen (1983) currency option model.
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
d = dividend yield
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
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Black-76 Options on Futures [Loxx]Black-76 Options on Futures is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options on Futures. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDvol, Speed
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho futures option
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The Black-Scholes-Merton model can be "generalized" by incorporating a cost-of-carry rate b. This model can be used to price European options on stocks, stocks paying a continuous dividend yield, options on futures , and currency options:
c = S * e^((b - r) * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^((b - r) * T) * N(-d1)
where
d1 = (log(S / X) + (b + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
b = r ... gives the Black and Scholes (1973) stock option model.
b = r — q ... gives the Merton (1973) stock option model with continuous dividend yield q.
b = 0 ... gives the Black (1976) futures option model. <== this is the one used for this indicator!
b = 0 and r = 0 ... gives the Asay (1982) margined futures option model.
b = r — rf ... gives the Garman and Kohlhagen (1983) currency option model.
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
d = dividend yield
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Indikator
Garman and Kohlhagen (1983) for Currency Options [Loxx]Garman and Kohlhagen (1983) for Currency Options is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version of BSMOPM is to price Currency Options. The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP, Speed
Theta Greeks: Theta
Rate/Carry Greeks: Rho, Rho futures option, Carry Rho, Phi/Rho2
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing for Currency Options
The Garman and Kohlhagen (1983) modified Black-Scholes model can be used to price European currency options; see also Grabbe (1983). The model is mathematically equivalent to the Merton (1973) model presented earlier. The only difference is that the dividend yield is replaced by the risk-free rate of the foreign currency rf:
c = S * e^(-rf * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^(-rf * T) * N(-d1)
where
d1 = (log(S / X) + (r - rf + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
For more information on currency options, see DeRosa (2000)
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
rf = Risk-free rate of the foreign currency
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Related indicators:
BSM OPM 1973 w/ Continuous Dividend Yield
Black-Scholes 1973 OPM on Non-Dividend Paying Stocks
Generalized Black-Scholes-Merton w/ Analytical Greeks
Generalized Black-Scholes-Merton Option Pricing Formula
Sprenkle 1964 Option Pricing Model w/ Num. Greeks
Modified Bachelier Option Pricing Model w/ Num. Greeks
Bachelier 1900 Option Pricing Model w/ Numerical Greeks
Indikator
Black-Scholes 1973 OPM on Non-Dividend Paying Stocks [Loxx]Black-Scholes 1973 OPM on Non-Dividend Paying Stocks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. Making b equal to r yields the BSM model where dividends are not considered. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton ( BSM ) formula. For our purposes here are, Analytical Greeks are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega , DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
**This version of the Black-Scholes formula can also be used to price American call options on a non-dividend-paying stock, since it will never be optimal to exercise the option before expiration.**
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Indikator
Generalized Black-Scholes-Merton Option Pricing Formula [Loxx]Generalized Black-Scholes-Merton Option Pricing Formula is an adaptation of the Black-Scholes-Merton Option Pricing Model including Numerical Greeks aka "Option Sensitivities" and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas".
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm, float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility (vega) when searching for the implied volatility. For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility, al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm, lies between CL and cH. The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility. Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv(i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility, E is the desired degree of accuracy, c(m) is the market price of the option, and dc/dv(i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility).
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Indikator
Boyle Trinomial Options Pricing Model [Loxx]Boyle Trinomial Options Pricing Model is an options pricing indicator that builds an N-order trinomial tree to price American and European options. This is different form the Binomial model in that the Binomial assumes prices can only go up and down wheres the Trinomial model assumes prices can go up, down, or sideways (shoutout to the "crab" market enjoyers). This method also allows for dividend adjustment.
The Trinomial Tree via VinegarHill Finance Labs
A two-jump process for the asset price over each discrete time step was developed in the binomial lattice. Boyle expanded this frame of reference and explored the feasibility of option valuation by allowing for an extra jump in the stochastic process. In keeping with Black Scholes, Boyle examined an asset (S) with a lognormal distribution of returns. Over a small time interval, this distribution can be approximated by a three-point jump process in such a way that the expected return on the asset is the riskless rate, and the variance of the discrete distribution is equal to the variance of the corresponding lognormal distribution. The three point jump process was introduced by Phelim Boyle (1986) as a trinomial tree to price options and the effect has been momentous in the finance literature. Perhaps shamrock mythology or the well-known ballad associated with Brendan Behan inspired the Boyle insight to include a third jump in lattice valuation. His trinomial paper has spawned a huge amount of ground breaking research. In the trinomial model, the asset price S is assumed to jump uS or mS or dS after one time period (dt = T/n), where u > m > d. Joshi (2008) point out that the trinomial model is characterized by the following five parameters: (1) the probability of an up move pu, (2) the probability of an down move pd, (3) the multiplier on the stock price for an up move u, (4) the multiplier on the stock price for a middle move m, (5) the multiplier on the stock price for a down move d. A recombining tree is computationally more efficient so we require:
ud = m*m
M = exp (r∆t),
V = exp (σ 2∆t),
dt or ∆t = T/N
where where N is the total number of steps of a trinomial tree. For a tree to be risk-neutral, the mean and variance across each time steps must be asymptotically correct. Boyle (1986) chose the parameters to be:
m = 1, u = exp(λσ√ ∆t), d = 1/u
pu =( md − M(m + d) + (M^2)*V )/ (u − d)(u − m) ,
pd =( um − M(u + m) + (M^2)*V )/ (u − d)(m − d)
Boyle suggested that the choice of value for λ should exceed 1 and the best results were obtained when λ is approximately 1.20. One approach to constructing trinomial trees is to develop two steps of a binomial in combination as a single step of a trinomial tree. This can be engineered with many binomials CRR(1979), JR(1979) and Tian (1993) where the volatility is constant.
Further reading:
A Lattice Framework for Option Pricing with Two State
Trinomial tree via wikipedia
Inputs
Spot price: select from 33 different types of price inputs
Calculation Steps: how many iterations to be used in the Trinomial model. In practice, this number would be anywhere from 5000 to 15000, for our purposes here, this is limited to 220.
Strike Price: the strike price of the option you're wishing to model
Market Price: this is the market price of the option; choose, last, bid, or ask to see different results
Historical Volatility Period: the input period for historical volatility ; historical volatility isn't used in the Trinomial model, this is to serve as a comparison, even though historical volatility is from price movement of the underlying asset where as implied volatility is the volatility of the option
Historical Volatility Type: choose from various types of implied volatility , search my indicators for details on each of these
Option Base Currency: this is to calculate the risk-free rate, this is used if you wish to automatically calculate the risk-free rate instead of using the manual input. this uses the 10 year bold yield of the corresponding country
% Manual Risk-free Rate: here you can manually enter the risk-free rate
Use manual input for Risk-free Rate? : choose manual or automatic for risk-free rate
% Manual Yearly Dividend Yield: here you can manually enter the yearly dividend yield
Adjust for Dividends?: choose if you even want to use use dividends
Automatically Calculate Yearly Dividend Yield? choose if you want to use automatic vs manual dividend yield calculation
Time Now Type: choose how you want to calculate time right now, see the tool tip
Days in Year: choose how many days in the year, 365 for all days, 252 for trading days, etc
Hours Per Day: how many hours per day? 24, 8 working hours, or 6.5 trading hours
Expiry date settings: here you can specify the exact time the option expires
Included
Option pricing panel
Loxx's Expanded Source Types
Related indicators
Implied Volatility Estimator using Black Scholes
Cox-Ross-Rubinstein Binomial Tree Options Pricing Model
Indikator
Implied Volatility Estimator using Black Scholes [Loxx]Implied Volatility Estimator using Black Scholes derives a estimation of implied volatility using the Black Scholes options pricing model. The Bisection algorithm is used for our purposes here. This includes the ability to adjust for dividends.
Implied Volatility
The implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of that option. The VIX , in contrast, is a model-free estimate of Implied Volatility. The latter is viewed as being important because it represents a measure of risk for the underlying asset. Elevated Implied Volatility suggests that risks to underlying are also elevated. Ordinarily, to estimate implied volatility we rely upon Black-Scholes (1973). This implies that we are prepared to accept the assumptions of Black Scholes (1973).
Inputs
Spot price: select from 33 different types of price inputs
Strike Price: the strike price of the option you're wishing to model
Market Price: this is the market price of the option; choose, last, bid, or ask to see different results
Historical Volatility Period: the input period for historical volatility ; historical volatility isn't used in the Bisection algo, this is to serve as a comparison, even though historical volatility is from price movement of the underlying asset where as implied volatility is the volatility of the option
Historical Volatility Type: choose from various types of implied volatility , search my indicators for details on each of these
Option Base Currency: this is to calculate the risk-free rate, this is used if you wish to automatically calculate the risk-free rate instead of using the manual input. this uses the 10 year bold yield of the corresponding country
% Manual Risk-free Rate: here you can manually enter the risk-free rate
Use manual input for Risk-free Rate? : choose manual or automatic for risk-free rate
% Manual Yearly Dividend Yield: here you can manually enter the yearly dividend yield
Adjust for Dividends?: choose if you even want to use use dividends
Automatically Calculate Yearly Dividend Yield? choose if you want to use automatic vs manual dividend yield calculation
Time Now Type: choose how you want to calculate time right now, see the tool tip
Days in Year: choose how many days in the year, 365 for all days, 252 for trading days, etc
Hours Per Day: how many hours per day? 24, 8 working hours, or 6.5 trading hours
Expiry date settings: here you can specify the exact time the option expires
*** the algorithm inputs for low and high aren't to be changed unless you're working through the mathematics of how Bisection works.
Included
Option pricing panel
Loxx's Expanded Source Types
Related Indicators
Cox-Ross-Rubinstein Binomial Tree Options Pricing Model
Indikator
Indikator
rv_iv_vrpThis script provides realized volatility (rv), implied volatility (iv), and volatility risk premium (vrp) information for each of CBOE's volatility indices. The individual outputs are:
- Blue/red line: the realized volatility. This is an annualized, 20-period moving average estimate of realized volatility--in other words, the variability in the instrument's actual returns. The line is blue when realized volatility is below implied volatility, red otherwise.
- Fuchsia line (opaque): the median of realized volatility. The median is based on all data between the "start" and "end" dates.
- Gray line (transparent): the implied volatility (iv). According to CBOE's volatility methodology, this is similar to a weighted average of out-of-the-money ivs for options with approximately 30 calendar days to expiration. Notice that we compare rv20 to iv30 because there are about twenty trading periods in thirty calendar days.
- Fuchsia line (transparent): the median of implied volatility.
- Lightly shaded gray background: the background between "start" and "end" is shaded a very light gray.
- Table: the table shows the current, percentile, and median values for iv, rv, and vrp. Percentile means the value is greater than "N" percent of all values for that measure.
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Volatility risk premium (vrp) is simply the difference between implied and realized volatility. Along with implied and realized volatility, traders interpret this measure in various ways. Some prefer to be buying options when there volatility, implied or realized, reaches absolute levels, or low risk premium, whereas others have the opposite opinion. However, all volatility traders like to look at these measures in relation to their past values, which this script assists with.
By the way, this script is similar to my "vol premia," which provides the vrp data for all of these instruments on one page. However, this script loads faster and lets you see historical data. I recommend viewing the indicator and the corresponding instrument at the same time, to see how volatility reacts to changes in the underlying price. Indikator
vol_premiaThis script shows the volatility risk premium for several instruments. The premium is simply "IV30 - RV20". Although Tradingview doesn't provide options prices, CBOE publishes 30-day implied volatilities for many instruments (most of which are VIX variations). CBOE calculates these in a standard way, weighting at- and out-of-the-money IVs for options that expire in 30 days, on average. For realized volatility, I used the standard deviation of log returns. Since there are twenty trading periods in 30 calendar days, IV30 can be compared to RV20. The "premium" is the difference, which reflects market participants' expectation for how much upcoming volatility will over- or under-shoot recent volatility.
The script loads pretty slow since there are lots of symbols, so feel free to delete the ones you don't care about. Hopefully the code is straightforward enough. I won't list the meaning of every symbols here, since I might change them later, but you can type them into tradingview for data, and read about their volatility index on CBOE's website. Some of the more well-known ones are:
ES: S&P futures, which I prefer to the SPX index). Its implied volatility is VIX.
USO: the oil ETF representing WTI future prices. Its IV is OVX.
GDX: the gold miner's ETF, which is usually more volatile than gold. Its IV is VXGDX.
FXI: a china ETF, whose volatility is VXFXI.
And so on. In addition to the premium, the "percentile" column shows where this premium ranks among the previous 252 trading days. 100 = the highest premium, 0 = the lowest premium. Indikator
vx_termsUSAGE
--------
This script helps train your intuition for changes in the VX term structure. I recommend using it on the VIX chart, so you can compare changes in the terms to changes in VIX. It's also nice for calendar spread traders who want to get a feel for the same changes.
1. Select a day, month, and year using the inputs
2. Observe the data table.
3. Open the input again and increment or decrement the day (and month, year as necessary).
4. Click "Ok".
5. Click to deselect the indicator, which allows the chart to load new data.
6. The data table will be reloaded with the next/previous day's data.
The data table has the following columns:
- contract: the VX contracts, in sequence. refer to the CBOE for month codes (F for January, etc.)
- close: the closing price of the contract.
- ma:mb: the spread (difference) between this row and the next row.
- ma:mb chg: the spread's change from prior close.
For example, given the following values for the first two columns:
VXQ2021, 16.5, -3.1, -0.2
VXU2021, 19.6, ..., ...
The front month (Q = august) closed at 16.5, $3.1 below the s\September contract. The negative spread enlarged by $0.20 from $2.90 on the previous trading day.
BUGS, ODDITIES, AND LIMITATIONS:
-------------------------------------------
- The first column will be greyed out after expiration day, which is the 3rd Tuesday of that month. Unfortunately, I can't load the next month's contract due to some limitations with TV.
- The active date is highlighted with a yellow background. When a non-trading date is selected, the highlight will disappear. However, the data table will sometimes fill with the nearest trading date, prematurely. No worries, just know that the data is probably for the previous Friday.
- The script is clunky and slow, but this is the best I can do with TV. Hopefully they add more continuous contracts or allow true dynamic symbol loading.
SPECIAL THANKS:
---------------------
Thanks to HeWhoMustNotBeNamed for helping me get through some messiness. Very helpful guy.
www.tradingview.com Indikator
Indikator
