QUANT.OPTION.GREEK OpenBI
One of an option's sensitivities: delta, gamma, vega, theta or rho.
Group: Quantitative finance. OpenBI’s own: DAX has no function of this name.
Syntax
QUANT.OPTION.GREEK ( <greek>, <optionType>, <spot>, <strike>, <valuationDate>, <expiry>, <volatility>, <riskFreeRate> [, <dividendYield>] [, <style>] )| Parameter | Type | Description |
|---|---|---|
greek | Text | "delta", "gamma", "vega", "theta" or "rho": which sensitivity. |
optionType | Text | "call" or "put". |
spot | Number | The price of what the option is on, today. |
strike | Number | The price at which the option lets its holder buy (a call) or sell (a put). |
valuationDate | Date | The day the option is valued. |
expiry | Date | The day the option expires; it must come after the valuation date. |
volatility | Number | The yearly volatility as a decimal: 0.2 for 20 %. |
riskFreeRate | Number | The risk-free rate as a decimal, continuously compounded. |
dividendYield | Number optional | A continuous dividend yield (or, for a commodity or a currency, its carry) as a decimal; 0 when left out. |
style | Text optional | "european" (when left out), exercised at expiry only, or "american", any day until then. |
Returns
Number. The sensitivity of the option's value, per unit of what moves (see the remarks).
Remarks
- Delta is the change in value for one unit of the spot, gamma the change in delta for one unit of the spot.
- Vega is for a volatility one whole unit higher (from 0.2 to 1.2): divide by 100 for one percentage point. Rho likewise for the rate.
- Theta is the change in value over a year of time passing, usually negative: divide by 365 for a day.
- For an American option, vega and rho are found by valuing it again with the volatility or the rate nudged up and down.
- Time runs from the valuation date to the expiry in days over 365. The rate, the dividend yield and the volatility are flat over that time.
- The greek's name is not case-sensitive; any other name is an error.
Compared with DAX
An OpenBI function: DAX has none like it, so a measure or query that uses it works in OpenBI only, not in Power BI or Analysis Services.
Examples
The greeks of a call at the money
The one-year call from QUANT.OPTION.PRICE's first example, with vega and rho for a percentage point and theta for a day.
EVALUATE
VAR Today = DATE ( 2026, 1, 1 )
VAR Expiry = DATE ( 2027, 1, 1 )
RETURN
ROW (
"Delta", QUANT.OPTION.GREEK ( "delta", "call", 100, 100, Today, Expiry, 0.2, 0.05 ),
"Gamma", QUANT.OPTION.GREEK ( "gamma", "call", 100, 100, Today, Expiry, 0.2, 0.05 ),
"Vega, a point", QUANT.OPTION.GREEK ( "vega", "call", 100, 100, Today, Expiry, 0.2, 0.05 ) / 100,
"Theta, a day", QUANT.OPTION.GREEK ( "theta", "call", 100, 100, Today, Expiry, 0.2, 0.05 ) / 365,
"Rho, a point", QUANT.OPTION.GREEK ( "rho", "call", 100, 100, Today, Expiry, 0.2, 0.05 ) / 100
)| Delta | Gamma | Vega, a point | Theta, a day | Rho, a point |
|---|---|---|---|---|
| 0.636830651175619 | 0.0187620173458469 | 0.375240346916938 | -0.0175726782094197 | 0.532324815453764 |
Delta across strikes
Deep in the money a call moves almost one for one with the spot; far out of it, hardly at all.
EVALUATE
SELECTCOLUMNS (
GENERATESERIES ( 70, 130, 15 ),
"Strike", [Value],
"Delta", ROUND ( QUANT.OPTION.GREEK ( "delta", "call", 100, [Value], DATE ( 2026, 1, 1 ), DATE ( 2027, 1, 1 ), 0.2, 0.05 ), 4 )
)| Strike | Delta |
|---|---|
| 70 | 0.9836 |
| 85 | 0.8775 |
| 100 | 0.6368 |
| 115 | 0.3636 |
| 130 | 0.1681 |
Related functions
QUANT.OPTION.PRICE, QUANT.OPTION.IMPLIEDVOL, QUANT.BOND.DV01.