Difference between revisions of "Programming/Kdb/Labs/Option pricing"
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* <math>t</math> is a time in years; we generally use <math>t = 0</math> as now; | * <math>t</math> is a time in years; we generally use <math>t = 0</math> as now; | ||
* <math>V(S, t)</math> is the price of the option; | * <math>V(S, t)</math> is the price of the option; | ||
* <math>S(t)</math> is the price of the underlying asset at time | * <math>S(t)</math> is the price of the underlying asset at time <math>t</math>; | ||
* <math>\sigma</math> is the volatility — the standard deviation of the asset's returns; | * <math>\sigma</math> is the volatility — the standard deviation of the asset's returns; | ||
* <math>r</math> is the annualized risk-free interest rate, continuously compounded; | * <math>r</math> is the annualized risk-free interest rate, continuously compounded; | ||
* <math>q</math> is the annualized (continuous) dividend yield. | * <math>q</math> is the annualized (continuous) dividend yield. |
Revision as of 22:22, 17 June 2021
Recall the celebrated Black-Scholes equation
Here
- is a time in years; we generally use as now;
- is the price of the option;
- is the price of the underlying asset at time ;
- is the volatility — the standard deviation of the asset's returns;
- is the annualized risk-free interest rate, continuously compounded;
- is the annualized (continuous) dividend yield.