Difference between revisions of "Programming/Kdb/Labs/Option pricing"
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Recall the celebrated Black-Scholes equation | Recall the celebrated '''Black-Scholes equation''' | ||
<center><math> | <center><math> | ||
\frac{\partial V}{\partial t} + \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + (r - q) S \frac{\partial V}{\partial S} - r V = 0. | \frac{\partial V}{\partial t} + \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + (r - q) S \frac{\partial V}{\partial S} - r V = 0. | ||
</math></center> | </math></center> | ||
Here | |||
* <math>V(S, t)</math> is the price of the option; | |||
* <math>S(t)</math> is the price of the underlying asset at time $t$; | |||
* <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>q</math> is the annualized (continuous) dividend yield. | |||
Revision as of 22:21, 17 June 2021
Recall the celebrated Black-Scholes equation
Here
- is the price of the option;
- is the price of the underlying asset at time $t$;
- 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.
