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 $t$;
* <math>S(t)</math> is the price of the underlying asset at time <math>t</math>;
* <math>\sigma</math> is the volatility &mdash; the standard deviation of the asset's returns;
* <math>\sigma</math> is the volatility &mdash; 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.