Calculation of European Option Pricing by Garman and Kohlhagen model(an extension Black-Scholes model).

Keyword

European Option Pricing,Garman and Kohlhagen model,an extension Black-Scholes model,Cumulative density function,Underlying Stock Price,Strike price,Time to maturity,Risk free rate of interest,Implied volatility,Rate of dividend,call,put.

Reference

・『ブラック・ショールズと確率微分方程式』（小林道正）.
・『Handbook of Mathematical Functions with Formulas,Graphs, and Mathematical Tables』（MILTON ABRMOWITZ and IRENE A. STEGUN）.
・『Price Risk and Bid-Ask Spreads of Currency Options』(Simon J. Pak,Maria E. de Boyrie,Yong O. Kim).

Remarks

Approximation Formula for Cumulative density function.N(d1),N(d2).
・P(x)=1-Z(x)*(a1*t+a2*t^2+a3*t^3)+ε(x). |ε(x)|<1*10^-5. a1=0.4361836. a2=-0.1201676. a3=0.9372980.
・t=1/(1+p*x). p=0.33267.
・Z(x)=1/(σ*(2*π)~0.5)*e^-1/2*((x-m)/σ)^0.5. σ=1. m=0. e=2.7183.

History

・2014/08/07：layout change.
・2009/03/22：Moved from www.am-consulting.co.jp to here.