APPLICATION OF STOCHASTIC METHODS IN INTEGRATION FOR EVALUATING OPTION PRICE

ABSTRACT
In evaluating the value of integration which can not be found exactly, we can implement numerical approach. The numerical method is categorized into deterministic and stochastic. Application of stochastic method in integration can be used for evaluating price of an European call option and European put option which approach the result of Black-Scholes formula.
European call option and European put option price is based on assumption that stock price follows a Geometric Brownian Motion with parameters r, , S, Sp, and T. Starting from a basic formula, the price of an European call option P= exp(-rt) E(max(ST –Sp,0)) and European put option P=exp(-rt)E( max(Sp - ST, 0)) are modified into multivariable integral form. Then, using random numbers generated in MATLAB and implementing stochastic method , the integral can be evaluated to approach option price.
The graph shows, the higher the amount of random number used in stochastic method in integration then error is smaller. Convergence of percentage error is proportional to convergence of 1/N.
Key Words : Integral, Stokastik, Option, Metode Stokastik Dalam Integral