Option Pricing Simulation Using C++

Abstract

In the field of financial mathematics, many problems, for instance the problem of finding the arbitrage-free value of a particular derivative security, boil down to the computation of a particular integral. In many cases these integrals can be valued analytically, and in still more cases they can be valued using numerical integration. However when the number of dimensions (or degrees of freedom) in the problem is large, numerical integration methods become intractable. In these cases it is common to resort to the more widely pplicable Monte Carlo method to solve the problem. For large dimension integrals as can very often happen in financial problems. Monte Carlo methods converge to the solution more quickly than numerical integration methods. The advantage of Monte Carlo methods increases as the dimension of the problem gets larger. This article introduces Monte Carlo techniques for option pricing. It also touches on the use of so-called "variance reduction technique". This method can produce enormous speed-ups compared with standard Monte Carlo

Keywords : monte carlo, financial problems, variance reduction technique