Monte Carlo Method Application In Option Pricing

In this paper, the modern theories of option pricing, and analytical solution of theBlack-Scholes formula are introduced firstly. After that, three most common methods ofoption pricing: Binomial options pricing model, finite difference model and Monte Carlooption model are presented. Monte Carlo option model uses Monte Carlo methods to calculatethe value of an option with multiple sources of uncertainty or with complicated features.Monte Carlo, a method of simulating many possible paths, is used in many different fields,also very important in option pricing. Especially, for path-dependent options, Monte Carlomethod is a very useful method for pricing this kind of options. Variance reductiontechnology is great important for Monte Carlo simulation. The basic idea of Monte Carlosimulation is calculating the average value based on the huge amount of samples, so thevariation of the simulation can be reduced by some proper samplings. The common variationreduction technologies include: common random numbers, antithetic variates, control variates,importance sampling and stratified sampling. Importance sampling is an important variancereduction technology which choosing the proper transformed probability space. Computersare used to implement Monte Carlo simulation. This paper use parallel computation toproduce the sample paths which can let the finance industry to use high performancecomputers to solve the problem of the time consuming of Monte Carlo computation. Sincecomputational nodes and computational architraves need to be allocated when parallelcomputation running, a magnificent parallel computer system becomes a must. WindowsHPC Server2008R2render a solution, on this platform, programmer from application sidecan develop the computational code concerned different needs independently, meanwhile theydo not have to pay extra attention on the details of parallel computational resourcesmanagement. This paper uses this platform to develop pricing model which includes the useof the variance reduction technology, and obtain the values of several options through thismodel.