Application of Monte Carlo Simulation in Pricing of Options
Ivan Popchev, Nadya Velinova
Institute of Information Technologies, 1113 Sofia
Abstract: In this paper we consider a Monte Carlo technique for
valuation of derivatives securities. Metropolis algorithm is used to sample
probability distribution of histories of underlying stocks. We consider options
on portfolios consisting of linear combinations of correlated log-normal assets,
including basket and spread options. The present purpose is to examine feasibility
and accuracy of the method, so we start with the simplest valuation problem of a
European call on a stock with constant volatility and no dividends, where we can
easily compare Monte Carlo results with the analytic Black- Scholes solution.
In this relation a practical example is discussed in part three.
Keywords: Monte Carlo simulation, Metropilis algorithm, assets.