tracey tullie

TULLIE, TRACEY ANDREW. Variance Reduction for Monte Carlo Simulation of European, American or Barrier Options in a Stochastic Volatility Environment. (Under the direction of Jean-Pierre Fouque.) In this work we develop a methodology to reduce the variance when applying Monte Carlo simulation to the pricing of a European, American or Barrier option in a stochastic volatility environment. We begin by presenting some applicable concepts in the theory of stochastic differential equations. Secondly, we develop the model for the evolution of an asset price under constant volatility. We next present the replicating portfolio and equivalent martingale measure approaches to the pricing of a European style option. Modeling an asset price utilizing constant volatility has been shown to be an inefficient model[8, 16]. One way to compensate for this inefficiency is the use of stochastic volatility models, which involves modeling the volatility as a function of a stochastic process[26]. A class o...

To determine the probability of exceedence Monte Carlo simulation of stochastic models is often used. Mathematically this requires the evaluation of an expectation of some function of a solution of a stochastic model. This can be reformulated as a Kolmogorov final value problem. It can thus be calculated numerically by either solving a deterministic partial differential equation (Kolmogorov's Backwards equations)