Abstract

We would like to thank Prof. Michael Rockinger for his helpful comments and for his continuous support in achieving our work. A special thank to Peng Cheng for useful references and observations. This paper attempts to implement Monte Carlo simulations in order to price and hedge exotic options. Many exotic options have no analytic solutions, either because they are too complex or because the volatility specification is wrong. Consequently, numerical solutions are a necessity. We discuss the advantages and the drawbacks of such a pricing approach for the main exotic options. Given the strong assumptions of the Black-Scholes world, we attempt to relax them and, in particular, we focus on stochastic volatility models. After a review of the literature, we analyze via simulations the impact of stochastic volatility on the valuation of Asian and spread options. Next we construct and evaluate a dynamic hedging strategy for an exchange option under discrete rebalancing, stochastic volatility and transaction costs. We study the effect of each of these market imperfections on the hedge performance. Finally, we shortly discuss possible hedging approaches for

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