Simulation and Numerical Procedures for Option Pricing

This thesis contains three essays on option pricing. The first discusses a way to measure the risk of the short trader of an option if he decides to hedge partially his position. The second deals with the pricing of American-style Asian options, and the third with call and put options embedded in bonds. The first essay considers the case of a short trader of an option who decides to partially hedge its position on some states of nature and not on the others. A partial hedge initially costs less than a perfect hedge, but may lead to a default position. It is of interest in that context to estimate the gain and the default risk. Some partial hedging strategies based on the price of the primitive asset at the horizon, its maximum over the trading period, and the time to maximum, are analyzed. Closedform solutions are derived in the Black and Scholes (1973) model, and efficient Monte Carlo estimators are computed in a stochastic volatility model. The results show how the gain and the default risk inversely change depending on the hedging event. The second essay deals with the pricing of Asian options based on the arithmetic average, under the Black and Scholes (1973) model. Their evaluation involves estimating an integral (a mathematical expectation) for which no analytical solution is available. Pricing their American-style counterparts, which provide