Valuation and hedging of exotic options: average options and spread products.

Summary This thesis studies the valuation of two derivative products: Asian options and quanto contracts. Asian options are path-dependent contingent assets whose final values vary according to the average calculated over a predetermined interval. Under standard assumptions, an exact analytical formula does not exist for their prices. Approximate analytical formulas are proposed in the first two chapters. These formulas are simple to use and have a satisfactory accuracy compared to Monte Carlo simulations. The third chapter extends the idea of mean option to interest rates. Formulas for evaluating options on the mean of interest rates are proposed and some numerical examples are given to show their use. The fourth and fifth chapters deal with the valuation and hedging of quanto contracts. A new model is developed using the equivalent martingale measurement technique. It includes risky assets denominated in two currencies and assumes correlated processes between the asset prices. The main conclusion is that a domestic investor does not need to distinguish between domestic and foreign assets under the martingale equivalent probability measure. The instantaneous return on a foreign asset is equal to the instantaneous foreign interest rate plus a sum of correlations that can be positive or negative. Explicit formulas are derived and examples are given to demonstrate the main results. The important role of correlation in a quanto contract is highlighted by numerical examples in the final chapter.