On the Pricing of Cliquet Options with Global Floor and Cap

In this thesis we present two methods for the pricing and hedging of cliquet options with global floor and/or cap within a Black-Scholes market model with fixed dividends and time dependent volatilities and interest rates. The first is a Fourier transform method giving integral formulas for the price and the greeks. A numerical integration scheme is proposed for the evaluation of these formulas. Using Ito’s Lemma it is proved that the vanilla Black-Scholes PDE is valid. In addition to giving us the gamma for free, it forms the basis for an explicit finite difference method. Both methods outperform Monte Carlo simulation in terms of computational time, with the Fourier method in most cases being the faster one for a given level of accuracy. This tendency is amplified as the number of reset periods increases. Potential future research includes local volatility models and early exercise features for the finite difference method and Levy-process market models for the Fourier method.