Pricing and hedging of spread options with stochastic component correlation

• Main Author: Hong, S. G.
• Published: University of Cambridge 2001
• Subjects: 332
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604205

Spread options are derivatives securities with payoffs dependent on the difference of two underlying market variables. Though the importance and wide applicability of this class of instruments have long been recognised, the theoretical problem of valuing them beyond the simple Geometric Brownian motion assumption has not been successfully tackled. This thesis proposes several new methods to solve the option pricing problem under multi-factor stochastic volatility models. The correlation structure between the stochastic components generated by these models is a function of time, the diffusion parameters and the volatility state variable, and thus permits greater degrees of freedom for calibrating to the observed market data or traders' forward views on the market. The numerical methods developed generalise the fast Fourier transform technique in the single-asset framework and can be applied so long as the characteristic function of the underlying process is available in closed-form. This includes a large set of existing diffusion models, giving the approach great flexibility in switching the underlying model assumptions. The thesis also documents the implementation of the transform methods proposed, as well as the industry standard Monte Carlo simulation and explicit finite differences schemes. Their numerical performance was compared, specifically, for a two-factor Geometric Brownian motion model and a three factor Stochastic Volatility model. The ability of the latter in generating a rich spread option pricing structure different from the two-factor model is demonstrated. Finally, a calibration procedure for the model to market data is proposed.