Lookback-style derivatives are contingent claims whose payoff depends on the extremum value of some underlying stochastic state variable realized over a specific period of time period within the option's life. The pricing of a multi-state lookback derivative is challenging due to the high dimensionality of the pricing models and the intrinsic path dependence of the lookback state variable. In this thesis, I consider the valuation of two types of multi-state lookback derivatives, namely, the dynamic fund protection under stochastic interest rates and European lookback option with the quanto feature. The pricing methodologies can be categorized into three different approaches: analytic derivation, semi-analytic formulation, and numerical computation. Under the assumption of correlated Geo...[ Read more ]

Lookback-style derivatives are contingent claims whose payoff depends on the extremum value of some underlying stochastic state variable realized over a specific period of time period within the option's life. The pricing of a multi-state lookback derivative is challenging due to the high dimensionality of the pricing models and the intrinsic path dependence of the lookback state variable. In this thesis, I consider the valuation of two types of multi-state lookback derivatives, namely, the dynamic fund protection under stochastic interest rates and European lookback option with the quanto feature. The pricing methodologies can be categorized into three different approaches: analytic derivation, semi-analytic formulation, and numerical computation. Under the assumption of correlated Geometric Brownian processes of the underlying state variables, I manage to derive the closed-form analytic price formula for the joint quanto fixed strike lookback call option under the Black-Scholes framework. When the analytic tractability of the lookback option model does not lead to analytic price formula, I manage to derive the corresponding semi-analytic formulation of the model. Following the extended Fortet method, I derive the integral equation for the first passage time density of the underlying state price process based on the Markovian properties of the state processes. I also develop efficient finite difference schemes for finding the numerical values of the prices of the lookback derivatives. The curse of dimensionality is resolved by adopting the Alternating Direction Implicit approach of splitting the multidimensional differential operator in the governing differential equation. I perform the numerical calculations to illustrate the robustness and versatility of the different numerical approaches. Pricing properties of the lookback derivatives are also investigated.