An in depth study of the pricing of Game contingent claims under a general diffusion market model, in which interest rate is non constant, is presented. With the idea of providing a few numerical examples of the valuation of such claims, we present a detailed description of a Bootstrapping procedure to obtain interest rate information from Swaps rates. We also present a Stripping procedure that can be used to obtain initial spot (caplet) volatility from Market quotes on Caps/FLoors. These methods are of general application and could be used in the calibration of diffusion models of interest rate. Then we show several examples of calibration of the Hull--White model of interest rates. Our calibration examples are later used in the numerical approximation of the value of a particular form of Game option.

Abstract Game contingent claims (GCCs), as introduced by Kifer (2000), are a generalization of American contingent claims where the writer has the opportunity to terminate the contract, and must then pay the intrinsic option value plus a penalty. In complete markets, GCCs are priced using no-arbitrage arguments as the value of a zero-sum stochastic game of the type described in Dynkin (1969). In incomplete markets, the neutral pricing approach of Kallsen and Kühn (2004) can be used. In Part I of this thesis, we introduce GCCs and their pricing, and also cover some basics of mathematical finance. In Part II, we present a new algorithm for valuing game contingent claims. This algorithm generalises the least-squares Monte-Carlo method for pricing American options of Longstaff and Schwartz (2001). Convergence proofs are obtained, and the algorithm is tested against certain GCCs. A more efficient algorithm is derived from the first one using the computational complexity analysis technique of Chen and Shen (2003). The algorithms were found to give good results with reasonable time requirements. Reference implementations of both algorithms are available for download from the author’s Github page https://github.com/del/ Game-option-valuation-library