Game contingent claims
Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
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
Place, publisher, year, edition, pages
2012. , 66 p.
Trita-MAT, ISSN 1401-2286 ; 2012:19
Game contingent claims, game options, Israeli options, Dynkin games, zero-sum games, non-zero-sum games, Monte-Carlo simulation, pricing
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-103080OAI: oai:DiVA.org:kth-103080DiVA: diva2:558452
Master of Science in Engineering -Engineering Physics
UppsokPhysics, Chemistry, Mathematics
Lang, Harald, Docent