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Game contingent claims
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics. (Matematisk statistik)
2012 (English)Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

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

Place, publisher, year, edition, pages
2012. , 66 p.
Series
Trita-MAT, ISSN 1401-2286 ; 2012:19
Keyword [en]
Game contingent claims, game options, Israeli options, Dynkin games, zero-sum games, non-zero-sum games, Monte-Carlo simulation, pricing
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-103080OAI: oai:DiVA.org:kth-103080DiVA: diva2:558452
Educational program
Master of Science in Engineering -Engineering Physics
Uppsok
Physics, Chemistry, Mathematics
Examiners
Available from: 2012-10-03 Created: 2012-10-03 Last updated: 2012-10-03Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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Output format
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