Dual representations for general multiple stopping problems
AbstractIn this paper, we study the dual representation for generalized multiple stopping problems, hence the pricing problem of general multiple exercise options. We derive a dual representation which allows for cashflows which are subject to volume constraints modeled by integer valued adapted processes and refraction periods modeled by stopping times. As such, this extends the works by Schoenmakers (2010), Bender (2011a), Bender (2011b), Aleksandrov and Hambly (2010), and Meinshausen and Hambly (2004) on multiple exercise options, which either take into consideration a refraction period or volume constraints, but not both simultaneously. We also allow more flexible cashflow structures than the additive structure in the above references. For example some exponential utility problems are covered by our setting. We supplement the theoretical results with an explicit Monte Carlo algorithm for constructing confidence intervals for the price of multiple exercise options and exemplify it by a numerical study on the pricing of a swing option in an electricity market.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1112.2638.
Date of creation: Dec 2011
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-12-19 (All new papers)
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- Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
- Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
- L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
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