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Primal-dual linear Monte Carlo algorithm for multiple stopping - An application to flexible caps

Please always quote using this URN:urn:nbn:de:0296-matheon-10129
  • In this paper we consider the valuation of Bermudan callable derivatives with multiple exercise rights. We present in this context a new primal-dual linear Monte Carlo algorithm that allows for e� cient simulation of lower and upper price bounds without using nested simulations (hence the terminology). The algorithm is essentially an extension of a primal{dual Monte Carlo algorithm for standard Bermudan options proposed in Schoenmakers et al. (2011), to the case of multiple exercise rights. In particular, the algorithm constructs upwardly a system of dual martingales to be plugged into the dual representation of Schoenmakers (2010). At each level the respective martingale is constructed via a backward regression procedure starting at the last exercise date. The thus constructed martingales are � nally used to compute an upper price bound. At the same time, the algorithm also provides approximate continuation functions which may be used to construct a price lower bound. The algorithm is applied to the pricing of exible caps in a Hull and White (1990) model setup. The simple model choice allows for comparison of the computed price bounds with the exact price which is obtained by means of a trinomial tree implementation. As a result, we obtain tight price bounds for the considered application. Moreover, the algorithm is generically designed for multi-dimensional problems and is tractable to implement.

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Metadaten
Author:Sven Balder, Antje Mahayni, John Schoenmakers
URN:urn:nbn:de:0296-matheon-10129
Referee:Dirk Becherer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/01/27
Release Date:2012/01/27
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G40 Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Preprint Number:896
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