TY - GEN A1 - Balder, Sven A1 - Mahayni, Antje A1 - Schoenmakers, John T1 - Primal-dual linear Monte Carlo algorithm for multiple stopping - An application to flexible caps N2 - 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. Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1012 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-10129 ER -