Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes
AbstractFast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a new algorithm to generate tight upper bounds on the Bermudan option price without nested simulation, under the jump-diffusion setting. By exploiting the martingale representation theorem for jump processes on the dual martingale, we are able to explore the unique structure of the optimal dual martingale and construct an approximation that preserves the martingale property. The resulting upper bound estimator avoids the nested Monte Carlo simulation suffered by the original primal-dual algorithm, therefore significantly improves the computational efficiency. Theoretical analysis is provided to guarantee the quality of the martingale approximation. Numerical experiments are conducted to verify the efficiency of our proposed algorithm.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1305.4321.
Date of creation: May 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-05-24 (All new papers)
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