Fast Convergence of Regress-Later Estimates in Least Squares Monte Carlo
AbstractThe Least Squares Monte Carlo (LSMC) method is widely applied to solve stochastic optimal control problems, such as pricing American-style options. A central part of LSMC is the approximation of conditional expectations across each time-step. Conventional algorithms regress the value function at the end of the time-step on a set of basis functions, which aremeasurable with respect to the information available at the beginning of the time-step. The corresponding regression error has two sources: an approximation error due to the finite number of basis functions, and a projection error due to the projection onto the coarser filtration at the beginning of the interval. The convergence speed for the conventional algorithms is determined by the projection error component, which converges relatively slowly. Glasserman and Yu (2002) propose the Regress-Later method, wherein the value function at the end of the time-step is regressed on a set of basis functions, which aremeasurable with respect to the information available at the end of the time-step. The conditional expectation across the time-step is then computed analytically for each basis function. We show in this paper that by using Regress-Later the projection error component is removed. This implies that the Regress Later method has the potential of converging significantly faster than the conventional algorithms. We provide sufficient conditions for achieving fast convergence on compact and non-compact sets and we give an explicit example.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1309.5274.
Date of creation: Sep 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-09-25 (All new papers)
- NEP-LAM-2013-09-25 (Central & South America)
- NEP-LTV-2013-09-25 (Unemployment, Inequality & Poverty)
- NEP-NEU-2013-09-25 (Neuroeconomics)
- NEP-ORE-2013-09-25 (Operations Research)
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