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Alexey MEDVEDEV and Olivier SCAILLET
In this paper we propose a new analytical approach that is both computational tractable and general enough to be successfully applied to a three-factor model. Our approach is based on the idea of substituting the optimal exercise rule with a simple one for which an approximate solution is easy to find. Similar ideas have already been explored in the literature (Broadie and Detemple (1996), Carr (1998), Ju (1998)). A typical rule is to exercise the option as soon as its moneyness measured in standard deviations reaches some predefined level. The price of such an option appears to have a regular asymptotic behavior near maturity with an asymptotic expansion available in a closed form for a broad class of models. The American option price is then approximated by the maximum over these option prices. In the paper we provide several numerical experiments showing that our method is competitive with existing ones with respect to computation time and accuracy. Under the Black-Scholes model our approximation is more accurate than a 1000-step binomial tree with a computational time equivalent to a 50-step tree.