Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity
28 Pages Posted: 7 Nov 2010 Last revised: 23 Jun 2011
Date Written: October 30, 2010
It can be shown that when the payoff function is convex and decreasing (respectively increasing) with respect to the underlying (multidimensional) assets, then the same is true for the value of the associated American option, provided some conditions are satisfied. In such a case, all Monte Carlo methods proposed so far in the literature do not preserve the convexity or monotonicity properties. In this paper, we propose a method of approximation for American options which can preserve both convexity and monotonicity. The resulting values can then be used to define exercise times and can also be used in combination with primal-dual methods to get sharper bounds. Other application of the algorithm include finding optimal hedging strategies.
Keywords: American Option, Simulation, Exercise Region, Snell Envelope
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