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Opciones americanas, valoración numérica y cálculo de la frontera de valores críticos
Alfonso Camaño |
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In this paper we analyzed American call and put vanilla options with finite maturity
as problems of optimal stopping. The problem of American contracts is always double, first we
have to find the value function and then later it is necessary to characterize the optimal strategy
for exercising them by mean of computing the critical points boundary. Both tasks are developed
and solved numerically in the paper.
It is assumed that the underlying is following a geometric brownian motion for which drift and
volatility are known.
The no arbitrage hypothesis and risk neutral valuation are used throughout the paper, however,
all analysis is made under the consideration of American options as problems of optimal
stopping so that we reach the free boundary problems for the Black & Scholes PDE by a path
completely different than the traditional way. We do not build up a portfolio free of risk by mean
of delta hedging as done by F. Black y M. Scholes in their milestone paper.
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