American Options with Stopping Time Constraints
19 Pages Posted: 12 Sep 2005
Date Written: 2005
This paper concerns the pricing of American options with stochastic stopping time constraints expressed in terms of the states of a Markov process. Following the ideas of Menaldi, Robin and Sun  we transform the constrained into an unconstrained optimal stopping problem. The transformation replaces the original payoff by the value of a generalized barrier option. We suggest a new Monte Carlo method to numerically calculate the option value also for multidimensional Markov processes. Because of presence of stopping time constraints the classical Longstaff-Schwartz least-square Monte Carlo algorithm or its extension introduced in  cannot be directly applied. We adapt the Longstaff-Schwartz algorithm to solve the stochastic Cauchy-Dirichlet problem related to the valuation problem of the barrier option along a set of simulated trajectories of the underlying Markov process.
Keywords: American options, optimal stopping under constraints, out-performance options, management options
JEL Classification: C60; G13
Suggested Citation: Suggested Citation
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