Double barrier options with curved boundaries.
On the optimal exercise boundary for an American put option.
The American straddle close to expiry.
Asymptotic analysis of American call options.
Using Monte Carlo Methods to Evaluate Sub-Optimal Exercise Policies for American Options
∗This research, which was funded by a grant from the Natural Sciences and Engineering Research Council of Canada, formed part of G.A.’s Ph.D. thesis [1]. In this paper we use a Monte Carlo scheme to find the returns that an uninformed investor might expect from an American option if he followed one of several näıve exercise strategies rather than the optimal exercise strategy. We consider several such strategies that an ill-advised investor might follow. We also consider how the expected...
A New Algorithm for Monte Carlo for American Options
2000 Mathematics Subject Classification: 91B28, 65C05. We consider the valuation of American options using Monte Carlo simulation, and propose a new technique which involves approximating the optimal exercise boundary. Our method involves splitting the boundary into a linear term and a Fourier series and using stochastic optimization in the form of a relaxation method to calculate the coefficients in the series. The cost function used is the expected value of the option using the the current...
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