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Let's talk about your first equation: If you exercised your option early, you got this payoff. But if you are a rational investor you'd realize that this is less than what you would get if you would just sell your option itself. i.e. the payoff at time t will be more than S(t)-K because the option is worth more than that as it also has some time value. so ...


there has been a huge amount of work on this. In terms of numerical studies, see my paper Beveridge, Christopher and Joshi, Mark S. and Tang, Robert, Practical Policy Iteration: Generic Methods for Obtaining Rapid and Tight Bounds for Bermudan Exotic Derivatives Using Monte Carlo Simulation (January 23, 2009). Available at SSRN: ...

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