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We consider the problem of finding a model-free upper bound on the price of an American put given the prices of a family of European puts on the same underlying asset. Specifically, we assume that the American put must be exercised at either T 1 or T 2 and that we know the prices of all vanilla European puts with these maturities. In this setting, we find a model which...
This paper reviews the basic properties of American options and the difficulties of applying Monte Carlo valuation to American options. Asymptotic results by Keller and co-workers are described for the singularity in the early exercise boundary for time t near the final time T. Recent progress on application of Monte Carlo to American options is described including the following: Branching processes...
We study the behavior of the critical price of an American put option near maturity in an exponential Lévy model. In particular, we prove that in situations where the limit of the critical price is equal to the strike price, the rate of convergence to the limit is linear if and only if the underlying Lévy process has finite variation. In the case of infinite variation, a variety of rates of convergence...
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