No-arbitrage bounds on American Put Options with a single maturity
Author(s)Shah, Premal (Premal Y.)
Massachusetts Institute of Technology. Operations Research Center.
Dimitris J. Bertsimas.
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We consider in this thesis the problem of pricing American Put Options in a model-free framework where we do not make any assumptions about the price dynamics of the underlying except those implied by the no-arbitrage conditions. Our goal is to obtain bounds on the price of an American put option with a given strike and maturity directly from the prices of other American put options with the same maturity but different strikes and the current price of the underlying. We proceed by first investigating the structural properties of the price curve of American Put Options of a fixed maturity and derive necessary and sufficient conditions that strike - price pairs of these options must satisfy in order to exclude arbitrage. Using these conditions, we can find tight bounds on the price of the option of interest by solving a very tractable Linear Programming Problem. We then apply the methods developed to real market data. We observe that the quality of bounds that we obtain compares well with the quoted bid-ask spreads in most cases.
Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2006.Includes bibliographical references (p. 63-64).
DepartmentMassachusetts Institute of Technology. Operations Research Center.
Massachusetts Institute of Technology
Operations Research Center.