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Robust option pricing : An [epsilon]-arbitrage approach

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dc.contributor.advisor Dimitris Bertsimas. en_US
dc.contributor.author Chen, Si, S.M. Massachusetts Institute of Technology en_US
dc.contributor.other Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.date.accessioned 2010-05-25T20:43:14Z
dc.date.available 2010-05-25T20:43:14Z
dc.date.copyright 2009 en_US
dc.date.issued 2009 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/55108
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009. en_US
dc.description In title on title-page, "[epsilon]" appears as the lower case Greek letter. Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 59-60). en_US
dc.description.abstract This research aims to provide tractable approaches to price options using robust optimization. The pricing problem is reduced to a problem of identifying the replicating portfolio which minimizes the worst case arbitrage possible for a given uncertainty set on underlying asset returns. We construct corresponding uncertainty sets based on different levels of risk aversion of investors and make no assumption on specific probabilistic distributions of asset returns. The most significant benefits of our approach are (a) computational tractability illustrated by our ability to price multi-dimensional options and (b) modeling flexibility illustrated by our ability to model the "volatility smile". Specifically, we report extensive computational results that provide empirical evidence that the "implied volatility smile" that is observed in practice arises from different levels of risk aversion for different strikes. We are able to capture the phenomenon by appropriately finding the right risk-aversion as a function of the strike price. Besides European style options which have fixed exercising date, our method can also be adopted to price American style options which we can exercise early. We also show the applicability of this pricing method in the case of exotic and multi-dimensional options, in particular, we provide formulations to price Asian options, Lookback options and also Index options. These prices are compared with market prices, and we observe close matches when we use our formulations with appropriate uncertainty sets constructed based on market-implied risk aversion. en_US
dc.description.statementofresponsibility by Si Chen. en_US
dc.format.extent 61 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US
dc.subject Computation for Design and Optimization Program. en_US
dc.title Robust option pricing : An [epsilon]-arbitrage approach en_US
dc.type Thesis en_US
dc.description.degree S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.identifier.oclc 591313102 en_US


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