Robust option pricing : An [epsilon]-arbitrage approach
Name
591313102-MIT.pdf
Description
Full printable version
Size
2.15 MB
Format
Adobe PDF
Checksum (MD5)
a2b8777ccb7a414a1fed7ee954eef230
Author(s)
Chen, Si, S.M. Massachusetts Institute of Technology
Advisor(s)
Dimitris Bertsimas.
Date Issued
2009
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.
In title on title-page, "[epsilon]" appears as the lower case Greek letter. Cataloged from PDF version of thesis.
Includes bibliographical references (p. 59-60).
Subjects
Computation for Design and Optimization Program.
MIT Department
Massachusetts Institute of Technology. Computation for Design and Optimization Program
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