This thesis explores option pricing and hedging in a discrete time regime-switching environment. If the regime risk cannot be hedged away, then we cannot ignore this risk and use the Black-Scholes pricing and hedging framework to generate a unique
pricing and hedging measure. We develop a risk neutral pricing measure by applying an Esscher Transform to the real world asset price process, with the focus on the issue of
incompleteness of the market. The Esscher transform turns out to be a convenient and effective tool for option pricing under the
discrete time regime switching models. We apply the pricing measure to both single variate European options and multivariate
options. To better understand the effect of the pricing method, we also compared the results with those generated from two
other risk neutral methods: the Black-Scholes model, and the natural equivalent martingale method.
We further investigate the difference in hedging associated with different pricing measures. This is of interest when the choice of pricing method is uncertain under regime switching models. We compare four hedging strategies: delta hedging for the three risk neutral pricing methods under
study, and mean variance hedging. We also develop a more general tool of tail
ordering for hedging analysis in a general incomplete market with the uncertainty of the risk neutral measures. As a result of the
analysis, we propose that pricing and hedging using the Esscher transform may be an effective strategy for a market where
the regime switching process brings uncertainty.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/7433 |
| Date | January 2013 |
| Creators | Qiu, Chao |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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