Student Number : 8804388Y -
MSc Dissertation -
School of Computational and Applied Mathematics -
Faculty of Science / This dissertation considers the pricing and hedging of contingent claims in a general
semimartingale market. Initially the focus is on a complete market, where it is
possible to price uniquely and hedge perfectly. In this context the two fundamental
theorems of asset pricing are explored. The market is then extended to incorporate
risk that cannot be hedged fully, thereby making it incomplete. Using quadratic
cost criteria, optimal hedging approaches are investigated, leading to the derivations
of the minimal martingale measure and the variance-optimal martingale measure.
These quadratic approaches are then applied to the problem of minimizing the basis
risk that arises when an option on a non-traded asset is hedged with a correlated
asset. Closed-form solutions based on the Black-Scholes equation are derived and
numerical results are compared with those resulting from a utility maximization
approach, with encouraging results.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/2084 |
| Date | 22 February 2007 |
| Creators | McWalter, Thomas Andrew |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 792826 bytes, application/pdf, application/pdf |
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