A practical guide to pricing and hedging with Levy processes
Date
2011-03-28
Authors
Eliasov, Ariel
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Abstract
This dissertation provides an accessible framework for simulating, pricing and hedging
options contracts, using L evy processes that offers several insights and advantages
when compared to conventional techniques (particularly when short dated options
or options near maturity are considered). A minimal review of L evy processes
is provided for those unacquainted with the subject, presenting fundamental theorems
central to the subsequent analysis. A flexible subclass (the Variance Gamma
`family') is then selected and studied, characterizing relevant properties, with which
simulation algorithms are then developed. The significance of risk neutral prices in
such a market made incomplete by jumps is described and an efficient method for
calculating such prices is given. In the final sections, several avenues for mitigating
risk by hedging in the underlying asset are explored and a numerical `hedging
race' is conducted and analyzed to compare the performance of several techniques
on realistic data.