A Modern View on Merton's Jump-Diffusion Model
AbstractMerton has provided a formula for the price of a European call option on a single stock where the stock price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. In Merton's analysis, the jump-risk is not priced. Thus the distribution of the jump-arrivals and the jump-sizes do not change under the change of measure. We go onto introduce a Radon-Nikodym derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the Radon-Nikodym derivative allows us to price the option under different financial-economic scenarios. We introduce a hedging argument that eliminates the jump-risk in some sort of averaged sense, and derive an integro-partial differential equation of the option price that is related to the one obtained by Merton.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 287.
Date of creation: 01 Jan 2011
Date of revision:
financial derivatives; compound Poisson processes; equivalent martingale measure; hedging portfolio;
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- Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
- Scalas, Enrico & Politi, Mauro, 2012.
"A parsimonious model for intraday European option pricing,"
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- Enrico Scalas & Mauro Politi, 2012. "A parsimonious model for intraday European option pricing," Papers 1202.4332, arXiv.org.
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