An Extension of Merton's Jump-Diffusion Model

G.H.L. Cheang (Singapore) and C. Chiarella (Australia)


Financial derivatives, compound Poisson processes, equiv alent martingale measure, hedging portfolio.


Merton 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 addi tion 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 introduce a Radon-Nikod´ym derivative process that induces the change of measure from the market measure to an equivalent mar tingale measure. The choice of parameters in the Radon Nikod´ym derivative allows us to price the option under dif ferent financial-economic scenarios. In our hedging portfo lio, two options of different maturities are required so that the jump-risk is properly priced in the portfolio.

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