Show that the price of a european call option

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Reference no: EM131240915

Consider the case of Merton's jump-diffusion model where jumps always reduce the asset price to zero. Assume that the average number of jumps per year is λ.

Show that the price of a European call option is the same as in a world with no jumps except that the risk-free rate is r + λ rather than r. Does the possibility of jumps increase or reduce the value of the call option in this case?

(Hint: Value the option assuming no jumps and assuming one or more jumps. The probability of no jumps in time T is e^-λT ).

Reference no: EM131240915

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