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 . 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+ 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***).

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