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 X. 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 + X 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~XT).