Exercise 14.13 Suppose that, under the risk-neutral probability measure Q, the underlying stock price follows the SDE

where ν = r − σ2/2 and where r, q, and σ are positive constants. Note that the model assumes the dividend rate to be δ(S, t) = qS log S. Show that

Also, show that the premium of the European call option with strike price K and maturity T written on the stock is given by

Finally, show that the price c is neither convex with respect to S nor increasing in σ. See Kijima (2002) for details.

Transcribed Image Text:

dlog S (v qlog S)dt+odz(t), 0