Hi All, I have a question relating to exchange options which are covered in chapter 9, pages 12-13. I wondered what Brownian motion process the underlying share price is assumed to adopt? When working on question 4.16 in the Q&A I found this quite interesting. The solution suggests that the stochastic process adopted by share 1 was assumed to be; S(t) = log N(mu(1)t, sigma(1)^2(t)) and a similar equation for share 2. Using this approach the answer can be pulled together and happy days. The question I have relates to why the share process isn't assumed to adopt the process stated in Chapter 5 for the underlying process? (which can be found on page 16 of Chapter 5). Namely S(t) = log N(log S(0) + (mu(1)-0.5t*sigma(1)^2)(t), (sigma(1)^2)(t)) I appreciate in the risk-neutral world mu(1) would be replaced for the risk-free rate (which effectively cancels our here). I wondered whether the solution used the correct process for modelling the underlying share price to allow for the BS model to be used to value the option? Thanks, O
Hi Owen Yes, I think there is a mistake in the solution here. The lognormal distributions for the share prices should include a log S(0) term in the "mu parameter". As you say, these don't affect the final answer, since the option price only depends on the risk-free interest rate, not the real-world growth rate. I'll add this to our list of corrections.
