In the solution for part (iv) the boundary condition is contradicting with the lower boundary for a European Call option, max(0, S_t-K.exp{rt}). Is this correct?
Q&A Bank 3.19 The boundary condition given for time T is just the payoff function for a call option. Your lower bound formula for general time t<=T isn't quite right. The "rt" you have in the exponential should read "-r(T-t)". Making this correction removes the apparent contradiction.
Hi Mike Please excuse my typo, but even so, the solution they provided is max(s-K,0) and the option in question is a European call, not American, which is why I thought this is contradicting with Chapter 9, page 18. Am I missing something here?
Q&A Bank 3.19 Since the option is European, the boundary condition holds at the boundary t=T, so in full we have f(T,s(T))=max[s(T)-K,0]. The lower bound is c(t)>=s(t)-K.exp{-r(T-t)}, which at time T becomes c(T)>=s(T)-K. So the boundary condition above satisfies this lower bound. I'm sorry, but I can't see where you think there's a contradiction. If you're still not happy with this, please feel free to go into more detail about where your unease lies.
