March 22nd, 2008, 6:00 pm
I got similar answer by using a hedge or replication perspective. Whenever the price touches 100 during the lifetime, option B is worth $1. For option A, there is approximately half chance for it to finish in the money, this equivalent to the fact that for a struck-at-the-money call, the probability that it finishes in the money is approximately 0.5 (precisely is N(d2) where d2=-sigma*sqrt(T-t)/2, close to 0 and N(d2) close to but strictly <0.5). This means the value of option A is approximately half of the option B.QuoteOriginally posted by: stt106QuoteOriginally posted by: MCarreiraIsn't it just a question about the rule-of-thumb of American Digitals being worth roughly twice than the European Digitals ?agree and more specifically, A is European digital call and B is American digital call which is one of the American options that have an analytic solution.In the case of zero interest rate, analytically, B's value is maximised when S = K and the optimal value is N(d1)+N(d2), whereas A's value is N(d2) ( when r = 0).Is this why you said B is roughly twice as much as A?