The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case a Merton-type formula is...

It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a...