--------------------------------------------------- # # # Chapter 5: The Black-Scholes Model # # as Continuous Time Limit # # of the Binomial Model # # # --------------------------------------------------- Summary: It is shown that the Black-Scholes Model can be obtained as the continuous time limit of a Binomial model with suitable returns. As a consequence, exact payoff replication is also possible in the Black-Scholes model. More mathematically phrased, the Black-Scholes model is a complete model. Furthermore, for a non-path dependent option payoff, we derive a one-dimensional integral representation for its theoretical fair value, for the option price.

Continuous Time Limit of the Binomial Model