Discrete time to continuous time…

As we segue from discrete-time (binomial) to continuous time (Black-Scholes-Merton) pricing models in Finance 4366, you will surely find this topic to be quite challenging. But it is essential, since a basic understanding of the continuous time framework is, as Hull puts it, “central to the pricing of derivatives”. As you read Hull’s textbook chapter entitled “Wiener Processes and Ito’s Lemma” and my teaching notes entitled “Applying Ito’s Lemma to determine the parameters of the probability distribution for the continuously compounded rate of return” and “Geometric Brownian Motion Simulations“, keep the following exhortation by Hull in mind (this appears as the third paragraph on the first page of the textbook chapter assigned for tomorrow):

“Many people feel that continuous-time stochastic processes are so complicated that they should be left entirely to ‘‘rocket scientists.’’ This is not so. The biggest hurdle to understanding these processes is the notation. Here we present a step-by-step approach aimed at getting the reader over this hurdle. We also explain an important result known as Ito’s lemma that is central to the pricing of derivatives.”


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