In this course, we'll address the basics of option pricing. We'll provide a short review of discounting and future value and also discuss the Law of No-arbitrage, along with examples that illustrate its utility in pricing.
We will also define two basic option types, call and puts, and explain their payoffs. The six key inputs that determine option prices will be examined and the relationship of each input’s effect on the call price and put price will be evaluated. The survey of the types of participants in options markets will also be discussed. The trading strategies used by these participants will be presented, both with single options, as well as with combinations of options. Next, option pricing will be analyzed in detail. First, a binomial model is used to compute the price of an option in discrete time. The underlying assumption of no-arbitrage is addressed again as the option is priced going backward in time, from option expiration to the present. The hedge ratio at each node is calculated to emphasize the notion of replication. Then the Black Scholes formula will be derived, along with explanations of the assumptions underlying the model. The mathematics are carefully interpreted at each step, resulting in an intuitive description of the partial derivatives, or Greek sensitivities, within the Black Scholes partial differential equation.
