Pricing and Hedging of Contingent Claims

Abstract

The goal of this chapter is to derive fair prices of derivatives contracts, that is, financial contracts that depend on an underlying stock. Furthermore, we shall discuss how one can hedge the risk associated with a position in a derivatives contract. The price dynamics of the underlying stock is assumed to be modelled by geometric Brownian motion, that is, the Black & Scholes model. One of the highlights of the chapter is the famous Black & Scholes option pricing formula, which states the fair value of a call option. Rather than restricting our attention to call and put options, we will consider a very general class of derivatives contracts called contingent claims. The reason for going to such generality is that we would like to include popular derivatives like Asian options, barrier options, chooser options etc. Unfortunately, American-type options will not fit into our framework.