Continuous Stochastic Processes

Abstract

In Chap. 3 we saw that stochastic differential equations play an important role in the pricing of derivatives. We here discuss various types of SDEs that can be used for the underlying process. We focus on SDEs that have simple solutions and thereby allow for an efficient implementation. As the drift term does not enter the pricing formula for derivatives, we often assume it to be zero. The European call option price formula is derived for the driftless SDEs. This is useful not only as call options are important by themselves, but also because they through static replication can be used to price any other fixed-time payment. Furthermore, exotics models are most often calibrated to European call options.