ABSTRACT
The classical multidimensional geometric Brownian motion (GBM) model offers fairly simple analytical tractability for many standard options written on multiple stocks. This chapter simplifies the framework to the classical multidimensional GBM model for the risky assets and also assumes nonrandom interest rates and stock dividends. This allows us to price several standard (as well as some path dependent) European-style derivatives whose payoffs are dependent on the prices of multiply correlated assets. The chapter discusses the risk-neutral pricing framework in the more general context of equivalent martingale measures that correspond to different choices of numéraire assets for pricing. As shown in the discrete-time models, there is a general numéraire invariant risk-neutral derivative pricing formula. Girsanov’s Theorem allows us to price derivatives under different choices of numéraires. The chapter presents some examples of how changing numéraires facilitates the pricing of some multi-asset derivatives.
