Quantitative Finance

Chapter 30

Options on Multiple Underlying Assets

30.1 INTRODUCTION

Sometimes, options are written on more than one asset. A very similar approach to that used in hedging a simple Black Scholes option also applies in this case. In this chapter, we develop the new Black Scholes partial differential equation (PDE) for perpetual options (now in one time and two “stock price” variables). We solve this PDE for the special case of the Margrabe exchange option.

Companies operating in multiple countries take on currency risk, in that they may have costs in one currency and sales in another. One way for them to hedge their risk is to enter into an options contract to exchange one currency for another. In energy markets, it is often quite instructive to ...