Pricing and Hedging Financial Derivatives: A Guide for Practitioners

9

Multi-Asset Derivatives

In the following chapter, we will analyse some typical risks that arise from multi-asset derivatives. In particular, we will focus on correlation risk for basket options and the correlation/cross-gamma risk for best-of and worst-of options.

From a pure pricing point of view, Monte Carlo simulation tends to be the most common approach (in some cases, the only possible approach). Monte Carlo simulation was described in detail in Chapter 5.

9.1 BASKET OPTIONS

9.1.1 Basket option definition and Greeks

A basket option is an option written on a basket of underlying assets. As a first approximation, we can think of a basket option (either a call or a put) like a vanilla option written on a “single underlying” where the single underlying is the basket itself. This approximation allows us to analyse the Greeks of the basket option in a similar way to the Greeks of a vanilla option. The buyer of, say, a basket call option on two equity indices (which we will call Index A and Index B for simplicity) will have the following exposures:

• Long delta exposure on the basket. The buyer will profit if the value of the basket increases and this can ultimately be seen also as a long exposure on the individual basket constituents (Index A and Index B).
• Long gamma exposure on the basket. As the level of the basket increases, so does the basket delta and when the level of the basket decreases, so the corresponding delta will fall. When analysing the gamma of the individual underlying ...