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.
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: