7.1 STATEMENT OF PROBLEM
Having derived the general form of multi‐factor pricing kernels in the preceding chapter, we look now to apply this knowledge first to a relatively simple problem, considering the joint distribution of equity and rates with a view to calculating a pricing kernel for rates‐equity hybrid derivatives. For rates we assume the short‐rate model of Hull and White , as described in Chapter 4, using the notation there introduced. We suppose the equity process to be given by
with given by (4.2), the dividend rate and a Brownian motion. Further, take this Brownian motion to be correlated with that driving the Hull–White rates model, with
As previously, define an auxiliary process implicitly by (3.45). It follows ...