In the forty years since the seminal article by Black and Scholes (1973), quantitative methods have become indispensable in the assessment, pricing and hedging of financial risk. This is most evident in the techniques used to price derivative financial instruments, but permeates all areas of...

We analyse contracts which pay out a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specified on the basis of a benchmark portfolio. These contracts are closely related to unit--linked life--insurance/savings plan products and can be considered as...