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...

Contracts paying a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specified relative to a benchmark portfolio, are closely related to unit-linked life-insurance products and can be considered as alternatives to direct investment in the underlying benchmark....