We derive the pricing formulas for guarantees whose guaranteed minimum rates of return are set relative to cross-currency stochastic rates of return, “GCSRs” for short, via a cross-currency framework. GCSRs are often embedded in contracts which include life and pension insurance policies, guaranteed investment contracts and index-linked bonds, etc. The valuation of such guarantees has not been investigated in previous literature regarding guarantees. Our research also finds that valuing GCSRs via a single-currency framework which is adopted in previous research on guarantees causes a significant underestimation of GCSRs under both maturity and multi-period guarantee. The underestimation of multi-period guarantee is much more significant than that of maturity guarantee. As a result, the pricing formulas derived in our research are more suitable, tractable and feasible for practice than those in previous relevant literature.
Asia-Pacific Journal of Financial Studies 43(4), pp.589–619