On the calibration of mortality forward curves

Johnny Siu‐Hang Li, Andrew Cheuk‐Yin Ng and Wai‐Sum Chan

Journal of Futures Markets, 2011, vol. 31, issue 10, 947-970

Abstract: In 2007, a major investment bank launched a product called “q‐forward,” which may be regarded as a forward contract on a mortality rate. The pricing of mortality forwards is similar to the pricing of other forward‐rate contracts, such as interest‐rate forwards or foreign exchange forwards. In particular, since investors require compensation to take on longevity risk, the forward mortality rate at which q‐forward contracts will trade will be smaller than the expected mortality rate. The relationship between the forward rate and the time to maturity is called a mortality forward curve. In this study, we contribute a method for calibrating mortality forward curves. This method consists of two parts, one of which is the generation of the distribution of future mortality rates, and the other of which is the transformation of the distribution into its risk‐neutral counterpart, using the idea of canonical valuation developed by Stutzer, M. ( 1996 ). To illustrate the method, mortality forward curves for English and Welsh males are calibrated. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark

Date: 2011
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