Modeling investment guarantees in Japan: A risk-neutral GARCH approach

The variable annuity market in Japan is still young, but growing rapidly. Most variable annuities in Japan are sold with one or more investment guarantees, such as a Guaranteed Minimum Maturity Benefit (GMMB), which guarantees that the ultimate annuity principal will not fall below a pre-set level regardless of the underlying investment performance. Of interest to financial institutions selling variable annuities is the cost associated with such a guarantee. Although the Black-Scholes option pricing formula can be applied readily, the resulting price might be inaccurate because returns on the Japanese stock price index do not seem to behave as assumed in the formula. In this study, we propose a method for valuing investment guarantees on the basis of a GARCH-type model, which better captures the characteristics of the stock price index. A difficulty in option-pricing with GARCH is the identification of a risk-neutral probability measure. We solve this problem by considering the conditional Esscher transform. Computational details of the proposed method are illustrated by valuing costs of two popular investment guarantees in Japan.