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

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  • Ng, Andrew Cheuk-Yin
  • Li, Johnny Siu-Hang
  • Chan, Wai-Sum

Abstract

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.

Suggested Citation

  • Ng, Andrew Cheuk-Yin & Li, Johnny Siu-Hang & Chan, Wai-Sum, 2011. "Modeling investment guarantees in Japan: A risk-neutral GARCH approach," International Review of Financial Analysis, Elsevier, vol. 20(1), pages 20-26, January.
    • Handle: RePEc:eee:finana:v:20:y:2011:i:1:p:20-26
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    Cited by:

    1. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Pricing annuity guarantees under a double regime-switching model," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 62-78.
    2. Dong, Bing & Xu, Wei & Sevic, Aleksandar & Sevic, Zeljko, 2020. "Efficient willow tree method for variable annuities valuation and risk management☆," International Review of Financial Analysis, Elsevier, vol. 68(C).
    3. Nitu Sharma & S. Dharmaraja & Viswanathan Arunachalam, 2021. "A Time Series Framework for Pricing Guaranteed Lifelong Withdrawal Benefit," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1225-1261, December.

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