Pricing Guaranteed Minimum Withdrawal Benefits under Stochastic Interest Rates

26 Pages Posted: 14 Jul 2009

See all articles by Jingjiang Peng

Jingjiang Peng

affiliation not provided to SSRN

Kwai Sun Leung

Hong Kong University of Science & Technology (HKUST)

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics

Date Written: June 20, 2009

Abstract

We consider the pricing of variable annuities with the Guaranteed Minimum Withdrawal Benefit (GMWB) under the Vasicek stochastic interest rates framework. The holder of the variable annuity contract pays an initial purchase payment to the insurance company, which is then invested in a portfolio of risky assets. Under the GMWB, the holder can withdraw a specified amount periodically over the term of the contract such that the return of the entire initial investment is guaranteed, regardless of the market performance of the underlying asset portfolio. The investors have the equity participation in the reference investment portfolio with protection on the downside risk. The guarantee is financed by paying annual proportional fees. Under the assumption of deterministic withdrawal rates, we develop the pricing formulation of the value function of a variable annuity with the GMWB. In particular, we derive analytic approximation solutions to the fair value of the GMWB under both equity and interest rate risks, obtaining both the lower and upper bound on the price functions. The pricing behavior of the embedded GMWB under various model parameter values is also examined.

Suggested Citation

Peng, Jingjiang and Leung, Kwai Sun and Kwok, Yue Kuen, Pricing Guaranteed Minimum Withdrawal Benefits under Stochastic Interest Rates (June 20, 2009). Available at SSRN: https://ssrn.com/abstract=1423205 or http://dx.doi.org/10.2139/ssrn.1423205

Jingjiang Peng

affiliation not provided to SSRN ( email )

Kwai Sun Leung

Hong Kong University of Science & Technology (HKUST) ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

Yue Kuen Kwok (Contact Author)

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

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