Pricing and Hedging Guaranteed Minimum Withdrawal Benefits under a General Lévy Framework Using the COS Method
Quantitative Finance. 2017, DOI:10.1080/14697688.2017.1357832
43 Pages Posted: 10 Feb 2017 Last revised: 17 Sep 2017
Date Written: July 10, 2017
This paper extends the Fourier-cosine (COS) method to the pricing and hedging of variable annuities embedded with guaranteed minimum withdrawal benefit (GMWB) riders. The COS method facilitates efficient computation of prices and hedge ratios of the GMWB riders when the underlying fund dynamics evolve under the influence of the general class of Lévy processes. Formulae are derived to value the contract at each withdrawal date using a backward recursive dynamic programming algorithm. Numerical comparisons are performed with results presented in Bacinello et al. (2014) and Luo and Shevchenko (2014) to confirm the accuracy of the method. The efficiency of the proposed method is assessed by making comparisons with the approach presented in Bacinello et al. (2014). We find that the COS method presents highly accurate results with notably fast computational times. The valuation framework forms the basis for GMWB hedging. A local risk minimisation approach to hedging inter-withdrawal date risks is developed. A variety of risk measures are considered for minimisation in the general Lévy framework. While the second moment and variance have been considered in existing literature, we show that the value-at-risk may also be of interest as a risk measure to minimise risk in variable annuities portfolios.
Keywords: variable annuity, GMWB, COS method, hedging, risk minimisation
JEL Classification: C63, G22
Suggested Citation: Suggested Citation