Pricing and Hedging Guaranteed Minimum Withdrawal Benefits under a General Levy Framework using the COS Method

Jennifer Alonso Garcia, Oliver Wood and Jonathan Ziveyi

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 Levy 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.