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

See all articles by Jennifer Alonso-García

Jennifer Alonso-García

Université Libre de Bruxelles (ULB) - Department of Mathematics; ARC Centre of Excellence in Population Ageing Research; Netspar

Oliver Wood

CommInsure

Jonathan Ziveyi

UNSW Australia

Date Written: July 10, 2017

Abstract

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

Alonso-García, Jennifer and Wood, Oliver and Ziveyi, Jonathan, Pricing and Hedging Guaranteed Minimum Withdrawal Benefits under a General Lévy Framework Using the COS Method (July 10, 2017). Quantitative Finance. 2017, DOI:10.1080/14697688.2017.1357832, Available at SSRN: https://ssrn.com/abstract=2914105 or http://dx.doi.org/10.2139/ssrn.2914105

Jennifer Alonso-García (Contact Author)

Université Libre de Bruxelles (ULB) - Department of Mathematics ( email )

Brussels
Belgium

ARC Centre of Excellence in Population Ageing Research ( email )

Level 6, Central Lobby (enter via East Lobby)
Australian School of Business Building
Sydney, New South Wales NSW 2052
Australia

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Oliver Wood

CommInsure ( email )

48 Martin Pl
Sydney, NSW 2000
Australia

Jonathan Ziveyi

UNSW Australia ( email )

School of Risk and Actuarial Studies
Level 6 East Wing, Business School
Sydney, NSW 2052
Australia
+61 2 9385 8006 (Phone)
+61 2 9385 1883 (Fax)

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