Fair Pricing of Variable Annuities with Guarantees under the Benchmark Approach

22 Pages Posted: 13 Jun 2019

See all articles by Jin Sun

Jin Sun

University of Technology Sydney (UTS)

Kevin Fergusson

University of Melbourne - Centre for Actuarial Studies

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Pavel V. Shevchenko

Macquarie University; Macquarie University, Macquarie Business School

Date Written: May 30, 2019

Abstract

In this paper we consider the pricing of variable annuities (VAs) with guaranteed minimum withdrawal benefits. We consider two pricing approaches, the classical risk-neutral approach and the benchmark approach, and we examine the associated static and optimal behaviors of both the investor and insurer. The first model considered is the so-called minimal market model, where pricing is achieved using the benchmark approach. The benchmark approach was introduced by Platen in 2001 and has received wide acceptance in the finance community. Under this approach, valuing an asset involves determining the minimum-valued replicating portfolio, with reference to the growth optimal portfolio under the real-world probability measure, and it both subsumes classical risk-neutral pricing as a particular case and extends it to situations where risk-neutral pricing is impossible. The second model is the Black-Scholes model for the equity index, where the pricing of contracts is performed within the risk-neutral framework. Crucially, we demonstrate that when the insurer prices and reserves using the Black-Scholes model, while the insured employs a dynamic withdrawal strategy based on the minimal market model, the insurer may be underestimating the value and associated reserves of the contract.

Keywords: variable annuity guarantee, stochastic optimal control, stochastic reserve, benchmark approach

JEL Classification: C61, G22

Suggested Citation

Sun, Jin and Fergusson, Kevin and Platen, Eckhard and Shevchenko, Pavel V., Fair Pricing of Variable Annuities with Guarantees under the Benchmark Approach (May 30, 2019). Available at SSRN: https://ssrn.com/abstract=3396279 or http://dx.doi.org/10.2139/ssrn.3396279

Jin Sun

University of Technology Sydney (UTS) ( email )

15 Broadway, Ultimo
PO Box 123
Sydney, NSW 2007
Australia

Kevin Fergusson (Contact Author)

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

Broadway
GPO Box 123
Sydney, NSW 2007, 2007
Australia
+61 2 9514 7759 (Phone)

HOME PAGE: http://datasearch.uts.edu.au/business/finance/staff/StaffDetails.cfm?UnitStaffId=90

University of Technology Sydney, School of Mathematical and Physical Sciences ( email )

P.O. Box 123
Broadway
Sydney, New South Wales 2007
Australia
+61 (02) 9514 2271 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Pavel V. Shevchenko

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

HOME PAGE: http://www.businessandeconomics.mq.edu.au/contact_the_faculty/all_fbe_staff/pavel_shevchenko

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

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