Valuation of Equity-Linked Life Insurance Contracts with Surrender Guarantees in a Regime-Switching Rational Expectation Model

29 Pages Posted: 14 Mar 2012 Last revised: 30 Apr 2012

See all articles by Filip Uzelac

Filip Uzelac

University of Bonn - The Bonn Graduate School of Economics

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration

Date Written: March 13, 2012

Abstract

We develop a two-state regime-switching rational expectation model with the economic states recession and expansion for the valuation of equity-linked life insurance contracts with surrender guarantees. Our valuation model jointly captures the empirically observed macroeconomical regime-dependency of both the lapsing and the fi nancial market dynamics. More precisely, our surrender model incorporates both the emergency fund and the interest rate hypothesis in an intensity-based approach via a countercyclical exogenous and a procyclical endogenous surrender intensity. On the equity side the reference fund evolution allows for a countercyclical volatility and a procyclical risk-free rate. The contract value of a representative policyholder is characterized as solution of a system of two coupled PDEs, which we solve numerically by the Crank-Nicolson scheme combined with a penalty method. In extensive numerical experiments we study the effect of the model parameters on the contract values and particularly surrender option values and also compare our regime-switching rational expectation model with the regime-switching American style surrender model.

Keywords: equity-linked life insurance, surrender guarantee, regime-switching, rational expectation

JEL Classification: G13, G22, C65

Suggested Citation

Uzelac, Filip and Szimayer, Alexander, Valuation of Equity-Linked Life Insurance Contracts with Surrender Guarantees in a Regime-Switching Rational Expectation Model (March 13, 2012). Available at SSRN: https://ssrn.com/abstract=2020981 or http://dx.doi.org/10.2139/ssrn.2020981

Filip Uzelac (Contact Author)

University of Bonn - The Bonn Graduate School of Economics ( email )

Adenauerallee 24-26
Bonn, D-53113
Germany

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

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