The Impacts of Surrender Options on Reserve Durations

• Date: 01 September 2012
• Published date: 01 September 2012
• Author: Chenghsien Tsai
• DOI: http://doi.org/10.1111/j.1540-6296.2012.01216.x

Risk Management and Insurance Review

C

Risk Management and Insurance Review, 2012, Vol.15, No. 2, 165-184

DOI: 10.1111/j.1540-6296.2012.01216.x

THE IMPACTS OF SURRENDER OPTIONS ON RESERVE

DURATIONS

Chenghsien Tsai

ABSTRACT

Estimating the interest rate risk of life insurance reserves is essential for insur-

ers, and surrender options are critical to the estimation. This article advances

our understanding of how surrender options affect the durations of reserves.

We identify a pattern of the reserve duration with respect to the interest rate

that is important in explaining how surrender rate levels and the interest-rate

sensitivity of surrenders affect reserve durations. We further found that the

surrender behavior that is more positively related to the interest rate produces

larger/smaller effective dollar durations when the interest rate is low/high.

INTRODUCTION

The reserves of life insurance policies are subject to significant interest rate risk because

of the guaranteed minimum returns as well as the long maturities. The main tools for

managing interest rate risk are duration and immunization (Schaefer, 1992). Duration

analysis has been used extensively in financial markets (Bierwag and Fooladi, 2006) and

is being adopted in the EU Solvency II and risk-based capital requirements implemented

in the United States, Taiwan, and other countries.

Scholars have examined the durations of life insurance liabilities since the middle of

the 1990s. Babbel (1995) estimated the option-adjusted durations of the liabilities for

about a dozen life insurance products.1Santomero and Babbel (1997) listed the effective

durations of the liabilities associated with several life insurance products. Briys and

Chenghsien Tsai is a Professor at the Department of Risk Management and Insurance, Na-

tional Chengchi University, Taiwan; phone: +886–2-2936–9647; fax: +886–2-2939–3864; e-mail:

ctsai@nccu.edu.tw. The author is grateful to Zn-Hong Chen, Cheng-Mao Su, and Fang-Shu Chan

for their competent programming assistance, to the Fulbright Scholar Program and the National

Science Council of Taiwan (Project numbers NSC 93–2416-H-004–041 and NSC 96–2416-H-004–

026-MY3) for the financial support, and to Georgia State University and Santa Clara University

for the kind support extended during the visit of the author.The major portion of the research was

completed while the author was visiting these universities. This article was subject to double-

blind peer review.

1The measures of interest-rate sensitivity that take into account the interest-rate-dependent

cash flows of an asset or a liability are referred to as “option-adjusted duration” or “effective

duration” by Santomero and Babbel (1997). “Macaulay duration” and “modified duration” are

the measures of interest-ratesensitivity assuming that cash flows are independent of movements

in interest rates.

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166 RISK MANAGEMENT AND INSURANCE REVIEW

Varenne (1997, 2001, chap. 5) calculated the effective duration of the liability of the

single-premium participating policy with a guaranteed minimum return. Kim (2005a)

analyzed how changes in the surrender rate resulting from changes of some explanatory

variables affect the durations of single-premium, interest-indexed annuities. Recently,

Tsai (2009) identified a term structurepattern of reserve durations. He further estimated

the durations of the aggregate reserves accumulated by policies sold in different years.

The estimation of liability durations should take surrender options into account. Life

insurers in many cases grant policyholders the options to terminate policies at any time

before maturities for predetermined cash values. Cox et al. (1992), Tsai et al. (2002),

Kuo et al. (2003), and Kim (2005b) found empirical evidence that surrender rates vary

with interest rates. Surrender options, therefore, make the cash flows associated with

insurance liabilities sensitive to changes in interest rates. This interest-rate sensitivity

may dramatically change the durations of life insurance liabilities. Babbel (1995) argued

that the duration measures unadjusted for the interest-rate sensitivity of cash flows are

far larger than what is reasonable. Santomero and Babbel (1997) stated that modified and

Macaulay durations cause overestimation errors so largeas to lead to reckless investment

decisions. Using these unadjusted duration measures to manage a life insurer’s liabilities

would result in an outsized mismatch between the asset and liability durations and

would jeopardize the solvency of the insurer (Briys and Varenne, 1997). Tsai (2009) also

documented significant differences between modified duration and effective duration.

This article advances our understanding of how surrender options affect the durations

of insurance liabilities, which has important implications for investment management

of life insurers. Although Babbel (1995) and Santomero and Babbel (1997) advocate the

importance of surrender options to reserve durations, they did not present methodolog-

ical and implementation information. They reported only the values of their estimated

durations without disclosing surrender rate models, interest rate models, policy spec-

ifications, and valuation methodologies. Tsai (2009) focused on analyzing how reserve

durations change with policy maturities and thus did not assess how the durations

may be affected by surrender options. The policies analyzed in Kim (2005a) are single-

premium, interest-indexed annuities. Single-premium policies are less common than

level-premium ones, and their duration features may differ from each other to a signif-

icant extent as Tsai (2009) pointed out. Furthermore, interest-indexed annuities contain

bonus options and have product features distinct from most other life and annuity prod-

ucts. Due to these missing details, analyses, and/or product features, the mechanism of

how surrender options affect the durations of life insurance liabilities remains obscure.

Our contribution to the literature is that we utilized an empirical surrender rate model

to systematically analyze how surrender options may affect the (dollar) durations of

reserves. Our analyses shed light on the missing link between surrender options and the

(dollar) durations of reserves, and they are meaningful to the asset-liability management

of life insurers.

This article analyzed in detail the impact of surrender options on the durations of policy

reserves. Following Tsai(2009), we estimated the effective durations of life insurance lia-

bilities using the empirical VARmodel of the interest rate and surrender rate established

in Tsai et al. (2002).2The impact of surrender options is analyzed in two aspects: the

2The literature presents few empirical models on the relation between surrender rates and

interest rates, and we found that the models established in Tsaiet al. (2002) and Kuo et al. (2003)