Pricing Guaranteed Annuity Options using a Stochastic Volatility model for equity prices

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

Guaranteed annuity options are options providing the right to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. These options were a common feature in UK retirement savings contracts issued in the 1970's and 1980's when interest rates were high, but caused problems for insurers as the interest rates began to fall in the 1990's. Currently, these options are frequently sold in the US and Japan as part of variable annuity products. The last decade the literature on pricing and risk management of these options evolved. Until now, for pricing these options generally a geometric Brownian motion for equity prices is assumed. However, given the long maturities of the insurance contracts a stochastic volatility model for equity prices would be more suitable. In this paper explicit expressions are derived for prices of guaranteed annuity options assuming stochastic volatility for equity prices and either a 1-factor or 2-factor Gaussian interest rate model. The results indicate that the impact of ignoring stochastic volatility can be significant. © 2010 Elsevier B.V.
Original languageEnglish
Pages (from-to)266-277
JournalInsurance Mathematics & Economics
Volume47
Issue number3
DOIs
Publication statusPublished - 2010

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Stochastic Volatility Model
Equity
Pricing
Stochastic Volatility
Interest Rates
Interest Rate Models
Geometric Brownian Motion
Option Pricing
Gaussian Model
Risk Management
Japan
Insurance
Convert
Stochastic volatility model
Guaranteed annuity options
Equity prices
Stochastic volatility
Factors
Interest rates

Cite this

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title = "Pricing Guaranteed Annuity Options using a Stochastic Volatility model for equity prices",
abstract = "Guaranteed annuity options are options providing the right to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. These options were a common feature in UK retirement savings contracts issued in the 1970's and 1980's when interest rates were high, but caused problems for insurers as the interest rates began to fall in the 1990's. Currently, these options are frequently sold in the US and Japan as part of variable annuity products. The last decade the literature on pricing and risk management of these options evolved. Until now, for pricing these options generally a geometric Brownian motion for equity prices is assumed. However, given the long maturities of the insurance contracts a stochastic volatility model for equity prices would be more suitable. In this paper explicit expressions are derived for prices of guaranteed annuity options assuming stochastic volatility for equity prices and either a 1-factor or 2-factor Gaussian interest rate model. The results indicate that the impact of ignoring stochastic volatility can be significant. {\circledC} 2010 Elsevier B.V.",
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}

Pricing Guaranteed Annuity Options using a Stochastic Volatility model for equity prices. / van Haastrecht, A.; Pelsser, A.

In: Insurance Mathematics & Economics, Vol. 47, No. 3, 2010, p. 266-277.

Research output: Contribution to JournalArticleAcademicpeer-review

TY - JOUR

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AU - van Haastrecht, A.

AU - Pelsser, A

PY - 2010

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AB - Guaranteed annuity options are options providing the right to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. These options were a common feature in UK retirement savings contracts issued in the 1970's and 1980's when interest rates were high, but caused problems for insurers as the interest rates began to fall in the 1990's. Currently, these options are frequently sold in the US and Japan as part of variable annuity products. The last decade the literature on pricing and risk management of these options evolved. Until now, for pricing these options generally a geometric Brownian motion for equity prices is assumed. However, given the long maturities of the insurance contracts a stochastic volatility model for equity prices would be more suitable. In this paper explicit expressions are derived for prices of guaranteed annuity options assuming stochastic volatility for equity prices and either a 1-factor or 2-factor Gaussian interest rate model. The results indicate that the impact of ignoring stochastic volatility can be significant. © 2010 Elsevier B.V.

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