Valuation of Guaranteed Annuity Options Using a Stochastic Volatility Model for Equity Prices

Haastrecht, A. van; Plat, Richard; Pelsser, Antoon

doi:10.2139/ssrn.1447283

Cited by 8 publications

(25 citation statements)

References 32 publications

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“…In the following subsection we explain in details the calibration of the three models. We summarize the calibration of the interest rate parameters and the calibration of the SZHW and the BSHW made in [28] and then we explain the calibration of the local volatility surface for the equity component in our LVHW model. In Subsection 5.3 we compare GAO values obtained by using the LVHW model with the SZHW and the BSHW prices studied in [28].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…We summarize the calibration of the interest rate parameters and the calibration of the SZHW and the BSHW made in [28] and then we explain the calibration of the local volatility surface for the equity component in our LVHW model. In Subsection 5.3 we compare GAO values obtained by using the LVHW model with the SZHW and the BSHW prices studied in [28]. In Subsection 5.4 and Subsection 5.5, we do the same study for path-dependent Variable Annuity Guarantees namely GMIB Riders and barrier type GAOs.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In [28] the authors have calibrated the equity model to market option prices maturing in 10 years time. In the LVHW model, the equity volatility is a local volatility surface and the calibration consists in building this surface using equation (7).…”

Section: Calibration To the Vanilla Option's Marketmentioning

confidence: 99%

“…Some authors consider the evolution of mortality stochastic as well (see for example [3] and [4]). In [28], van Haastrecht et al have studied the impact of the volatility of the fund on the price of GAO by using a stochastic volatility approach.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Variable Annuity Guarantees in a local volatility framework

Deelstra

Rayée

2013

Insurance: Mathematics and Economics

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In this paper, we study the price of Variable Annuity Guarantees, especially of Guaranteed Annuity Options (GAO) and Guaranteed Minimum Income Benefit (GMIB), and this in the settings of a derivative pricing model where the underlying spot (the fund) is locally governed by a geometric Brownian motion with local volatility, while interest rates follow a Hull-White one-factor Gaussian model. Notwithstanding the fact that in this framework, the local volatility depends on a particularly complicated expectation where no closed-form expression exists and it is neither directly related to European call prices or other liquid products, we present in this contribution different methods to calibrate the local volatility model. We further compare Variable Annuity Guarantee prices obtained in three different settings, namely the local volatility, the stochastic volatility and the constant volatility models all combined with stochastic interest rates and show that an appropriate volatility modelling is important for these long-dated derivatives. More precisely, we compare prices of GAO, GMIB Rider and barrier types GAO obtained by using local volatility, stochastic volatility and constant volatility models. arXiv:1204.0453v2 [q-fin.PR]

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Calibration To the Vanilla Option's Marketmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pricing Variable Annuity Guarantees in a local volatility framework

Deelstra

Rayée

2013

Insurance: Mathematics and Economics

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“…In the actuarial literature, this is known as the 'normal power approximation' (see, for example, Daykin et al 1994;Eling, Gatzert, and Schmeiser 2009). Another motivation for considering skewness is the use of Edgeworth expansions to model insurance claims (Chaubey, Garrido, and Trudeau 1998;Albers 1999;Brito and Freitas 2008;van Haastrecht, Plat, and Pellser 2010).…”

Section: Actuarial Sciencementioning

confidence: 99%

Skewed distributions in finance and actuarial science: a review

Adcock

Eling

Loperfido

2012

The European Journal of Finance

122

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That the returns on financial assets and insurance claims are not well described by the multivariate normal distribution is generally acknowledged in the literature. This paper presents a review of the use of the skew-normal distribution and its extensions in finance and actuarial science, highlighting known results as well as potential directions for future research. When skewness and kurtosis are present in asset returns, the skew-normal and skew-Student distributions are natural candidates in both theoretical and empirical work. Their parameterization is parsimonious and they are mathematically tractable. In finance, the distributions are interpretable in terms of the efficient markets hypothesis. Furthermore, they lead to theoretical results that are useful for portfolio selection and asset pricing. In actuarial science, the presence of skewness and kurtosis in insurance claims data is the main motivation for using the skew-normal distribution and its extensions. The skew-normal has been used in studies on risk measurement and capital allocation, which are two important research fields in actuarial science. Empirical studies consider the skew-normal distribution because of its flexibility, interpretability, and tractability. This paper comprises four main sections: an overview of skew-normal distributions; a review of skewness in finance, including asset pricing, portfolio selection, time series modeling, and a review of its applications in insurance, in which the use of alternative distribution functions is widespread. The final section summarizes some of the challenges associated with the use of skew-elliptical distributions and points out some directions for future research. C. Adcock et al.those of Arditti and Levy (1975) and Kraus and Litzenberger (1976), marks the point at which the modern theory of finance started revealing evidence of skewness analogous to that provided by Markowitz, Sharpe, Lintner, Tobin, and others.In the context of actuarial science, it is important to recognize that insurance risks have skewed distributions (see, for example, Lane 2000), which is why in many cases, the classical normal distribution is an inadequate model for insurance risks or losses. Some insurance risks also exhibit heavy tails, especially those exposed to catastrophes (see Embrechts, McNeil, and Straumann 2002). The skew-normal distribution and its extensions thus might be promising since they preserve the advantages of the normal distribution with the additional benefit of flexibility with regard to skewness and kurtosis. The skew-normal distribution and its extensions have been used recently in studies on risk management, capital allocation, and goodness-of-fit (Vernic 2006;Bolance et al. 2008;Eling 2012).This review paper is motivated by the belief that asymmetry in asset returns, and skewness in particular, is an important field of research. Such research has two clear themes. The first is the never-ending and entirely natural wish to develop better univariate models for asset returns. Such model developme...

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Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates

Kang

Ziveyi

2018

Insurance: Mathematics and Economics

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In this paper we analyse how the policyholder surrender behaviour is influenced by changes in various sources of risk impacting a variable annuity (VA) contract embedded with a guaranteed minimum maturity benefit rider that can be surrendered anytime prior to maturity. We model the underlying mutual fund dynamics by combining a Heston (1993) stochastic volatility model together with a Hull and White (1990) stochastic interest rate process. The model is able to capture the smile/skew often observed on equity option markets (Grzelak and Oosterlee, 2011) as well as the influence of the interest rates on the early surrender decisions as noted from our analysis. The annuity provider charges management fees which are proportional to the level of the mutual fund as a way of funding the VA contract. To determine the optimal surrender decisions, we present the problem as a 4-dimensional freeboundary partial differential equation (PDE) which is then solved efficiently by the method of lines (MOL) approach. The MOL algorithm facilitates simultaneous computation of the prices, fair management fees, optimal surrender boundaries and hedge ratios of the variable annuity contract as part of the solution at no additional computational cost. A comprehensive analysis on the impact of various risk factors in influencing the policyholder's surrender behaviour is carried out, highlighting the significance of both stochastic volatility and interest rate parameters in influencing the policyholder's surrender behaviour. With the aid of the hedge ratios obtained from the MOL, we construct an effective dynamic hedging strategy to mitigate the provider's risk and compare different hedging performances when the policyholders' surrender behaviour is either optimal or sub-optimal.

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Valuation of Guaranteed Annuity Options Using a Stochastic Volatility Model for Equity Prices

Cited by 8 publications

References 32 publications

Pricing Variable Annuity Guarantees in a local volatility framework

Pricing Variable Annuity Guarantees in a local volatility framework

Skewed distributions in finance and actuarial science: a review

Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates

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