An identity of hitting times and its application to the valuation of guaranteed minimum withdrawal benefit

Feng, Runhuan; Volkmer, Hans

doi:10.1007/s11579-015-0153-5

Cited by 24 publications

(11 citation statements)

References 26 publications

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“…When the management fee of the policyholder's wealth account is zero, and deterministic withdrawal behavior is assumed, Hyndman and Wenger (2014) and Fung et al (2014) show that risk-neutral pricing of guaranteed withdrawal benefits in both a policyholder's and an insurer's perspectives will result in the same fair insurance fee. Feng and Volkmer (2016) obtains similar results based on an application of an identity of hitting times. Several studies that take management fees into account in the pricing of VA guarantees include Bélanger et al (2009 and Kling et al (2011).…”

Section: Introductionsupporting

confidence: 56%

The Impact of Management Fees on the Pricing of Variable Annuity Guarantees

Sun

Shevchenko

Fung

2018

Risks

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Variable annuities, as a class of retirement income products, allow equity market exposure for a policyholder’s retirement fund with optional guarantees to limit the downside risk of the market. Management fees andguarantee insurance fees are charged respectively for the market exposure and for the protection from the downside risk. We investigate the pricing of variable annuity guarantees under optimal withdrawal strategies when management fees are present. We consider from both policyholder’s and insurer’s perspectives optimal withdrawal strategies and calculate the respective fair insurance fees. We reveal a discrepancy where the fees from the insurer’s perspective can be significantly higher due to the management fees serving as a form of market friction. Our results provide a possible explanation of lower guarantee insurance fees observed in the market than those predicted from the insurer’s perspective. Numerical experiments are conducted to illustrate the results.

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Section: Introductionsupporting

confidence: 56%

The Impact of Management Fees on the Pricing of Variable Annuity Guarantees

Sun

Shevchenko

Fung

2018

Risks

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“…It is promising that the spectral methods can be further extended for the pricing and risk management of many more advanced variable annuity guaranteed benefits as well. Such an example can be seen in Feng and Volkmer (2013) for the guaranteed minimum withdrawal benefit (GMWB). We can show that…”

Section: Summary and Future Workmentioning

confidence: 99%

Spectral Methods for the Calculation of Risk Measures for Variable Annuity Guaranteed Benefits

Feng¹,

Volkmer²

2014

ASTIN Bull.

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Spectral expansion techniques have been extensively exploited for the pricing of exotic options. In this paper, we present novel applications of spectral methods for the quantitative risk management of variable annuity guaranteed benefits such as guaranteed minimum maturity benefits and guaranteed minimum death benefits. The objective is to find efficient and accurate solution methods for the computation of risk measures, which is the key to determining risk-based capital according to regulatory requirements. Our example calculations show that two spectral methods used in this paper are highly efficient and numerically more stable than conventional known methods. Hence these approaches are more suitable for intensive calculations involving death benefits.

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“…K * . Since the integrands are nonnegative, we exchange the order of integration and obtain An analytic expression for the first term in (6.28) is already obtained in Feng and Volkmer [9,Proposition 3.4]. 1 Therefore, the only unknown quantity to be determined is the third term in (6.28).…”

Section: Joint Laplace Transform Of the Geometric Brownian Motion Wit...mentioning

confidence: 99%

“…1 In Feng and Volkmer [9], this quantity was represented as the time-integral of the process X t up to the earlier of the first time it hits zero and a fixed time T , i.e. E τ ∧T 0 X t dt , where τ := inf{t : X t ≤ 0}.…”

Section: Joint Laplace Transform Of the Geometric Brownian Motion Wit...mentioning

confidence: 99%

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Geometric Brownian motion with affine drift and its time-integral

Feng

Jiang

Volkmer

2020

Preprint

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The joint distribution of a geometric Brownian motion and its time-integral was derived in a seminal paper by Yor (1992) using Lamperti's transformation, leading to explicit solutions in terms of modified Bessel functions. In this paper, we revisit this classic result using the simple Laplace transform approach in connection to the Heun differential equation. We extend the methodology to the geometric Brownian motion with affine drift and show that the joint distribution of this process and its time-integral can be determined by a doubly-confluent Heun equation. Furthermore, the joint Laplace transform of the process and its time-integral is derived from the asymptotics of the solutions. In addition, we provide an application by using the results for the asymptotics of the double-confluent Heun equation in pricing Asian options. Numerical results show the accuracy and efficiency of this new method.

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An identity of hitting times and its application to the valuation of guaranteed minimum withdrawal benefit

Cited by 24 publications

References 26 publications

The Impact of Management Fees on the Pricing of Variable Annuity Guarantees

The Impact of Management Fees on the Pricing of Variable Annuity Guarantees

Spectral Methods for the Calculation of Risk Measures for Variable Annuity Guaranteed Benefits

Geometric Brownian motion with affine drift and its time-integral

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