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

Feng, Runhuan; Volkmer, Hans

doi:10.1017/asb.2014.14

Cited by 27 publications

(20 citation statements)

References 25 publications

(30 reference statements)

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“…This result can be obtained from the spectral method used in Feng and Volkmer (2013) to determine risk measures (Section 3.2). We can verify that (4.3) agrees with (4.6).…”

Section: )mentioning

confidence: 99%

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

Feng

Volkmer²

2015

Math Finan Econ

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In this paper we explore an identity in distribution of hitting times of a finite variation process (Yor's process) and a diffusion process (geometric Brownian motion with affine drift), which arise from various applications in financial mathematics. As a result, we provide analytical solutions to the fair charge of variable annuity guaranteed minimum withdrawal benefit(GMWB) from a policyholder's point of view, which was only previously obtained in the literature by numerical methods. We also use complex inversion methods to derive analytical solutions to the fair charge of the GMWB from an insurer's point of view, which is used in the market practice, however, based on Monte Carlo simulations. Despite of their seemingly different formulations, we can prove under certain assumptions the two pricing approaches are equivalent.

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“…This result can be obtained from the spectral method used in Feng and Volkmer (2013) to determine risk measures (Section 3.2). We can verify that (4.3) agrees with (4.6).…”

Section: )mentioning

confidence: 99%

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

Feng

Volkmer²

2015

Math Finan Econ

Self Cite

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“…For example, Feng and Volkmer (2012) used properties of geometric Brownian motion to develop analytical methods for the calculation of risk measures, such as VaR and conditional tail expectation (CTE) for VA guarantees. The same authors also later used spectral expansion methods to compute risk measures related to GMMB and GMDB types of guarantees on VA products (Feng and Volkmer 2014). Gan and Lin (2017) used a two-level approach to estimating the Greeks associated with a portfolio of VA guarantees.…”

Section: Introductionmentioning

confidence: 99%

Using Neural Networks to Price and Hedge Variable Annuity Guarantees

Doyle¹,

Groendyke

2018

Risks

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This paper explores the use of neural networks to reduce the computational cost of pricing and hedging variable annuity guarantees. Pricing these guarantees can take a considerable amount of time because of the large number of Monte Carlo simulations that are required for the fair value of these liabilities to converge. This computational requirement worsens when Greeks must be calculated to hedge the liabilities of these guarantees. A feedforward neural network is a universal function approximator that is proposed as a useful machine learning technique to interpolate between previously calculated values and avoid running a full simulation to obtain a value for the liabilities. We propose methodologies utilizing neural networks for both the tasks of pricing as well as hedging four different varieties of variable annuity guarantees. We demonstrated a significant efficiency gain using neural networks in this manner. We also experimented with different error functions in the training of the neural networks and examined the resulting changes in network performance.

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“…In addition, a high level of precision up the 4th of 5th significant digit can be commonly required. On the other hand, faster computational methods based on analytical expressions have recently been introduced in Feng and Volkmer (2012), Feng and Volkmer (2014) for the computation of risk measures of GMDBs and GMMBs.…”

Section: Introductionmentioning

confidence: 99%

“…More computationally efficient expressions for those risk measures have been presented in Feng and Volkmer (2014) based on identities in law for the geometric Brownian motion with affine drift…”

Section: Introductionmentioning

confidence: 99%

Fast Computation of Risk Measures for Variable Annuities With Additional Earnings by Conditional Moment Matching

Privault

Wei

2017

ASTIN Bull.

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We propose an approximation scheme for the computation of the risk measures of guaranteed minimum maturity benefits (GMMBs) and guaranteed minimum death benefits (GMDBs), based on the evaluation of single integrals under conditional moment matching. This procedure is computationally efficient in comparison with standard analytical methods while retaining a high degree of accuracy, and it allows one to deal with the case of additional earnings and the computation of related sensitivities.

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

Cited by 27 publications

References 25 publications

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

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

Using Neural Networks to Price and Hedge Variable Annuity Guarantees

Fast Computation of Risk Measures for Variable Annuities With Additional Earnings by Conditional Moment Matching

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