Analytical calculation of risk measures for variable annuity guaranteed benefits

Feng, Runhuan; Volkmer, Hans

doi:10.1016/j.insmatheco.2012.09.007

Cited by 44 publications

(39 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…See American Academy of Actuaries publications [9], [16] and [10] for details on a selection of equity return models. Computations of risk measures for variable annuity guaranteed benefits based on exponential functionals of Brownian motion can be found in Feng and Volkmer [7,8]. In this paper, we are interested in the exponential Lévy processes, primarily for two reasons: (i) such models have been shown to explain various stylized facts of empirical data and (ii) they often lead to analytical solutions, not only for pricing problems of exotic options, which are wellstudied in finance literature, but also for risk measures of extreme liabilities in equity-linked insurance products, thereby providing fast algorithms for computation needed for capital requirement and other risk management purposes.…”

Section: Introductionmentioning

confidence: 99%

Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Feng

Kuznetsov

Yang

2019

Stochastic Processes and their Applications

Self Cite

View full text Add to dashboard Cite

Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black-Scholes model is appealing because of mathematical tractability, yet empirical evidence shows that geometric Brownian motion does not adequately capture features of market equity returns. One popular alternative for modeling equity returns consists in replacing the geometric Brownian motion by an exponential of a Lévy process. In this paper we use this latter model to study variable annuity guaranteed benefits and to compute explicitly the distribution of certain exponential functionals.where we have denoted (x) + = max(x, 0) andis the exponential functional of the process X. Since the no-arbitrage price of an Asian option in the Black-Scholes model is determined by the expected present value of its payoff under a risk-neutral probability measure, the key to the computation of Asian option price is the distribution of the exponential functional J T . There has been a vast amount of work in the literature devoted to the distribution of J T . To name a few, Yor [28] employs the Lamperti transformation relating the geometric Brownian motion and the exponential functional to a Bessel process. Linetsky [17] starts with an identity in distribution J t d = U t := e Xt t 0

show abstract

Section: Introductionmentioning

confidence: 99%

Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Feng

Kuznetsov

Yang

2019

Stochastic Processes and their Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…There is a wide variety of contractual annuity payoffs, ranging from fixed payouts to variable annuities, possibly with guaranteed benefits features. The pricing and valuation of such contracts have been considered in the actuarial literature, under different choices of equity price, mortality and interest rate models [18,25,35,10,33]. Most of the theoretical work on variable annuities in the literature is in a continuous-time setting, although in practice these instruments are defined and simulated in discrete time.…”

Section: Introductionmentioning

confidence: 99%

Discrete sums of geometric Brownian motions, annuities and Asian options

Pirjol¹,

Zhu

2016

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

Abstract. The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of geometric Brownian motions with geometric stopping time, and the finite sum of the geometric Brownian motions. These results are extended to the discrete sum of the exponential Lévy process. We derive tail asymptotics and compute numerically the asymptotic distribution function. We compare the results against the known results for the continuous time integral of the geometric Brownian motion up to an exponentially distributed time. The results are illustrated with numerical examples for life annuities with discrete payments, and Asian options.

show abstract

“…Dynamic hedging (Hardy 2003) is a popular risk management approach for variable annuities and is adopted by many insurance companies. Since VA contracts embedding guarantees are relatively complex, the calculation of their fair market values cannot be done in closed form except for special cases Shiu 2003, Feng andVolkmer 2012). In practice, insurance companies rely on the Monte Carlo simulation method to determine the fair market values of VA contracts.…”

Section: Introductionmentioning

confidence: 99%

Application of metamodeling to the valuation of large variable annuity portfolios

Gan¹

2015

2015 Winter Simulation Conference (WSC)

View full text Add to dashboard Cite

Variable annuities are long-term investment vehicles that have grown rapidly in popularity recently. One major feature of variable annuities is that they contain guarantees. The guarantees embedded in variable annuities are complex and the values of the guarantees cannot be obtained from closed-form formulas. Insurance companies rely heavily on Monte Carlo simulation to calculate the fair market values of the guarantees. Valuation and risk management of a large portfolio of variable annuities are a big challenge to insurance companies because the Monte Carlo simulation model is very time consuming. In this paper, we propose to use a metamodeling approach to speed up the valuation of large portfolios of variable annuities. Our numerical results show that the metamodeling approach can reduce the runtime significantly and produce accurate approximations.

show abstract

Analytical calculation of risk measures for variable annuity guaranteed benefits

Cited by 44 publications

References 11 publications

Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Discrete sums of geometric Brownian motions, annuities and Asian options

Application of metamodeling to the valuation of large variable annuity portfolios

Contact Info

Product

Resources

About