Pricing and hedging GMWB in the Heston and in the Black–Scholes with stochastic interest rate models

Goudenège, Ludovic; Molent, Andrea; Zanette, Antonino

doi:10.1007/s10287-018-0304-2

Cited by 14 publications

(21 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this Section we present the GMWB contract and the numerical method. Following Chen and Forsyth [4] and Goudenège et al [13], we focus on a simplified version of the contract.…”

Section: The Gmwb Contract and Its Appraisalmentioning

confidence: 99%

“…The parameters which identify the Heston Hull-White model are the initial volatility v 0 , the rate of mean reversion k v , the long run variance θ v , the volatility of volatility ω v , the correlation ρ v , the initial interest rate r 0 , the rate of mean reversion k r , the volatility of the interest rate ω r and the correlation ρ r . In order to compute the fair price and the Greeks of a GMWB contract in the Heston Hull-White model, we apply the HPDE method, introduced by Briani et al [3] for option pricing and successfully employed in the framework of VAs by Goudenège et al [12,13] while considering the Heston and the Black-Scholes Hull-White models. The HPDE is a backward induction algorithm that works following a finite difference PDE method in the direction of the share process and following a tree method in the direction of the volatility and of the interest rate.…”

Section: The Stochastic Model For the Underlying And The Gmwb Appraisalmentioning

confidence: 99%

“…Chen and Forsyth [4] and Donnelly et al [7] introduce partial derivative equations, while Costabile [5] propose pricing methods based on the use of trees. More recently, Goudenège et al apply the Hybrid Tree-PDE method in order to compute the price and the Greeks of GLWB and GMWB contracts [12,13]. However, as these techniques are more and more efficient, calculation times remain non-negligible, especially when the stochastic model considered to represent the market dynamics includes many random factors, such as stochastic volatility and stochastic interest rate.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Gaussian Process Regression for Pricing Variable Annuities with Stochastic Volatility and Interest Rate

Goudenège¹,

Molent²,

Zanette³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper we investigate price and Greeks computation of a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity (VA) when both stochastic volatility and stochastic interest rate are considered together in the Heston Hull-White model. We consider a numerical method the solves the dynamic control problem due to the computing of the optimal withdrawal. Moreover, in order to speed up the computation, we employ Gaussian Process Regression (GPR). Starting from observed prices previously computed for some known combinations of model parameters, it is possible to approximate the whole price function on a defined domain. The regression algorithm consists of algorithm training and evaluation. The first step is the most time demanding, but it needs to be performed only once, while the latter is very fast and it requires to be performed only when predicting the target function. The developed method, as well as for the calculation of prices and Greeks, can also be employed to compute the no-arbitrage fee, which is a common practice in the Variable Annuities sector. Numerical experiments show that the accuracy of the values estimated by GPR is high with very low computational cost. Finally, we stress out that the analysis is carried out for a GMWB annuity but it could be generalized to other insurance products.

show abstract

“…In this Section we present the GMWB contract and the numerical method. Following Chen and Forsyth [4] and Goudenège et al [13], we focus on a simplified version of the contract.…”

Section: The Gmwb Contract and Its Appraisalmentioning

confidence: 99%

Section: The Stochastic Model For the Underlying And The Gmwb Appraisalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Gaussian Process Regression for Pricing Variable Annuities with Stochastic Volatility and Interest Rate

Goudenège¹,

Molent²,

Zanette³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Interest rates are another relevant factor in Variable Annuities evaluation. As observed by Goudenège et al (2018), since GMWB contracts have long maturities that could last almost 25 years, the Black-Scholes model seems to be unsuitable for such a long time interval as it assumes constant interest rate and volatility. Several authors have investigated the possibility of evaluating GMWB contracts while considering a stochastic interest rate.…”

Section: Introductionmentioning

confidence: 99%

“…This model has already been employed in other research works concerning GMWB Variable Annuities (e.g. Donnelly et al, 2014;Dai et al, 2015;Goudenège et al, 2018Goudenège et al, , 2019. We stress out that considering both taxation and stochastic interest rate is a challenging task because of the computational effort required to consider many factors together.…”

Section: Introductionmentioning

confidence: 99%

Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model

Molent

2020

ASTIN Bull.

Self Cite

View full text Add to dashboard Cite

Modeling taxation of Variable Annuities has been frequently neglected, but accounting for it can significantly improve the explanation of the withdrawal dynamics and lead to a better modeling of the financial cost of these insurance products. The importance of including a model for taxation has first been observed by Moenig and Bauer (2016) while considering a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity. In particular, they consider the simple Black–Scholes dynamics to describe the underlying security. Nevertheless, GMWB are long-term products, and thus accounting for stochastic interest rate has relevant effects on both the financial evaluation and the policyholder behavior, as observed by Goudenège et al. (2018). In this paper, we investigate the outcomes of these two elements together on GMWB evaluation. To this aim, we develop a numerical framework which allows one to efficiently compute the fair value of a policy. Numerical results show that accounting for both taxation and stochastic interest rate has a determinant impact on the withdrawal strategy and on the cost of GMWB contracts. In addition, it can explain why these products are so popular with people looking for a protected form of investment for retirement.

show abstract

A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate

Lu,

Dang

2023

Numerical Methods Partial

View full text Add to dashboard Cite

We develop an efficient pricing approach for guaranteed minimum withdrawal benefits (GMWBs) with continuous withdrawals under a realistic modeling setting with jump‐diffusions and stochastic interest rate. Utilizing an impulse stochastic control framework, we formulate the no‐arbitrage GMWB pricing problem as a time‐dependent Hamilton‐Jacobi‐Bellman (HJB) Quasi‐Variational Inequality (QVI) having three spatial dimensions with cross derivative terms. Through a novel numerical approach built upon a combination of a semi‐Lagrangian method and the Green's function of an associated linear partial integro‐differential equation, we develop an ‐monotone Fourier pricing method, where is a monotonicity tolerance. Together with a provable strong comparison result for the HJB‐QVI, we mathematically demonstrate convergence of the proposed scheme to the viscosity solution of the HJB‐QVI as . We present a comprehensive study of the impact of simultaneously considering jumps in the subaccount process and stochastic interest rate on the no‐arbitrage prices and fair insurance fees of GMWBs, as well as on the holder's optimal withdrawal behaviors.

show abstract

Pricing and hedging GMWB in the Heston and in the Black–Scholes with stochastic interest rate models

Cited by 14 publications

References 28 publications

Gaussian Process Regression for Pricing Variable Annuities with Stochastic Volatility and Interest Rate

Gaussian Process Regression for Pricing Variable Annuities with Stochastic Volatility and Interest Rate

Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model

A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate

Contact Info

Product

Resources

About