Valuation Of Guarantees Research Articles

Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model

This article investigates the valuation of annuity guarantees under a regime-switching model when the dynamics of the underlying stock price follow a self-exciting switching jump-diffusion process. In this framework, we add a jump component to a regime-switching geometric Brownian for large shocks on the stock price. The intensity of shock arrivals is a Hawkes process modulated by a continuous time hidden Markov chain with a finite number of states. The interest rate used for discounting is stochastic and correlated to the stock market. In an incomplete market, we define an equivalent martingale measure to price a variable annuity contract that guarantees a minimum living or death benefit. Under this equivalent martingale measure, we propose closed-form approximation formulas using the inverse Fourier transform technique. A numerical implementation highlights the impact of self-exciting jumps and economic regimes on the valuation of guarantees.

Superiority of Monte Carlo simulation in valuing real options within public–private partnerships

Monte Carlo simulation and geometric Brownian motion are the two methods employed for valuation of guarantees in public–private partnership projects. In this article we argue that any guarantee within the projects that exhibit non-constant growth rate of demand should always be evaluated using Monte Carlo simulation. Namely, we find that in a typical infrastructure project geometric Brownian motion underestimates cash flows and overestimates the value of the granted guarantee of public partner. In economic terms, our results imply more implemented projects, which are urgently needed, and thus a higher impact on economic well-being through better risks sharing mechanisms and project risk management. We also contribute to the literature by arguing that proper capture of the growth rate is much more important than the proper capture of volatility, already reported in the field.

Valuation of large variable annuity portfolios under nested simulation: A functional data approach

A variable annuity (VA) is equity-linked annuity product that has rapidly grown in popularity around the world in recent years. Research up to date on VA largely focuses on the valuation of guarantees embedded in a single VA contract. However, methods developed for individual VA contracts based on option pricing theory cannot be extended to large VA portfolios. Insurance companies currently use nested simulation to valuate guarantees for VA portfolios but efficient valuation under nested simulation for a large VA portfolio has been a real challenge. The computation in nested simulation is highly intensive and often prohibitive. In this paper, we propose a novel approach that combines a clustering technique with a functional data analysis technique to address the issue. We create a highly non-homogeneous synthetic VA portfolio of 100,000 contracts and use it to estimate the dollar Delta of the portfolio at each time step of outer loop scenarios under the nested simulation framework over a period of 25 years. Our test results show that the proposed approach performs well in terms of accuracy and efficiency.

Valuation of Large Variable Annuity Portfolios Under Nested Simulations: A Functional Data Approach

Variable annuities are equity-linked annuity products that have rapidly grown in popularity around the world in recent years. Research up to date on variable annuity largely focuses on the valuation of guarantees embedded in a single variable annuity contract. However, methods developed for individual VA contracts based on option pricing theory cannot be extended to large variable annuity portfolios. Insurance companies currently use nested simulations to value guarantees for variable annuity portfolios but efficient valuation under nested simulations for a very large variable annuity portfolio has been a real challenge. The computation in nested simulations are highly intensive and often prohibitive. In this paper, we propose a novel method that combines a clustering technique with a functional data analysis technique to address this issue. We create a highly non-homogeneous synthetic variable annuity portfolio of 100,000 contracts and use it to estimate the dollar Deltas of the portfolio at each time step of outer loop scenarios under the nested simulation framework over a period of 30 years. Our test results show that the proposed method performs well in terms of accuracy and efficiency.

Application of data clustering and machine learning in variable annuity valuation

The valuation of variable annuity guarantees has been studied extensively in the past four decades. However, almost all the studies focus on the valuation of guarantees embedded in a single variable annuity contract. How to efficiently price the guarantees for a large portfolio of variable annuity contracts has not received enough attention. This paper fills the gap by introducing a novel method based on data clustering and machine learning to price the guarantees for a large portfolio of variable annuity contracts. Our test results show that this method performs very well in terms of accuracy and speed.

Application of Data Clustering and Machine Learning in Variable Annuity Valuation

The valuation of variable annuity guarantees has been studied extensively in the past four decades. However, almost all the studies focus on the valuation of guarantees embedded in a single variable annuity contract. How to efficiently price the guarantees for a large portfolio of variable annuity contracts has not received enough attention. This paper fills the gap by introducing a novel method based on data clustering and machine learning to price the guarantees for a large portfolio of variable annuity contracts. Our test results show that this method performs very well in terms of accuracy and speed.

Modelling and Valuation of Guarantees in With-Profit and Unitised With Profit Life Insurance Contracts

The purpose of this paper is to develop suitable valuation techniques for the broad category of participating life insurance policies. The nature of the liability implied by these contracts allows treating them as options written on the reference portfolio backing the policy. Consequently, our valuation approach is based on the classical contingent claim theory; in particular, Monte Carlo techniques are used to compute the values of the so called 'policy reserve', that is the guaranteed payoff and the reversionary bonus, and the terminal bonus. The numerical results obtained are used to investigate the sensitivity of the policy reserve and the terminal bonus to changes in the model parameters. The paper also addresses the issue of a fair contract design for with-profit life insurance policies. Bearing in mind that the parameters characterizing the financial market are in general not under the control of the life insurance offce, the implemented valuation procedure is used to determine the feasible set of design parameters that would lead to a fair contract.