The purpose of the article is to apply contingent claim theory to the valuation of the type of participating life insurance policies commonly sold in the UK. The article extends the techniques ...developed by Haberman, Ballotta, and Wang (2003) to allow for the default option. The default option is a feature of the design of these policies, which recognizes that the insurance company's liability is limited by the market value of the reference portfolio of assets underlying the policies that have been sold. The valuation approach is based on the classical contingent claim pricing "machinery," underpinned by Monte Carlo techniques for the computation of fair values. The article addresses in particular the issue of a fair contract design for a complex type of participating policy and analyzes in detail the feasible set of policy design parameters that would lead to a fair contract and the trade-offs between these parameters.
In this communication, we review the fair value-based accounting framework promoted by the IASB Insurance Project for the case of a life insurance company. In particular, for the case of a simple ...participating contract with minimum guarantee, we show that the fair valuation process allows for the identification of a suitable safety loading to hedge against default risk; furthermore, we show that, when compared with the “traditional” accounting system based on the construction of mathematical reserves, the fair value approach offers a sounder reporting framework in terms of covering of the liability, implementation costs, volatility of assets and liabilities and solvency capital requirements.
This paper proposes a market consistent valuation framework for variable
annuities with guaranteed minimum accumulation benefit, death benefit and
surrender benefit features. The setup is based on a ...hybrid model for the
financial market and uses time-inhomogeneous L\'evy processes as risk drivers.
Further, we allow for dependence between financial and surrender risks. Our
model leads to explicit analytical formulas for the quantities of interest, and
practical and efficient numerical procedures for the evaluation of these
formulas. We illustrate the tractability of this approach by means of a
detailed sensitivity analysis of the price of the variable annuity and its
components with respect to the model parameters. The results highlight the role
played by the surrender behaviour and the importance of its appropriate
modelling.
This chapter defines Brownian motion (BM) and presents its main properties. The main tool in stochastic calculus is It's formula, a stochastic Taylor formula. Quadratic variation (QV) is a measure of ...volatility. QV plays a major role in stochastic calculus, but is hardly ever met in standard calculus due to the fact that smooth functions have zero quadratic variation. The chapter reviews the most important SDEs in finance, such as: geometric Brownian motion (GBM); Vasicek mean‐reverting process; Cox‐Ingersoll‐Ross mean‐reverting process; constant elasticity of variance (CEV) model; stochastic volatility (SV) Heston model; and Brownian bridge (BB). Stochastic volatility models are widely used in investment banks and financial institutions. Brownian motion is a process which is continuous in time and space. Brownian motion is, in fact, Gaussian, that is, it has symmetric distribution with zero excess kurtosis.
This paper proposes a market consistent valuation framework for variable annuities with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a ...hybrid model for the financial market and uses time-inhomogeneous Lévy processes as risk drivers. Further, we allow for dependence between financial and surrender risks. Our model leads to explicit analytical formulas for the quantities of interest, and practical and efficient numerical procedures for the evaluation of these formulas. We illustrate the tractability of this approach by means of a detailed sensitivity analysis of the price of the variable annuity and its components with respect to the model parameters. The results highlight the role played by the surrender behaviour and the importance of its appropriate modelling.
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