A Lévy process-based framework for the fair valuation of participating life insurance contracts

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn this communication, we develop suitable valuation techniques for a with-profit/unitized with profit life insurance policy providing interest rate guarantees, when a jump-diffusion process for the evolution of the underlying reference portfolio is used. Particular attention is given to the mispricing generated by the misspecification of a jump-diffusion process for the underlying asset as a pure diffusion process, and to which extent this mispricing affects the profitability and the solvency of the life insurance company issuing these contracts.

A general asset–liability management model for the efficient simulation of portfolios of life insurance policies

“…In [22] stocks and bonds are modelled via a coupled system of two geometric Brownian motions with different drift and volatility parameters. In [5,26] more complex jumpdiffusion processes and Markov-modulated geometric Brownian motions are used to model the behaviour of the asset base of the company. The simulation of these models is much more involved, though.…”

Pricing and Capital Requirements for With Profit Contracts: Modelling Considerations

“…More specifically, for ease of exposition, we adopt the same contract considered in Ballotta (2005); however, we consider the full specification of the policy, allowing for both leverage and terminal bonus rate (like in Ballotta et al, 2006.b). This policy is representative of a typical UK accumulating (unitized) with profit contract; however, the analysis proposed in this paper can be easily extended to any other type of participating contract, like the equity-linked policies which are so common in the North-American countries.…”

“…All these contributions use either a standard Black-Scholes (1973) framework or its extensions to incorporate stochastic interest rates; in any case, the main assumption is that market returns (and therefore the returns on the asset fund backing the insurance policy) move continuously because driven by a diffusion process. Following this observation, Ballotta (2005), and Kassberger et al (2008) extend the pricing framework to the case of a market specification based on different Lévy processes in order to allow for discontinuities in the returns, and therefore a more realistic description of the market.…”

On the Stochastic Properties of Carbon Futures Prices

“…Adding a jump component to a continuous component (leading to a mixture model) or considering a jump component only allows to fit the data better than with a continuous component only. 2 In addition, given the presence of jumps in the data, pure jump models are preferred by users as they are easier to handle for practical applications such as derivatives pricing or real-life problems such as valuation of insurance contracts (see Ballotta (2005) or Kassberg et al (2008)) or real-option valuation (Martzoukos and Trigeorgis, 2002). 3 As a simple motivating example, let us consider European energy utilities that have to plan future investments.…”