Market value of life insurance contracts under stochastic interest rates and default risk

Bernard, Carole; Courtois, Olivier Le; Quittard-Pinon, François

doi:10.1016/j.insmatheco.2005.01.002

Cited by 59 publications

(38 citation statements)

References 19 publications

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“…In contrast, other publications allow for a stochastic evolution of interest rates. However, these articles consider point-to-point guarantees rather than cliquet style guarantees (see Barbarin and Devolder (2005), Bernard et al (2005), or Briys and de Varenne (1997)), or do not allow for the consideration of typical distribution schemes or option features embedded in many life insurance contracts (see, e.g., Miltersen and Persson (1999)). …”

Section: Introductionmentioning

confidence: 99%

Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment

Zaglauer

Bauer

2008

Insurance: Mathematics and Economics

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Over the last years the valuation of life insurance contracts using concepts from financial mathematics has become a popular research area for actuaries as well as financial economists. In particular, several methods have been proposed of how to model and price participating policies, which are characterized by an annual interest rate guarantee and some bonus distribution rules. However, despite the long terms of life insurance products, most valuation models allowing for sophisticated bonus distribution rules and the inclusion of frequently offered options assume a simple Black-Scholes setup and, in particular, deterministic or even constant interest rates.We present a framework in which participating life insurance contracts including predominant kinds of guarantees and options can be valuated and analyzed in a stochastic interest rate environment. In particular, the different option elements can be priced and analyzed separately. We use Monte Carlo and discretization methods to derive the respective values.The sensitivity of the contract and guarantee values with respect to multiple parameters is studied using the bonus distribution schemes as introduced in Bauer et al. (2006). Surprisingly, even though the value of the contract as a whole is only moderately affected by the stochasticity of the short rate of interest, the value of the different embedded options is altered considerably in comparison to the value under constant interest rates. Furthermore, using a simplified asset portfolio and empirical parameter estimations, we show that the proportion of stock within the insurer's asset portfolio substantially affects the value of the contract.

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Section: Introductionmentioning

confidence: 99%

Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment

Zaglauer

Bauer

2008

Insurance: Mathematics and Economics

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“…We shall study in this article a particular type of contract (GP-LIC) that is a generalization of the participating contract (CP-LIC) studied in Bernard, Le Courtois and Quittard-Pinon [2005]. The originality of this new contract lies in its minimum guarantee which is proportional to the value of a basket of Government bonds and hence stochastic.…”

Section: Design Of a New Contractmentioning

confidence: 99%

“…As a conclusion, there is a huge diversity of products, models and numerical methods to tackle the challenge of valuing in fair value life-insurance contracts. Bernard, Le Courtois and Quittard-Pinon [2005] priced some participating contracts under default risk and a stochastic term structure of interest rates. They model the firm assets by a standard geometric Brownian motion that is correlated with the driving factor of the interest rates.…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we construct a new type of contract that is close to the one valued in Bernard, Le Courtois and Quittard-Pinon [2005] but where the minimum guaranteed rate is of a different nature. We assume that, under this new contract, the life-insurance company guarantees a Government rate to the insured, in other words a stochastic interest rate: if and when the company defaults, the covenant guarantees a sum proportional to the value of a basket of Government Bonds -whose value is unknown at present by definition.…”

Section: Introductionmentioning

confidence: 99%

“…We shall denote these new contracts by GP-LICs, meaning "Government rate guarantee Participating Life Insurance Contracts". In a similar fashion, the more classical contracts studied by Bernard, Le Courtois and Quittard-Pinon [2005] will be denoted by CP-LICs, where it is meant "Constant rate guarantee Participating Life Insurance Contracts".…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Development and Pricing of a New Participating Contract

Bernard

Courtois

Quittard-Pinon

2006

North American Actuarial Journal

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The purpose of this article is to design and price a new type of participating life insurance contract. Participating contracts are popular in France, Denmark, the UK (where they are called with-profit contracts)... They satisfy various covenants and obey various regulations depending on the country where they are issued. The standard literature is Briys and de Varenne [1994, 1997a] and Grosen and Jørgensen [2000], to quote only a few. Bernard, Le Courtois and Quittard-Pinon [2005] study a particular type of participating contract, where an HJM term structure of interest rates is assumed and where the potential default of the issuing company is taken into account. In this paper, we design a new participating contract very similar to the one considered in the above-mentioned study, but where the guaranteed rate corresponds to the return of a portfolio of Government bonds. We show that this new type of contract can be valued in closed-form even when interest rates are stochastic and default of the company is taken into account. Also, this new type of contract is likely to reduce the default risk of the issuing companies, and is less sensitive to interest risk than more standard contracts.

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Pricing of Defaultable Securities under Stochastic Interest

Kordzakhia

Novikov

2008

Mathematical Control Theory and Finance

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We reduce the problem of pricing continuously monitored defaultable securities (namely, barrier type options, corporate debts) under a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. For the case when the interest rate is governed by linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also provide an estimation for a rate of convergence of the suggested approximation as a function of number of nodes and illustrate the results by numerical examples.

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Market value of life insurance contracts under stochastic interest rates and default risk

Cited by 59 publications

References 19 publications

Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment

Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment

Development and Pricing of a New Participating Contract

Pricing of Defaultable Securities under Stochastic Interest

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