Olivier Le Courtois

A New Procedure for Pricing Parisian Options

In this article, we propose a new method to price numerically Parisian options by inversion of Laplace transform. We compare this method to other more traditional approaches (Monte-Carlo simulations and partial differential equation solving). We show that this method converges more rapidly and yields quasi-instantaneous answers to the valuation and hedging problem at stake.

Development and Pricing of a New Participating Contract

Abstract This article designs and prices a new type of participating life insurance contract. Participating contracts are popular in the United States and European countries. They present many different covenants and depend on national regulations. In the present article we design a new type of participating contract very similar to the one considered in other studies, but with the guaranteed rate matching the return of a government bond. We prove that this new type of contract can be valued in closed form when interest rates are stochastic and when the company can default.

The Computation of Risk Budgets Under the Lévy Process Assumption

Cet article presente le calcul de la Value-at-Risk et d’autres indicateurs de risque lorsque des processus de Levy sont employes pour modeliser les dynamiques de rentabilites d’actifs. Nous proposons tout d’abord une nouvelle presentation des processus Variance Gamma avec derive : nous les reconstruisons de maniere originale en partant de la distribution exponentielle. Nous obtenons ensuite des formules generales par transformee de Fourier qui permettent de calculer la VaR rapidement et efficacement, ainsi que d’autres indicateurs de risque typiques comme la Tail Conditional Expectation (TCE). Sur la base d’une de ces formules, nous conduisons une etude de la structure par terme de la VaR et fournissons une discussion des cadres reglementaires de Basle 2 et de Solvency II.

An intensity model for credit risk with switching Lévy processes

We develop a switching regime version of the intensity model for credit risk pricing. The default event is specified by a Poisson process whose intensity is modeled by a switching Levy process. This model presents several interesting features. First, as Levy processes encompass numerous jump processes, our model can duplicate the sudden jumps observed in credit spreads. Also, due to the presence of jumps, probabilities do not vanish at very short maturities, contrary to models based on Brownian dynamics. Furthermore, as the parameters of the Levy process are modulated by a hidden Markov chain, our approach is well suited to model changes of volatility trends in credit spreads, related to modifications of unobservable economic factors.

Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a Least-Squares Monte-Carlo Approach

The calculation of Net Asset Values and Solvency Capital Requirements in a Solvency 2 context–and the derivation of sensitivity analyses with respect to the main financial and actuarial risk drivers–is a complex procedure at the level of a real company, where it is illusory to be able to rely on closed-form formulas. The most general approach to performing these computations is that of nested simulations. However, this method is also hardly realistic because of its huge computation resources demand. The least-squares Monte Carlo method has recently been suggested as a way to overcome these difficulties. The present paper confirms that using this method is indeed relevant for Solvency 2 computations at the level of a company.

Decreasing Downside Risk Aversion and Background Risk

In this paper, we show that risk vulnerability can be associated with the concept of downside risk aversion (DRA) and an assumption about its behavior, namely that it is decreasing in wealth. Specifically, decreasing downside risk aversion in the Arrow–Pratt and Ross senses are respectively necessary and sufficient for a zero-mean background risk to raise the aversion to other independent risks.

Portfolio Optimisation with Jumps: Illustration with a Pension Accumulation Scheme

In this paper, we address portfolio optimisation when stock prices follow general Levy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Levy processes. We apply this procedure to both the Variance Gamma process and a Levy process whose arrival rate of jumps exponentially decreases with size. We show through a numerical example that when jumps, and therefore asymmetry and leptokurtosis, are suitably taken into account, then the optimal portfolio share of the risky asset is around half that obtained in the Gaussian framework.

Health and Portfolio Choices: A Diffidence Approach

The effect of health status on portfolio decisions has been extensively studied from an empirical viewpoint. In this paper, we propose a theoretical model of individuals’ choice of financial assets under bivariate utility functions depending on wealth and health. Our approach makes an extensive use of the diffidence theorem. We establish the conditions under which the share of wealth held in risky assets falls as: (1) individuals’ health status deteriorates and; (2) individuals’ health status becomes risky. These conditions are shown to be related to the behavior of the intensities of correlation aversion and of cross prudence as wealth increases.

Protection of a Company Issuing a Certain Class of Participating Policies in a Complete Market Framework

Abstract In this article we examine to what extent policyholders buying a certain class of participating contracts (in which they are entitled to receive dividends from the insurer) can be described as standard bondholders. Our analysis extends the ideas of Biihlmann and sequences the fundamental advances of Merton, Longstaff and Schwartz, and Briys and de Varenne. In particular, we develop a setup where these participating policies are comparable to hybrid bonds but not to standard risky bonds (as done in most papers dealing with the pricing of participating contracts). In this mixed framework, policyholders are only partly protected against default consequences. Continuous and discrete protections are also studied in an early default Black and Cox-type setting. A comparative analysis of the impact of various protection schemes on ruin probabilities and severities of a life insurance company that sells only this class of contracts concludes this work.

Credit risk and solvency capital requirements

AbstractCredit risk permeates the assets of most insurance companies. This article develops a framework for computing credit capital requirements under the constant position paradigm and taking into account recovery rates. Although this framework was originally derived under the Solvency 2 regulation, it also provides concepts that can be useful under other international regulations. After a brief survey of the existing technology on rating transitions and default probabilities, the paper provides new results on risk premium adjustment factors. Then, three different procedures for reconstructing constant position market-consistent histories of credit portfolios from quoted Merrill Lynch indices are given. The reconstructed historical credit values are modeled via mixed empirical-Generalized Pareto Distribution (GPD) dynamics and a detailed parameter estimation is performed. Several validations of the estimation are also provided. Finally, credit Solvency Capital Requirements are computed and an analysis of the results per rating class is given.