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Dive into the research topics where Carole Bernard is active.

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Featured researches published by Carole Bernard.


Journal of Risk and Insurance | 2015

Value-at-Risk Bounds with Variance Constraints

Carole Bernard; Ludger Rüschendorf; Steven Vanduffel

Recent literature deals with bounds on the Value-at-Risk (VaR) of risky portfolios when only the marginal distributions of the components are known. In this paper we study Value-at-Risk bounds when the variance of the portfolio sum is also known, a situation that is of considerable interest in risk management.We provide easy to calculate Value-at-Risk bounds with and without variance constraint and show that the improvement due to the variance constraint can be quite substantial. We discuss when the bounds are sharp (attainable) and point out the close connections between the study of VaR bounds and convex ordering of aggregate risk. This connection leads to the construction of a new practical algorithm, called Extended Rearrangement Algorithm (ERA), that allows to approximate sharp VaR bounds. We test the stability and the quality of the algorithm in several numerical examples.We apply the results to the case of credit risk portfolio models and verify that adding the variance constraint gives rise to significantly tighter bounds in all situations of interest. However, model risk remains a concern and we criticize regulatory frameworks that allow financial institutions to use internal models for computing the portfolio VaR at high confidence levels (e.g., 99.5%) as the basis for setting capital requirements.


Journal of Banking and Finance | 2015

A New Approach to Assessing Model Risk in High Dimensions

Carole Bernard; Steven Vanduffel

A central problem for regulators and risk managers concerns the risk assessment of an aggregate portfolio defined as the sum of d individual dependent risks Xi. This problem is mainly a numerical issue once the joint distribution of X1,X2,…,Xd is fully specified. Unfortunately, while the marginal distributions of the risks Xi are often known, their interaction (dependence) is usually either unknown or only partially known, implying that any risk assessment of the portfolio is subject to model uncertainty.


Journal of Derivatives | 2011

Locally Capped Investment Products and the RetailInvestor

Carole Bernard; Phelim P. Boyle; William Gornall

This article explores a different type of structured retail product with a payoff that is heavily path dependent. Formally, these securities are “locally capped and globally floored.”That is, the payoff consists of an overall minimum guaranteed return over the contract’s lifetime, plus a variable return cumulated over a series of subperiods, which is calculated as the lower of the actual percentage change in an underlying index in that period or a fixed ceiling rate. Again, this highly path-dependent payoff is difficult to value. The contracts are typically substantially overpriced relative to their fair values, by about 6.5% on average. But beyond showing that average investor returns are below what they should be, the authors offer some insight into why unsophisticated investors buy products that they don’t fully understand. They show how the issuers offer cherry-picked examples in their promotional literature in which the investor’s return from the contract is better than that from alternative strategies, without explaining how improbable the scenarios are relative to the much more likely cases in which the instrument underperforms.


Journal of Derivatives | 2005

A New Procedure for Pricing Parisian Options

Carole Bernard; Olivier Le Courtois; François Quittard-Pinon

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.


Mathematical Finance | 2015

Optimal Insurance Design Under Rank‐Dependent Expected Utility

Carole Bernard; Xue Dong He; Jia-An Yan; Xun Yu Zhou

We consider an optimal insurance design problem for an individual whose preferences are dictated by the rank-dependent expected utility (RDEU) theory with a concave utility function and an inverse-S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave.


The Finance | 2013

Explicit Representation of Cost-Efficient Strategies

Carole Bernard; Phelim P. Boyle; Steven Vanduffel

Dans cet article, nous donnons une representation explicite de la strategie de cout le plus bas (strategie de cout optimal) qui reproduit une distribution donnee. Pour toute strategie non optimale, nous proposons des instruments financiers derives qui dominent dans le sens de la dominance stochastique de premier ou de second ordre. Nous mettons en evidence les liens entre l’optimalite du cout d’une strategie et sa dependance avec le marche. Cela nous permet d’etendre la theorie en presence de contraintes sur la dependance avec le marche. Nous montrons en particulier que les strategies dependant de la trajectoire du sous-jacent ne sont pas optimales dans le cadre de Black et Scholes mais peuvent le devenir en presence de contraintes sur la dependance avec le marche financier.


Applied Mathematical Finance | 2014

Prices and Asymptotics for Discrete Variance Swaps

Carole Bernard; Zhenyu Cui

We study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull--White and Schobel--Zhu stochastic volatility models, we give simple explicit expressions (improving Broadie and Jain (2008a). The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11 (8), 761--797) in the case of the Heston model). We give conditions on parameters under which the fair strike of a discrete variance swap is higher or lower than that of the continuous variance swap. The interest rate and the correlation between the underlying price and its volatility are key elements in this analysis. We derive asymptotics for the discrete variance swaps and compare our results with those of Broadie and Jain (2008a. The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11 (8), 761--797), Jarrow et al. (2013. Discretely sampled variance and volatility swaps versus their continuous approximations. Finance and Stochastics, 17 (2), 305--324) and Keller-Ressel and Griessler (2012. Convex order of discrete, continuous and predictable quadratic variation and applications to options on variance . Working paper. Retrieved from http://arxiv.org/abs/1103.2310.


Astin Bulletin | 2014

State-Dependent Fees for Variable Annuity Guarantees

Carole Bernard; Mary R. Hardy; Anne MacKay

For variable annuity policies, management fees for the most standard guarantees are charged at a constant rate throughout the term of the policy. This creates a misalignment of risk and income - the fee income is low when the option value is high, and vice versa. In turn, this may create adverse incentives for policyholders, for example, encouraging surrenders when the options are far out-of-the-money.In this paper we explore a new fee structure for variable annuities, where the fee rates supporting the cost of guarantees depends on the moneyness of those guarantees. We derive formulas for calculating the fee rates assuming fees are paid only when the guarantees are in-the-money, or are close to being in-the-money, and we illustrate with some numerical examples. We investigate the effect of this new fee structure on the surrender decision.


Journal of Computational Finance | 2011

Pricing Timer Options

Carole Bernard; Zhenyu Cui

In this paper, we discuss a newly introduced exotic derivative called the “Timer Option”. Instead of being exercised at a fixed maturity date as a vanilla option, it has a random date of exercise linked to the accumulated variance of the underlying stock. Unlike common quadratic-variation-based derivatives, the price of a timer option generally depends on the assumptions on the underlying variance process and its correlation with the stock (unless the risk-free rate is equal to zero). In a general stochastic volatility model, we first show how the pricing of a timer call option can be reduced to a one-dimensional problem. We then propose a fast and accurate almost-exact simulation technique coupled with a powerful (model-free) control variate. Examples are derived in the Hull and White and in the Heston stochastic volatility models.


winter simulation conference | 2008

Fast simulation of equity-linked life insurance contracts with a surrender option

Carole Bernard; Christiane Lemieux

In this paper, we consider equity-linked life insurance contracts that give their holder the possibility to surrender their policy before maturity. Such contracts can be valued using simulation methods proposed for the pricing of American options, but the mortality risk must also be taken into account when pricing such contracts. Here, we use the least-squares Monte Carlo approach of Longstaff and Schwartz coupled with quasi-Monte Carlo sampling and a control variate in order to construct efficient estimators for the value of such contracts. We also show how to incorporate the mortality risk into these pricing algorithms without explicitly simulating it.

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Steven Vanduffel

Vrije Universiteit Brussel

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Zhenyu Cui

Stevens Institute of Technology

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Don McLeish

University of Waterloo

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Phelim P. Boyle

Wilfrid Laurier University

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Weidong Tian

University of North Carolina at Charlotte

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