Franck Moraux

The Predictive Power of the French Market Volatility Index: A Multi Horizons Study

The main purpose of this paper is to examine empirically the time series properties of the French Market Volatility Index (VX1). We also examine the VX1s ability to forecast future realized market volatility and finds a strong relationship. More importantly, we show how the index can be used to generate volatility forecasts over different horizons and that these forecasts are reasonably accurate predictors of future realized volatility. JEL classification codes: G14, C53, C13.

On perpetual American strangles

This article analyzes perpetual American strangles with no recourse to advanced numerical techniques. Our analytical approach rests on an analogy with asymmetric rebates of double knock-out barrier options. The optimal exercise policy is modeled by a couple of boundaries that simultaneously solve a system of two nonlinear equations. Numerical investigations then highlight salient features of American strangles and compare them with portfolios of options that may be used as proxies. Overall, results show that these latter are significantly upward biased in terms of prices and that, more dramatically, they lead the holder to exercise inappropriately.

Quadratic, Affine and Hybrid Gaussian Term Structure Models in Discrete Time: Theory and Evidence

MostofthepapersabouttheTermStructureModelling(TSM)arerelativetothefamilyof the Affine Term Structure Models (ATSM). This family of models considers a linearrelationbetweenthelogpriceofabondanditsstatesfactors. Thosemodelshavebeenfirstdeveloped by Vasicek (1977)and Cox, Ingersolland Ross (1985b). Later, Duffie&Kan(1996)clarifiedtheprimitiveassumptionsunderlyingthisframework. Sincethefirstmodels,asnotedbyDai&Singleton(1999),theATSMhaveincreasedinperformancebutarestillfacingtwomainissueswhichsuggesttolookingforanewfamilyofmodels. Thefirstissueisthattobeadmissible,anATSMneedsnonzeroconditionalcorrelationofitsstatesvariables. Thisconditionisincompatiblewithcertainstructureofthebondpricevolatilityespeciallytheoneswhichdonotallownegativenominalinterestrate. Then,oneneeds to do a trade off between those two objectives. Secondly, the form of the pricingerrorforATSMsuggeststhatnonlinearityisomittedinthisfamilyofmodels.RegardingthedevelopmentoftheATSM,theothershavebeenlessdevelopedastheQuadratic Term Structure Model (QTSM). This family, first introduce by Beaglehole& Tammey (1991) and Constantinides (1992) are now more developed in the literatureespeciallybecauseoftheissuesencounteredwiththeATSM.Furthermore,theyarenowalsoappliedtothepricingofcontingentclaims(Lieppold&Wu(2002,2003))andtothecreditriskpricing(Chen,FilipovicandPoor(2004)).ThemainmodelanalysedinthispaperisindiscretetimeandbelongstotheQTSMsfamily. It has been theoretically presented by Realdon (2006) and is derived from thecontinuousQTSMofDai-Le-Singleton(2005). Regardingthecontinuoustime,thediscretetimeallowsmoreflexibilityinthespecificationofthemarketpriceofriskasmentionbyDai-Le-Singleton(2005). ThispropertyremainsaslongasthefactorstransitiondensityremainsGaussian. Furthermore,asnotedbyRealdon(2006),whenthediscretetimestepsconvergetozero,adiscretetimemodelconvergestoacontinuousone. Then,theclassof3

Sensitivity Analysis of Credit Risk Measures in the Beta Binomial Framework

This article reconsiders the beta binomial approach for modeling default risk in a homogenous credit portfolio. It first introduces a new parameterization of the beta mixing distribution that is now a function of the common default probability and the common default correlation. It then focuses on the correlation parameter and derives closed-form expressions for sensitivities of key credit risk indicators. Results of the sensitivity and elasticity analysis show that the common default correlation impacts the credit at risk and expected shortfall quite differently. The article also examines an application on CDOs to highlight the key role of the common default correlation on the different tranches.

Valuing Callable Convertible Bonds : a reduced approach

This paper analyses the pricing of corporate callable convertible bonds. It reconciles the applicability of the reduced form approach with optimal strategies usually discussed in the structural approach. One demonstrates that some conditions causing rational voluntary conversions may be effectively neglected. The main contribution of the paper is to show that adjusted American Capped Call options well duplicate ‘classical’ optimal strategies. Numerical experiments are then conducted.

The dynamics of the term structure of interest rates: an Independent Component Analysis

The movements of a term structure of interest rates are commonly assumed to be driven by a small number of uncorrelated factors. Identified to the level, the slope, and the curvature, these factors are routinely obtained by a Principal Component Analysis (PCA) of historical bond prices (interest rates). In this paper, we focus on the Independent Component Analysis (ICA). The central assumption here is that observed multivariate time series reflect the reaction of a system to some (few) statistically independent time series. The ICA seeks to extract out independent components (ICs) as well as the mixing process. Both ICA and PCA are linear transform of the observed series. But, whereas a PCA obtains uncorrelated (principal) components, ICA provides statistically independent components. In contrast to PCA algorithms that use only second order statistical information, ICA algorithms (like JADE) exploit higher order statistical information for separating the signals. This approach is required when financial data are suspected to be not gaussian.

Pricing Credit Derivatives in Credit Classes Frameworks

Many credit management systems, based on different underlying frameworks, are now available to measure and control default and credit risks1. Homogeneous credit classes and associated transition matrix may thus be constructed within many different frameworks. For illustration, the KMV Corporation provides a transition matrix within a structural approach a la Black-Sholes-Merton (Crouhy-Galai-Mark [5]). Independentely from the underlying framework, a methodology based on credit classes may therefore be used to price any claim contingent on credit events among which the default.

Analytical pricing of european bond options within one-factor quadratic term structure models

Jamshidian developed a model for pricing bond options within a Vasicek one-factor framework, with the very useful property that it allows an option on a coupon bond to be decomposed into a set of options on the individual coupons. In the Vasicek framework, the “Jamshidian trick” produces yields to maturity on the coupons that are linear functions of the underlying state variable. But it has not been clear whether this approach could extend to more complicated interest rate processes. In this article, Leblon and Moraux show how to extend the Jamshidian technique to quadratic interest rate processes and use it to derive analytic formulas for European call options on coupon bonds. Finally, they verify that the required conditions appear to hold in the real world.

A Multifactor Self-Exciting Jump Diffusion Approach for Modelling the Clustering of Jumps in Equity Returns

This paper introduces a new jump diffusion process where the occurrence and the size of past jumps have an impact on both the instantaneous and the long term propensities of observing a jump instantaneously. Here, the intensity of jump arrival is a multifactor self-excited process whereas the jump size is a double exponential random variable. This specification capture many dynamic features of asset returns; it can for instance handle with the jump clustering effects explored by Ait-Sahalia et al. (2015). Moreover, it remains analytically tractable, as we can prove that these multifactor self-excited processes are similar to single factor processes whose kernel function is the sum of two exponential functions. We can derive various closed and semi-closed form expressions for the mean and the variance of the intensity as well as for the moment generating of log returns. We also find a class of changes of measure that preserves the dynamics of the process under the risk neutral measure. To motivate empirically the multifactor model, we calibrate the model by a peak over threshold approach and filter state variables by sequential Monte Carlo algorithm. We also investigate if self-excitation is induced by positive, negative or both jumps. So as to illustrate the applicability of our modeling for derivatives, we next evaluate European options and analyze the sensitivity of implied volatilities to parameters and factors.

What Moves Euro-Bund Futures Contracts on Eurex? Surprises!

This paper investigates the rarely studied Euro-Bund Futures contract to measure how and how long intraday prices react to a list of macroeconomic news. We emphasize the key role of information content which is the unexpected component of news or, for short, the surprise. We collect a long and recent (1997–2007) database made of hand-collected macroeconomic news releases and median forecasts as well as prices sampled at a 1-min frequency. We find that the gap between expected values and finally announced values matters for modeling returns and volatility. Moreover, the information content of U.S. macroeconomic news can influence the price dynamics significantly and more than German news. Returns and volatility behave quite differently however. While returns adjust almost instantaneously, volatility is impacted over several minutes up to 50 min long. The information content is also found to be important for the Euro Bund Futures next price, while the pure news release effect is key for volatility. Finally we provide preliminary evidences that the timing of news should not be neglected and that one should take care about the negative or positive message conveyed by the information content.