Olivier Scaillet

Testing for equality between two copulas

We develop a test of equality between two dependence structures estimated through empirical copulas. We provide inference for independent or paired samples. The multiplier central limit theorem is used for calculating p-values of the Cram´er-von Mises test statistic. Finite sample properties are assessed with Monte Carlo experiments. We apply the testing procedure on empirical examples in finance, psychology, insurance and medicine.

Density estimation using inverse and reciprocal inverse Gaussian kernels

This paper introduces two new nonparametric estimators for probability density functions which have support on the non-negative real line. These kernel estimators are based on some inverse Gaussian (IG) and reciprocal inverse Gaussian (RIG) probability density functions used as kernels. We show that they share the same properties as those of gamma kernel estimators: they are free of boundary bias, always non-negative and achieve the optimal rate of convergence for the mean integrated squared error (MISE). Monte Carlo results concerning finite sample properties are reported for different distributions and sample sizes.

Testing for continuous-time models of the short-term interest rate

The recent financial literature has been much concerned with the short-term interest rate. Several models have been proposed and studied quite extensively. Despite the number of models, relatively little is known about their empirical comparison. A first approach of this problem is proposed in CHAN, KAROLYI, LONGSTAFF and SANDERS (1992) using a Generalized Method of Moments. In this paper, we give a general form encompassing the most usual models and derive a well specified discrete time version. Then we study the ergodic properties in order to build a consistent econometric procedure based on a maximum likelihood approach. An empirical comparison is performed using U.S. Treasury Bill data. Finally we propose an estimation strategy, based on a two-step indirect simulated method, to account for the discretization bias.

Consistency of asymmetric kernel density estimators and smoothed histograms with application to income data

We consider asymmetric kernel density estimators and smoothed histograms when the unknown probability density function f is defined on [0,+infinity). Uniform weak consistency on each compact set in [0,+infinity) is proved for these estimators when f is continuous on its support. Weak convergence in L_1 is also established. We further prove that the asymmetric kernel density estimator and the smoothed histogram converge in probability to infinity at x=0 when the density is unbounded at x=0. Monte Carlo results and an empirical study of the shape of a highly skewed income distribution based on a large micro-data set are finally provided.

On the way to recovery: A nonparametric bias free estimation of recovery rate densities

In this paper we analyse recovery rates on defaulted bonds using the Standard and Poor’s/PMD database for the years 1981-1999. Due to the specific nature of the data (observations lie within 0 and 1), we must rely on nonstandard econometric techniques. The recovery rate density is estimated nonparametrically using a beta kernel method. This method is free of boundary bias, and Monte Carlo comparison with competing nonparametric estimators show that the beta kernel density estimator is particularly well suited for density estimation on the unit interval. We challenge the usual market practice to model parametrically recovery rates using a beta distribution calibrated on the empirical mean and variance. This assumption is unable to replicate multimodal distributions or concentration of data at total recovery and total loss. We evaluate the impact of choosing the beta distribution on the estimation of credit Value-at-Risk.

Linear-Quadratic Jump-Diffusion Modeling

We aim at accommodating the existing affine jump-diffusion and quadratic models under the same roof, namely the linear-quadratic jump-diffusion (LQJD) class. We give a complete characterization of the dynamics of this class by stating explicitly the structural constraints, as well as the admissibility conditions. This allows us to carry out a specification analysis for the three-factor LQJD models. We compute the standard transform of the state vector relevant to asset pricing up to a system of ordinary differential equations. We show that the LQJD class can be embedded into the affine class using an augmented state vector. This establishes a one-to-one equivalence relationship between both classes in terms of transform analysis.

Nonparametric tests for positive quadrant dependence

We consider distributional free inference to test for positive quadrant dependence, i.e. for the probability that two variables are simultaneously small (or) large being at least as great as it would be were they dependent. Tests for its generalisation in higher dimensions, namely positive orthant dependences, are also analysed. We propose two types of testing procedures. The first procedure is based on the specification of the dependence concepts in terms of distribution functions, while the second procedure exploits the copula representation. For each specification a distance test and an intersection-union test for inequality constraints are developed depending on the definition of null and alternative hypotheses. An empirical illustration is given for US and Danish insurance claim data. Practical implications for the design of reinsurance treaties are also discussed.

Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators

We consider semiparametric asymmetric kernel density estimators when the unknown density has support on [0, ∞). We provide a unifying framework which contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature. This framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification. We further develop a specification test to determine if a density belongs to a particular parametric family. The proposed estimators outperform rival non- and semiparametric estimators in finite samples and are simple to implement. We provide applications to loss data from a large Swiss health insurer and Brazilian income data.

Pricing American Options under Stochastic Volatility and Stochastic Interest Rates

We introduce a new analytical approach to price American options. Using an explicit and intuitive proxy for the exercise rule, we derive tractable pricing formulas using a short-maturity asymptotic expansion. Depending on model parameters, this method can accurately price options with time-to-maturity up to several years. The main advantage of our approach over existing methods lies in its straightforward extension to models with stochastic volatility and stochastic interest rates. We exploit this advantage by providing an analysis of the impact of volatility mean-reversion, volatility of volatility, and correlations on the American put price.

Path Dependent Options on Yields in the Affine Term Structure Model

Abstract. We give analytical pricing formulae for path dependent options on yields in the framework of the affine term structure model. More precisely, European call options such as the arithmetic average call, the call on maximum and the lookback call are examined. For the two last options approximate formulae using the law of hitting times of an Ornstein-Uhlenbeck process are proposed. Numerical implementation is also briefly discussed and results are given in the case of the arithmetic average option.