Olivier Renault

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.

An Autoregressive Conditional Binomial Option Pricing Model

This paper offers an option pricing framework grounded in econometric microstructure modelling. We consider a model where stock price dynamics follow a pure jump process with constant jump size similar to a binomial setting with random time steps. Jump arrival times are described as an Autoregressive Conditional Duration (ACD) process while conditional probabilities of up-moves and down-moves are given by the logistic transformation of an autoregressive prices. We derive no-arbitrage pricing formulae under the minimal martingale measure and illustrate the use of our Autoregressive Conditional Binomial (ACB) option pricing model on intraday IBM stock date.

An Empirical Investigation in Credit Spread Indices

We study the dynamics of the spread between U.S. corporate and Treasury bonds. We focus on Aaa and Baa corporate yield indices and estimate nonparametrically the dynamics of the spreads assuming that they follow a univariate diffusion process. Using techniques developed for interest rate processes we try to infer from the data what acceptable process can be used to model aggregate credit spreads for option pricing or risk management purposes. We find that there is significant evidence of mean reversion especially for higher rated spreads and that the volatility of Aaa spreads exhibit a U-shape while the volatility of Baa spreads is monotonically increasing in the level of spreads. Based on these observations and on the evidence of jumps in the series, we propose a new model for credit spread indices (an Ornstein-Uhlenbeck with jumps) and estimate it by maximum likelihood.

Business and Financial Indicators: What are the Determinants of Default Probability Changes?

This paper investigates some common determinants of default probability changes of individual firms using Standard & Poors ratings database. We analyze and quantify the responses of hazard rates to changes in various economic variables, namely financial markets, business cycle and credit indicators, and examine their persistency. First, we show that including non-financial information largely improves the poor explanatory power of financialbased factor models. More importantly, in comparison with market factors, business and credit factors become dominant as the issuer quality decreases. Second, we highlight the benefits of past information. Our results prove that both past shocks and subsequent economic trends are of prime importance in explaining probability changes. To draw these conclusions, we introduce a semi-parametric framework accommodating the continuous nature of probability changes and ageing effects. It allows us to recover default probabilities over any desired time horizon.