Modelling bonds and credit default swaps using a structural model with contagion

This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters

A Non-Gaussian Option Pricing Model with Skew

Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to include volatility-stock correlations consistent with the leverage effect. A generalized Black-Scholes partial differential equation for this model is obtained, together with closed-form approximate solutions for the fair price of a European call option. In certain limits, the standard Black-Scholes model is recovered, as is the Constant Elasticity of Variance (CEV) model of Cox and Ross. Alternative methods of solution to that model are thereby also discussed. The model parameters are partially fit from empirical observations of the distribution of the underlying. The option pricing model then predicts European call prices which fit well to empirical market data over several maturities.Comment: 37 pages, 11 ps figures, minor changes, typos corrected, to appear in Quantitative Financ

Large Vector Auto Regressions

One popular approach for nonstructural economic and financial forecasting is to include a large number of economic and financial variables, which has been shown to lead to significant improvements for forecasting, for example, by the dynamic factor models. A challenging issue is to determine which variables and (their) lags are relevant, especially when there is a mixture of serial correlation (temporal dynamics), high dimensional (spatial) dependence structure and moderate sample size (relative to dimensionality and lags). To this end, an \textit{integrated} solution that addresses these three challenges simultaneously is appealing. We study the large vector auto regressions here with three types of estimates. We treat each variable's own lags different from other variables' lags, distinguish various lags over time, and is able to select the variables and lags simultaneously. We first show the consequences of using Lasso type estimate directly for time series without considering the temporal dependence. In contrast, our proposed method can still produce an estimate as efficient as an \textit{oracle} under such scenarios. The tuning parameters are chosen via a data driven "rolling scheme" method to optimize the forecasting performance. A macroeconomic and financial forecasting problem is considered to illustrate its superiority over existing estimators

A Multivariate Jump-Driven Financial Asset Model

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behavior of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a sto- chastic time-change technique and provide the details for a Gamma change. The main feature of the model is the fact that - opposite to other, non jointly Gaussian settings - its risk neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.Lévy processes, multivariate asset modelling, copulas, risk neutral dependence.

The Crux of the Matter: Ratings and Credit Risk Valuation at the heart of the Structured Finance Crisis

The 2007/2008 global credit crisis was born out of opaque securitization transactions. Introducing structured products risk estimation techniques shows how the most basic investment analysis could not be done without detailed and updated knowledge on the assets of the pool. Access to such details was crucial for investors to perform an autonomous valuation, the lack of which led to a pervading acceptance of ratings at face value. The crisis brought numerous delusions to naïve users of these privately issued opinions. Coming back to the central role that investor played during the previous speculative episode and introducing a theoretical discussion on the dynamics of market finance, it is shown that trusting market discipline and due diligence was bound to end up being misguiding. Given that unprecedented rating volatility brought a share of the blame game to rating firms, strategies that would aim at securing an informed use of ratings are finally outlined.financial crisis, credit risk, rating agencies

Can feedback from the jumbo-CD market improve bank surveillance?

We examine the value of jumbo certificate-of-deposit (CD) signals in bank surveillance. To do so, we first construct proxies for default premiums and deposit runoffs and then rank banks based on these risk proxies. Next, we rank banks based on the output of a logit model typical of the econometric models used in off-site surveillance. Finally, we compare jumbo-CD rankings and surveillance-model rankings as tools for predicting financial distress. Our comparisons include eight out-of-sample test windows during the 1990s. We find that rankings obtained from jumbo-CD data would not have improved on rankings obtained from conventional surveillance tools. More importantly, we find that jumbo-CD rankings would not have improved materially over random rankings of the sample banks. These findings validate current surveillance practices and, when viewed with other recent empirical tests, raise questions about the value of market signals in bank surveillance.Finance ; Banks and banking ; Bank supervision

Estimating the Structural Credit Risk Model When Equity Prices Are Contaminated by Trading Noises

The transformed-data maximum likelihood estimation (MLE) method for struc- tural credit risk models developed by Duan (1994) is extended to account for the fact that observed equity prices may have been contaminated by trading noises. With the presence of trading noises, the likelihood function based on the observed equity prices can only be evaluated via some nonlinear filtering scheme. We devise a particle filtering algorithm that is practical for conducting the MLE estimation of the structural credit risk model of Merton (1974). We implement the method on the Dow Jones 30 firms and on 100 randomly selected firms, and find that ignoring trading noises can lead to significantly over-estimating the firm's asset volatility. A simulation study is then conducted to ascertain the performance of the estimation method.Particle filtering, maximum likelihood, option pricing, credit risk, simulation

PERFORMANCE MEASUREMENT AND EVALUATION

This chapter discusses methods and techniques for measuring and evaluating performance for the purpose of controlling the investment process. However, many of the methods discussed in this chapter are also used in communicating investment performance between the investment management company and it’s (potential) customers. Therefore, performance measurements also play an important role in the competition between investments management companies. Substantial evidence from the net sales of mutual funds shows that investors buy mutual funds with good past performance records although they fail to sell funds with bad past performance.Performance measurement; risk-adjusted performance