The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Quantifying credit portfolio losses under multi-factor models

In this work, we investigate the challenging problem of estimating credit risk measures of portfolios with exposure concentration under the multi-factor Gaussian and multi-factor t-copula models. It is well-known that Monte Carlo (MC) methods are highly demanding from the computational point of view in the aforementioned situations. We present efficient and robust numerical techniques based on the Haar wavelets theory for recovering the cumulative distribution function of the loss variable from its characteristic function. To the best of our knowledge, this is the first time that multi-factor t-copula models are considered outside the MC framework. The analysis of the approximation error and the results obtained in the numerical experiments section show a reliable and useful machinery for credit risk capital measurement purposes in line with Pillar II of the Basel Accords

Quantifying credit portfolio losses under multi-factor models

In this work, we investigate the challenging problem of estimating credit risk measures of portfolios with exposure concentration under the multi-factor Gaussian and multi-factor t-copula models. It is well-known that Monte Carlo (MC) methods are highly demanding from the computational point of view in the aforementioned situations. We present efficient and robust numerical techniques based on the Haar wavelets theory for recovering the cumulative distribution function of the loss variable from its characteristic function. To the best of our knowledge, this is the first time that multi-factor t-copula models are considered outside the MC framework. The analysis of the approximation error and the results obtained in the numerical experiments section show a reliable and useful machinery for credit risk capital measurement purposes in line with Pillar II of the Basel Accords

Polynomial models in finance

This thesis presents new flexible dynamic stochastic models for the evolution of market prices and new methods for the valuation of derivatives. These models and methods build on the recently characterized class of polynomial jump-diffusion processes for which the conditional moments are analytic. The first half of this thesis is concerned with modelling the fluctuations in the volatility of stock prices, and with the valuation of options on the stock. A new stochastic volatility model for which the squared volatility follows a Jacobi process is presented in the first chapter. The stock price volatility is allowed to continuously fluctuate between a lower and an upper bound, and option prices have closed-form series representations when their payoff functions depend on the stock price at finitely many dates. Truncating these series at some finite order entails accurate option price approximations. This method builds on the series expansion of the ratio between the log price density and an auxiliary density, with respect to an orthonormal basis of polynomials in a weighted Lebesgue space. When the payoff functions can be similarly expanded, the method is particularly efficient computationally. In the second chapter, more flexible choices of weighted spaces are studied in order to obtain new series representations for option prices with faster convergence rates. The option price approximation method can then be applied to various stochastic volatility models. The second half of this thesis is concerned with modelling the default times of firms, and with the pricing of credit risk securities. A new class of credit risk models in which the firm default probability is linear in the factors is presented in the third chapter. The prices of defaultable bonds and credit default swaps have explicit linear-rational expressions in the factors. A polynomial model with compact support and bounded default intensities is developed. This property is exploited to approximate credit derivatives prices by interpolating their payoff functions with polynomials. In the fourth chapter, the joint term structure of default probabilities is flexibly modelled using factor copulas. A generic static framework is developed in which the prices of high dimensional and complex credit securities can be efficiently and exactly computed. Dynamic credit risk models with significant default dependence can in turn be constructed by combining polynomial factor copulas and linear credit risk models

A comparison of the methods used to determine the portfolio credit loss distribution and the pricing of synthetic CDO tranches

This work aims to provide an introduction to the methodologies used for determining the loss distribution of a heterogeneous portfolio of credit default swaps. For all the methods considered, the theory and the algorithms are presented and their computational efficiency and accuracy investigated. The loss distribution is then used to value synthetic CDO tranches. The multi-step and the default-time approach are the primary methods considered. For the multi-step approach, three approaches in the literature to the computationally demanding task of obtaining the default thresholds are compared. A synthetic CDO tranche was then evaluated and it was found that the choice of method used to determine the default thresholds is significant. The default-time approach was found to be computationally more efficient than the multi-step approach though with significant differences in the tail region of the loss distribution. Both these approaches rely on Monte Carlo simulation, which is computationally inefficient. Semi-analytic approximations to the default-time approach are considered. These are the numerical inversion of the characteristic function, exact recursion and the compound Poisson approximation. A unique presentation that aids in the understanding and implementation of the numerical inversion of the characteristic function is given. The approximation techniques though computationally more efficient than Monte Carlo, are not as accurate

Systemic risk measures: the simpler the better.

We compute six different sets of systemic risk measures for a sample of the 20 biggest European and 13 biggest US banks from January 2004 to November 2009. The six measures are based on i) Principal components of the bank’s Credit Default Swaps (CDSs), ii) Interbank interest rate spreads, iii) Structural credit risk models, iv) Collateralized Debt Obligations (CDOs) indexes and their tranches, v) Multivariate densities computed from CDS spreads and vi) Co-Risk measures. We then rank the measures using three different criteria: i) Causality tests, ii) Price discovery tests and iii) their correlation with an index of systemic events. For the European and US markets, the best indicators are the first Principal Component of the single-name CDSs and the LIBOR-OIS or LIBOR-TBILL spreads, respectively, whereas the least reliable indicators are the Co-Risk measures and the systemic spreads extracted from the CDO indexes and their tranches.Systemic risk; CDS; Libor spreads; CoVaR;

Affine processes on positive semidefinite matrices

This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.Comment: Published in at http://dx.doi.org/10.1214/10-AAP710 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Analyse von Ausfallrisiken

This thesis comprises three essays on the pricing of default risk. It analyzes latest developments in this field empirically and theoretically delivering deeper insights into the questions of how firms default and how default risk is priced in interest rate and equity instruments