Abstract:

Risk management, even if flawlessly executed, does not guarantee that big losses will not occur. Big losses can occur because of business decisions and bad luck. Even so, the events of 2007 and 2008 have highlighted serious deficiencies in risk models. For some firms, risk models failed because of known unknowns. These include model risk, liquidity risk, and counterparty risk. In 2008, risk models largely failed due to unknown unknowns, which include regulatory and structural changes in capital markets. Risk management systems need to be improved and place a greater emphasis on stress tests and scenario analysis. In practice, this can only be based on position-based risk measures that are the basis for modern risk measurement architecture. Overall, this crisis has reinforced the importance of risk management.

Abstract:

Revisions to the Basel II market risk framework, finalized in July 2009, require that banks develop a methodology for calculating a new incremental risk charge (IRC). The IRC is defined to capture credit default and migration risks that are incremental to the risks captured by the market VaR calculation of the bank's trading book positions on unsecuritised credit products. IRC is based on the assumption of a constant level of risk over the one-year capital horizon. This assumption implies that exposures are rolled-over when they mature and positions whose credit characteristics have improved or deteriorated over the liquidity horizon are replaced with positions that have credit characteristics equivalent to those at the start of the liquidity horizon.

In this talk, we discuss the basic principles behind the IRC requirements. We present a robust methodology to compute IRC and discuss various modelling choices, which arise in practical implementations. The methodology combines the repeated application of single-step credit portfolio models with advanced convolution methods to model the constant level of risk principle. In contrast to a brute-force dynamic multi-step simulation, the methodology is transparent and does not require heavy parameterization or operational assumptions. It further leverages existing credit portfolio tools, already used by banks. We present a practical example and further discuss how the approach can be used as a comprehensive stress testing tool, which allows us to understand the components of credit risk, the major risk contributors, and the capital benefits from long-short positions and diversification. Finally, we discuss the application to portfolios which include tranches and baskets (correlation trading).

Abstract:

Standard portfolio models for credit risk capital estimation introduce randomness via systematic and specific risk factors. A systematic risk factor influences the credit worthiness of many borrowers. For example, future developments in an industry branch. The models usually assign the same probability for an improvement as for a deterioration of current conditions. In mathematical language this translates into a symmetric probability distribution having an expected value that implies no changes in the economic framework.

What if one expects quite negative/positive developments in a certain industry branch or country? This question is important for portfolio management. The goal is to estimate changes in risk measures like expected loss or risk capital as a consequence of (stress) scenarios representing anticipated trends in systematic risk factors. In the context of a multi-factor model, the proposed approach can also incorporate forecasts for macro-economic variables in the scenario design. Resulting changes in dependence measures (like e.g. correlations) are taken into account.

Abstract:

In light of the recent turmoil in credit markets, it has been argued that investors placed exaggerated emphasis on expected losses as measured by credit ratings. However, selecting an investment based solely on a default probability and a yield can be misleading. Two firms with the same default probability can justify very different yield spreads as a result of their systematic risk. For the same reason, two firms with the same spread can have very different default probabilities. To properly assess an investment in credit sensitive fixed income securities, it is necessary to separately measure the expected loss and risk premium components of spreads.

In this talk I will address risk premia in both corporate bond and credit derivative markets, drawing on several recent papers. In the first part, I show that risk premia in equity and bond markets may superficially appear difficult to reconcile, sometimes, counter intuitively, moving in opposite directions. I argue that in fact they behave as theory predicts when adjusting for movements in leverage, volatility and bond contractuals. The risk premium metric I develop helps improve the explanatory power of credit spread regressions, in particular, usefully, for high grade bonds.

In a second step I show that systematic risk impacts default swaps and stock options through the same channel. Equity puts and credit default swaps are economically similar contracts - they insure against adverse shocks to a firm's value. I find that puts and credit default swaps for firms with greater systematic risk are more expensive all else equal. They are both similarly influenced by the proportion of systematic volatility for a firm's stock. Traditional option and credit risk models predict that the contemporaneous relationship between a derivative's price and the underlying is independent of systematic risk. Our findings contradict this.

Abstract:

The Basle Capital Accord issued from the Basle Committee on Banking supervision has imposed a multiplier between 3 and 4 on the bank's internal 10-day Value-at-Risk calculated for market risk exposure. This ad hoc factor has not been fully explained and is poorly justified by arguing that the standard classical models of stock price dynamics do not adequately capture actual market risks. In this paper, we tackle this issue by adopting a probabilistic framework based on Lévy processes with both finite and infinite activity, but with finite variation. We accommodate bank regulator concerns with several types of Lévy processes which allow to exhibit a factor 3 between Brownian-VaR and Lévy-VaR, and we show that the Lévy-VaR is more consistent with the reality of market risk. On the technical side our paper provides a new general Fourier formula that allows to compute VaR quickly and efficiently as soon as the characteristic function of the process under study is known, so for a wide class of stochastic processes. Our study can be of interest for the computation of Solvency Capital Requirements in the context of the preparation of Solvency 2.

Resumen:

Consideraremos un modelo HJM general para describir la evolución de las curvas de descuento y estimación (en una y varias monedas), bajo la probabilidad de riesgo neutro asociada a la curva de factores de descuento de la economía doméstica. Encontraremos condiciones sobre el término de deriva de las ecuaciones que permitan al modelo ser consistente con la práctica de mercado para construir las curvas.