Hans Byström

Extreme Value Theory and Extremely Large Electricity Price Changes

Nord Pool, the first multinational exchange for electricity trading, has existed since January 1996. Typical characteristics of electricity prices on Nord Pool are a very high volatility and a large number of very large, or extreme, price changes. In this paper we look at hourly spot prices on NordPool and apply extreme value theory to investigate the tails of the price change distribution. We find a good fit of both the generalized extreme value distribution and the generalized Pareto distribution to AR-GARCH filtered price change series, and accurate estimates as well as forecasts of extreme quantiles are produced. Generally, our results suggest extreme value theory to be of interest to both risk managers and portfolio managers in the highly volatile electricity market.

CreditGrades and the iTraxx CDS Index Market

In the study reported, the CreditGrades model was used to calculate credit default swap spreads and the spreads were compared with empirically observed CDS spreads for eight iTraxx indices covering Europe. Theoretical and empirical spread changes were found to be significantly correlated. Also, lagged theoretical spread changes were correlated with current iTraxx spread changes. The correlations indicate a close relationship between the stock market and the CDS market and also indicate some predictive ability of the CreditGrades model. Simple trading strategies based on the autocorrelation and predictive ability of the model produced positive profits, before trading costs, when trading was within the bid–ask spread. Credit default swaps are credit derivatives that protect the buyer against losses arising from some kind of predefined credit event (delayed payment, restructuring, bankruptcy, etc.) involving a reference name (company). The price of a credit default swap depends on the probability of the underlying reference name experiencing a credit event in the future. For companies that are listed on stock exchanges, this probability is often estimated from information contained in the company’s stock price. In this study, I thus calculated the theoretical CDS spreads through a simple implementation of the stock market–based CreditGrades (CG) model. A CDS index is a portfolio of credit default swaps. One of the major families of CDS indices is the iTraxx CDS indices. In this article, I compared empirically observed CDS prices (spreads) with the CG-implied CDS prices (spreads) in the iTraxx market. I compared the spreads for eight iTraxx indices covering Europe—seven investment-grade indices and a subinvestment-grade index—with the CG-implied CDS spreads for June 2004 to March 2006. I found theoretical and empirical spread changes to be significantly correlated. I also found one-day-lagged theoretical spread changes to be correlated with current iTraxx spread changes. The significant correlations were confirmed by significant ordinary least-squares (OLS) regression parameters and indicate a fairly close relationship between the stock market and the CDS market, as well as a certain predictive ability of the CG model. Although I found no autocorrelation among the theoretical CG spread changes, I did find significant autocorrelation in the iTraxx market. One-day-lagged theoretical spread changes were also found to be significantly correlated with current iTraxx spread changes. The correlations were confirmed by significant OLS regression parameters and indicate a fairly close relationship between the stock market and the CDS market. This finding also suggests a certain predictive ability of the CG model. Based on these findings, I show how simple trading strategies (autoregression, capital structure arbitrage, and a combined strategy) can produce positive profits if the trades are within the bid–ask spread. The introduction of realistic transaction costs, however, significantly reduced the profitability of the trading strategies. Readers should keep in mind, however, that the iTraxx market is young. In the years to come, the growing maturity of the market will most likely lead to a fall in transaction costs (bid–ask spreads). In addition, the period I studied was one with few credit defaults. Both the risks and the rewards are likely to increase with any marketwide credit deterioration. Finally, trading strategies that are more advanced than the simple strategies I illustrate may produce increased after-cost profits.

Merton Unraveled: A Flexible Way of Modelling Default Risk

Popular approaches to default probability estimation are often based on the approach initially described in Merton [1974]. By explicitly modeling a firms market value, market value volatility and liability structure over time using contingent claims analysis the Merton model defines a firm as defaulted when the firms value falls below its debt. This article demonstrates how a simplified “spread sheet” version of the Merton model produces distance to default measures similar to the original Merton model. Moreover, when applied to a sample of US firms, the simplified model gives a relative ranking of firms that is essentially unchanged compared to the Merton model.

Orthogonal GARCH and Covariance Matrix Forecasting in a Stress Scenario: The Nordic Stock Markets During the Asian Financial Crisis 1997-1998

In risk management, modelling large numbers of assets and their variances and covariances in a unified framework is often important. In such multivariate frameworks, it is difficult to incorporate GARCH models and thus a new member of the ARCH-family, Orthogonal GARCH, has been suggested as a remedy to inherent estimation problems in multivariate ARCH modelling. Orthogonal GARCH creates positive definite covariance matrices of any size but builds on assumptions that partly break down during stress scenarios. This article therefore assesses the stress performance of the model by looking at four Nordic stock indices and covariance matrix forecasts during the highly volatile years of 1997 and 1998. Overall, Orthogonal GARCH is found to perform significantly better than traditional historical variance and moving average methods. Out-of-sample evaluation measures include symmetric loss functions (RMSE), asymmetric loss functions, operational methods suggested by the Basle Committee on Banking Supervision, as well as a forecast evaluation methodology based on pricing of simulated ‘rainbow options’.

Using simulated currency rainbow options to evaluate covariance matrix forecasts

When choosing evaluation measures for variance and covariance forecasts one has to consider what the actual purpose of these forecasts is. In this paper we extend the results of Gibson and Boyer (1998) by looking at portfolios of rainbow currency options and how simulated trading of such options portfolios can be used as a preference free evaluation measure for the forecasted covariance matrix. The advantage of using portfolios instead of single options is the possibility it gives of relying on shorter return series. We apply the methodology to a system of four U.S. dollar exchange rates and compare the relative performance of different forecasting models. In doing this, we also apply and evaluate the fairly new Orthogonal GARCH technique to exchange rates, both with the option evaluation technique and with standard statistical measures

Using Credit Derivatives to Compute Market Wide Default Probability Term Structures

This article suggests a simple way of backing out marketwide risk-neutral default probability (and default density) distributions from quoted credit default swap (CDS) index spreads. It applies the approach to two marketwide European portfolios represented by two frequently traded iTraxx Europe CDS indexes, and the resulting analytical default probability term structures are updated on a daily basis. Such instantaneous default probability term structures should be useful not only for risk managers in commercial banks but also for hedge funds and others involved in speculation and arbitrage, as well as for supervisory authorities such as central banks in their quest for financial stability.

An alternative way of estimating asset values and asset value correlations

In this article, the author suggests a new way of modeling the dynamics of a firm’s asset value and discusses how it could be useful in the computation of asset value correlations in multivariate credit risk models. The method relies on credit spreads from the credit default swap market, and by combining these spreads with stock prices and leverage ratios, the author shows how one can construct a proxy for the asset value. This proxy is then used to calculate asset value correlations among a group of major European banks selected from the stress test conducted by the Committee of European Banking Supervisors in 2010. The asset correlations are presented as a function of bank size, default risk, and geographic location.

Stock Prices and Stock Return Volatilities Implied by the Credit Market

In this article, the author compares equity and credit investors’ opinions on price formation in the equity market. More exactly, he inverts the CreditGrades model in order to back out credit-implied stock prices and stock return volatilities from credit default swap spreads for companies in the DJIA index. The credit-implied stock prices often deviate significantly from actual stock prices over the long term. Meanwhile, their day-to-day movements are significantly correlated with actual stock returns for most firms in the DJIA. In an attempt to demonstrate potential applications of credit-implied stock prices, the author constructs simple “capital structure arbitrage” trading strategies based on past credit-implied prices. These strategies only require the buying and selling of stocks and differ from traditional cross-capital structure strategies by being suitable for retail investors and other investors without access to the credit derivatives market. The credit-implied volatilities, in turn, behave rather similarly to observed stock market volatilities but without any ghost effects. The author demonstrates how an alternative credit-based “fear gauge,” comparable to the CBOE VIX but emanating from the credit market, can be constructed using the credit-implied volatilities. He calls this implied volatility index the Credit-Implied Volatility Index (CIVX). Finally, a plot of the entire term structure of implied volatilities demonstrates a distinct maturity volatility skew.

An index to evaluate fund and fund manager performance

I propose a new index, the b-index, to measure the performance of funds and fund managers. A fund or fund manager has a b-index equal to b if b is the highest number for which it holds that the fund/fund manager has returned more than b% at least b years throughout the history of the fund/fund manager.

Using extreme value theory to estimate the likelihood of banking sector failure

Abstract The growing interest in management of credit risk and estimation of default probabilities has given rise to a range of more or less elaborate credit risk models. While these models work well for non-financial firms they are usually not very successful in capturing the financial strength of banks. As an answer to this, Hall and Miles suggest a simple approach of estimating bank failure probabilities based solely on their stock prices. This paper suggests an extension to the Hall and Miles model using extreme value theory and applies the extended model to the Swedish banking sector around the banking crisis of the early 1990s. The extended model captures very well the increased likelihood of a systemic banking sector failure around the peak of the crisis and it produces default probabilities that are more stable, more realistic and more consistent with Moody’s and Fitch rating implied default rates than probabilities from the original Hall and Miles model.