Asset Correlation Research Articles

Pricing multivariate options under stochastic volatility lévy processes

The aim of this article is to study the valuation of multivariate options based on correlated multidimensional time-changed Lévy processes, where two time changes are used to describe diffusion part and jump part stochastic volatilities as well as assets correlation structures. The main contribution of this article is two-folds: First, we build a flexible enough framework to model assets' dependent structure and volatility clustering; second, by employing extended Esscher transform to reduce the problem's dimension, and generalized Fourier transform to simplify the integration involving the terminal payoff , we dramatically reduce the complexities of this problem, and get very accurate solutions in a relatively short computation time.

The asymmetric behavior and procyclical impact of asset correlations

This paper examines the behavior of asset correlations with the market returns in the asymptotic single risk factor (ASRF) approach of the Basel II accord on regulatory capital requirement. Over a sample period from 1988 to 2007, we find that asset correlations are positively related to firm size, but negatively related to firm default probability. Asset correlations are also industry specific, as firms in media, transportation, pharmaceutical, and semiconductor industries exhibit higher asset correlations than those in retail and consumer staples. Most importantly, asset correlations are asymmetric and have a procyclical impact on the real economy after controlling for these effects. They tend to rise during economic downturns, but decline during economic upturns. The average magnitude of the rise is larger than that of the decline. These findings suggest that asset correlations may be underestimated during economic downturns, and may provide policy implications for the capital requirement framework.

Dynamic Correlations Among Asset Classes: REIT and Stock Returns

We use the Dynamic Conditional Correlation model with Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) developed by Engle (Journal of Business & Economic Statistics 20(3):339–350, 2002) to examine dynamics in the correlation of returns between publicly traded REITs and non-REIT stocks. The results suggest that REIT-stock correlations form three distinct periods. During the first period, ending in August 1991 with the start of the modern REIT era, correlations were high and without trend, never dipping below 59%. During the second period, ending in September 2001 with the inclusion of REITs in broad stock market indexes, correlations declined precipitously to 30%, enabling substantially higher portfolio allocations to both high-return asset classes and therefore higher portfolio returns without increasing portfolio volatility. During the third period, since September 2001, correlations increased steadily but only reached 59% in late 2008. A simple portfolio optimization suggests that asset managers would be willing to pay 20 basis points per year, plus the difference in transaction costs, for the ability to use DCC-GARCH modeling of dynamic correlations in place of rolling 24-month asset correlations.

Asset correlation, portfolio diversification and regulatory capital in the Basel Capital Accord

In this paper, we analyze the properties of the KMV model of credit portfolio loss. This theoretical model constitutes the cornerstone of Basel II’s Internal Ratings Based(IRB) approach to regulatory capital. Our results show that this model tends to overestimate the probability of portfolio loss when the probability of default of a single firm and the firms’ asset correlations are low. On the contrary, probabilities of portfolio loss are underestimated when the probability of default of a single firm and asset correlations are high. Moreover, the relationship between asset correlation and probability of loan portfolio loss is only consistent at very high quantiles of the portfolio loss distribution. These are precisely those adopted by the Basel II Capital Accord for the calculations of capital adequacy provisions. So, although the counterintuitive properties of the KMV model do not extend to Basel II, they do restrict its generality as a model of credit portfolio loss.

Systemic Risk Contributions

We adopt a systemic risk indicator measured by the price of insurance against systemic financial distress and assess individual banks' marginal contributions to the systemic risk. The methodology is applied using publicly available data to the 19 bank holding companies covered by the U.S. Supervisory Capital Assessment Program (SCAP), with the systemic risk indicator peaking around $1.1 trillion in March 2009. Our systemic risk contribution measure shows interesting similarity to and divergence from the SCAP expected loss measure. In general, we find that a bank's contribution to the systemic risk is roughly linear in its default probability but highly nonlinear with respect to institution size and asset correlation.

Book-to-Market Equity, Operating Risk, and Asset Correlations: Implications for Basel Capital Requirementer

Book-to-Market Equity, Operating Risk, and Asset Correlations: Implications for Basel Capital Requirementer

Systemic Risk Contributions: A Credit Portfolio Approach

We put forward a Merton-type multi-factor portfolio model for assessing banks' contributions to systemic risk. This model accounts for the major drivers of banks' systemic relevance: size, default risk and correlation of banks' assets as a proxy for interconnectedness. We measure systemic risk in terms of the portfolio expected shortfall (ES). Banks' (marginal) risk contributions are calculated based on partial derivatives of the ES in order to ensure a full risk allocation among institutions. We compare the performance of an importance sampling algorithm with a fast analytical approximation of the ES and the marginal risk contributions. Furthermore, we show empirically for a portfolio of large international banks how our approach could be implemented to compute bank-specific capital surcharges for systemic risk or stabilisation fees. We find that size alone is not a reliable proxy for the systemic importance of a bank in this framework. In order to smooth cyclical fluctuations of the risk measure, we explore a time-varying confidence level of the ES.

Fat Tails and their (Un)Happy Endings: Correlation Bias and its Implications for Systemic Risk and Prudential Regulation

The correlation bias refers to the fact that claim subordination in the capital structure of the firm influences claim holders’ preferred degree of asset correlation in portfolios held by the firm. Using the copula capital structure model, it is shown that the correlation bias shifts shareholder preferences towards highly correlated assets, making financial institutions more prone to fail and increasing systemic risk given interconnectedness in the financial system. The implications for systemic risk and prudential regulation are assessed under the prism of Basel III, and potential solutions involving changes to the prudential framework and corporate governance are suggested.

What Is Wrong with this Picture? A Problem with Comparative Return Plots on Finance Websites and a Bias Against Income-Generating Assets

This paper brings to light and discusses a systemic issue in the calculation and display of relative return information as currently seen on some of the most prominent finance websites; income-generating events such as dividends and interest are not included in relative return calculations and all comparative return graphics. The resulting ranking of the securities, based on such incomplete returns, is essentially meaningless from a total return perspective, yet they are being served to millions of investors every day. This could lead to the formation of a possible availability heuristic and an optical bias against fixed-income and other income generating assets. This problem has gone unnoticed for many years with no discussion of the topic either in the academic or practitioner press. The ready availability of such unclear or inaccurate information from sources generally perceived to be credible can, in this age of do-it-yourself portfolio management, have serious and damaging financial consequences to the unsuspecting investor. The paper also shows the effect of this return differential on the calculation of the asset correlation matrices and the subsequent effect on the resulting asset-weight vectors that are used to generate Markowitz style mean-variance portfolios. The visual discrepancies are then supported by the application of the Gibbons, Ross and Shanken [1989] W-test for portfolio efficiency. The authors’ proposed correction, based on elementary finance, fixes the problem.

Regime Shifts in Mean-Variance Efficient Frontiers: Some International Evidence

Regime switching models have been assuming a central role in financial applications because of their well-known ability to capture the presence of rich non-linear patterns in the joint distribution of asset returns. This paper examines how the presence of regimes in means, variances, and correlations of asset returns translates into explicit dynamics of the Markowitz mean-variance frontier. In particular, the paper shows both theoretically and through an application to international equity portfolio diversification that substantial differences exist between bull and bear regime-specific frontiers, both in statistical and in economic terms. Using Morgan Stanley Capital International (MSCI) investable indices for five countries/macro-regions, it is possible to characterize the mean-variance frontiers and optimal portfolio strategies in bull periods, in bear periods, and in periods where high uncertainty exists on the nature of the current regime. A recursive back-testing exercise shows that between 1998 and 2010, adopting a switching mean-variance strategy may have yielded considerable risk-adjusted payoffs, which are the largest in correspondence to the 2007-2009 financial crisis.

Convexity Adjustments for the ASFR Model

The ASFR model computes a credit value at risk for a given default probability and asset correlation. Since the default probability is usually estimated from historical default data, the value at risk may also be considered to be an estimate, based on the same data. We demonstrate that even if the default probability is estimated without bias, the value at risk estimation will be biased due to the non-linearity of the VaR function. The bias is negative so that the value at risk is underestimated systematically. We suggest how to compute a correction term which reduces the bias. This may be interpreted as including 'estimation risk' into the risk calculation.

Estimating asset correlations from stock prices or default rates—Which method is superior?

This paper sets out to help explain why estimates of asset correlations based on equity prices tend to be considerably higher than estimates based on default rates. Resolving this empirical puzzle is highly important because, firstly, asset correlations are a key driver of credit risk and, secondly, both data sources are widely used to calibrate risk models of financial institutions. By means of a simulation study, we explore the hypothesis that differences in the correlation estimates are due to a substantial downward bias characteristic of estimates based on default rates. By varying the time horizon, the default probability, the asset correlation and the number of firms in the portfolio, we investigate these estimators in a systematic comparative study. Our results suggest that correlation estimates from equity returns are more efficient than those from default rates. This finding still holds if the model is misspecified such that asset correlations follow a Vasicek process which affects foremost the estimates from equity returns. The results lend support for the hypothesis that the downward bias of default-rate based estimates is an important although not the only factor to explain the differences in correlation estimates. Furthermore, our results help to quantify the estimation error of asset correlations dependent on the true values of default probability and asset correlation.

Reconciling credit correlations

The credit crisis has created a new impetus for regulators to analyse the framework for determining regulatory capital requirements, in particular the assessment of credit risk will be challenged. Confronted with a lack of default statistics it is common practice by industry practitioners to apply a financial approach, also known as Merton’s model of the firm, and we remark that the latter approach also underpins modern solvency standards such as Basel II and Solvency II.However, while Merton’s theory is an academic beauty its implementation does not make full use of available default statistics but relies on the concept of so-called asset correlations instead. We study the different estimates used for asset correlations that have been mentioned in the literature and analyse to which extent these estimates are in line with each other, with available default statistics as well as with our own findings.Our results are in line with the majority of the literature but deviate away from the results reported by some major software providers as well as the Basel II and Solvency II figures. We offer several explanations as an attempt to reconcile the differences and point to several other features that should not be overlooked when building credit portfolio models.

Spillover Effects of the US Financial Crisis on Financial Markets in Emerging Asian Countries

We estimate dynamic conditional correlations of financial asset returns across countries by an array of multivariate GARCH models and analyze spillover effects of the recent US financial crisis on 5 emerging Asian countries. We confirm the existence of financial contagion around the collapse of Lehman Brothers in September 2008. There appears to be a regime shift to substantially high conditional correlations that persisted for a fairly short-period of time. We also propose a novel approach that allows simultaneous estimations of the conditional correlation coefficient and the effects of its determining factors over time, which can be used to identify channels of contagion. We find the dominant role of foreign investment for the conditional correlations in international equity markets. The dollar Libor-OIS spread, the sovereign CDS premium, and foreign investment are found to play significant roles in foreign exchange markets.

Dynamic Correlations Among Asset Classes: REIT and Stock Returns

We use the Dynamic Conditional Correlation model with Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) developed by Engle (Journal of Business & Economic Statistics 20(3):339–350, 2002) to examine dynamics in the correlation of returns between publicly traded REITs and non-REIT stocks. The results suggest that REIT-stock correlations form three distinct periods. During the first period, ending in August 1991 with the start of the modern REIT era, correlations were high and without trend, never dipping below 59%. During the second period, ending in September 2001 with the inclusion of REITs in broad stock market indexes, correlations declined precipitously to 30%, enabling substantially higher portfolio allocations to both high-return asset classes and therefore higher portfolio returns without increasing portfolio volatility. During the third period, since September 2001, correlations increased steadily but only reached 59% in late 2008. A simple portfolio optimization suggests that asset managers would be willing to pay 20 basis points per year, plus the difference in transaction costs, for the ability to use DCC-GARCH modeling of dynamic correlations in place of rolling 24-month asset correlations.

Implied asset correlation in retail loan portfolios

Credit risk arises from the interaction of multiple connected factors, but the most frequently-used models designed to measure it assume only one. These models — which, inter alia, fit distributions to loss data — are heavily influenced by the common correlation between loan values and the single factor (commonly assumed to be some gauge of economic health). Scarce and shoddy loss data for retail loan classes hamper the estimation of this correlation. A technique is proposed to calculate asset correlations embedded in empirical loss data. These values are then compared with those stipulated by the Basel II Accord for minimum capital requirements.

Contagion of Financial Crises with Special Emphasis on Cee Economies: A Meta-Analysis

The paper offers new insights on the subject of financial contagion using a meta-analysis methodology and paying particular attention to the transition economies of Central and Eastern Europe (CEE). The results show that on average, asset market correlations have increased during turbulent periods, but the increase is rather moderate. When correlation coefficients are adjusted for the presence of heteroscedasticity, the increase is considerably smaller, but still statistically significant. The crises have been more and less contagious, but the level of development of the chosen afflicted country seems not to have played a significant role in determining whether crises spread there or not. Transition economies in CEE have on average been somewhat less susceptible to financial contagion than the sample as a whole, but the increase in the asset prices correlation during times of crisis is statistically insignificant. Interestingly, the financial contagion ‘snowball’ seems to have affected the CEE transition economies most after crises in the US rather than one in Russia or the Czech Republic.

Risk‐Based Capital and Credit Insurance Portfolios

This paper analyzes the risk‐management practices of a vulnerable credit insurer by studying the effects of time‐varying correlations, asset risks and loan maturities on the risk‐based capital that backs credit insurance portfolios. Since asset correlations may change over a business cycle, we have analyzed these effects by means of a one‐factor Gaussian stochastic model as part of an extended contingent claims analysis. Our results show the need to account for cyclical changes to correlations in the pricing of credit insurance. When compared with the reserve of risk‐based capital recommended by the Basel II Internal Ratings‐Based (IRB) approach, our model provides a better capital buffer against extreme credit losses, especially in times of recession and/or in a risky business environment. Using a risk‐adjusted performance metric (RAPM), we find insurers perform better when insuring relatively short‐term loans. We also make several policy recommendations on creating a reserve of risk‐based capital to protect against possible loan losses.

Default and Asset Correlation: An Empirical Study for Italian SMEs

This paper addresses the estimation of confidence sets for asset correlation for credit risk assessment in the Italian market. Research on the estimation of asset correlation using endogenous default probabilities data has focused the impact of concentration risk factors, such as industry and firm size. The empirical evidence shows that assumptions underlying the Regulatory Capital formula are not substantiated and benefits receiving from the respect of the granularity could be reduced or even removed. This effect could depend on the positive relationship between asset correlation and default probability, the negative relationship between asset correlation and size, and the positive link between default correlation and default probability. The regulatory impact is that the purpose to level the playing field could be failed, setting up a regulatory arbitrage opportunity and the risk that some firms, clustered by size and industry, could suffered by the credit crunch.

Risk Management of Hedge Funds: Role of Funding and Redemption Options on Leverage

We develop a model of hedge fund returns, which reflect the contractual relationships between a hedge fund, its investors and its prime brokers. These relationships are modelled as short option positions held by the hedge fund, wherein the “funding option” reflects the short option position with prime brokers and the “redemption option” reflects the short option position with the investors. Given an alpha producing human capital, the hedge fund0s ability to deploy leverage is shown to be sharply constrained by the presence of these short options. We show that the hedge funds typically have an optimal level of leverage. Optimal leverage is shown to differ across hedge funds reflecting their de-levering costs, Sharpe ratios, correlation of assets, secondary market liquidity of their assets, and the volatility of the assets. Using a minimum level of unencumbered cash level as a risk limit, we show how a hedge fund can optimally allocate its risk capital across different risk-taking units to maximize alpha in the presence of these short option positions. Implications of our analysis for hedge fund investors and policy makers are summarized.