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on Risk Management |
| By: | John Cotter; Kevin Dowd; Wyn Morgan |
| Abstract: | Risk is an inherent feature of agricultural production and marketing and accurate measurement of it helps inform more efficient use of resources. This paper examines three tail quantile-based risk measures applied to the estimation of extreme agricultural financial risk for corn and soybean production in the US: Value at Risk (VaR), Expected Shortfall (ES) and Spectral Risk Measures (SRMs). We use Extreme Value Theory (EVT) to model the tail returns and present results for these three different risk measures using agricultural futures market data. We compare the estimated risk measures in terms of their size and precision, and find that they are all considerably higher than normal estimates; they are also quite uncertain, and become more uncertain as the risks involved become more extreme. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5962&r=rmg |
| By: | Michael McAleer (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, and Institute of Economic Research, Kyoto University); Juan-Ángel Jiménez-Martín (Department of Quantitative Economics, Complutense University of Madrid); Teodosio Pérez-Amaral (Department of Quantitative Economics, Complutense University of Madrid) |
| Abstract: | The Basel II Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models to measure Value-at-Risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realised losses exceed the estimated VaR. In this paper we define risk management in terms of choosing sensibly from a variety of risk models, and discuss the selection of optimal risk models. A new approach to model selection for predicting VaR is proposed, consisting of combining alternative risk models, and comparing conservative and aggressive strategies for choosing between VaR models. We then examine how different risk management strategies performed during the 2008-09 financial crisis. These issues are illustrated using Standard and Poor's 500 Index, with an emphasis on how market risk management practices were encouraged by the Basel II Accord regulations during the financial crisis. |
| Keywords: | Value-at-Risk (VaR), daily capital charges, exogenous and endogenous violations, violation penalties, optimizing strategy, risk forecasts, aggressive or conservative risk management strategies, Basel II Accord, global financial crisis. |
| JEL: | G32 G11 C53 C22 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:767&r=rmg |
| By: | John Cotter; Kevin Dowd |
| Abstract: | This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user's risk-aversion function. It compares these to VaR and Expected Shortfall (ES) risk measures, and compares the precision of their estimators. It also discusses the usefulness of these risk measures in the context of clearinghouses setting initial margin requirements, and compares these to the SPAN measures typically used. Keywords: Spectral risk measures, Expected Shortfall, Value at Risk, Extreme Value |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5653&r=rmg |
| By: | john cotter; kevin dowd |
| Abstract: | This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk (VaR) and Expected Shortfall (ES). The spectral risk measures are conditioned on the coefficient of absolute risk aversion, and the latter two are conditioned on the confidence level. Our findings indicate that all risk measures increase dramatically and their estimators deteriorate in precision when their respective conditioning parameter increases. Results also suggest that estimates of spectral risk measures and their precision levels are of comparable orders of magnitude as those of more conventional risk measures. Running head: financial risk measures for futures positions |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5666&r=rmg |
| By: | John Cotter |
| Abstract: | Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5649&r=rmg |
| By: | Kevin Dowd; John Cotter |
| Abstract: | This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes a Monte Carlo method that is free of some of the limitations of existing approaches. It then investigates the distribution of risk estimators, and presents simulation results suggesting that the common practice of relying on asymptotic normality results might be unreliable with the sample sizes commonly available to them. Finally, it investigates the relationship between the precision of different risk estimators and the distribution of underlying losses (or returns), and yields a number of useful conclusions. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5665&r=rmg |
| By: | John Cotter; Jim Hanly |
| Abstract: | We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value at Risk (CVAR). Comparisons are applied to a number of hedging strategies including OLS and both Symmetric and Asymmetric GARCH models. Our findings show that asymmetry reduces in-sample hedging performance and that there are significant differences in hedging performance between short and long hedgers. Thus, tail specific performance metrics should be applied in evaluating hedging effectiveness. We also find that the Ordinary Least Squares (OLS) model provides consistently good performance across different measures of hedging effectiveness and estimation methods irrespective of the characteristics of the underlying distribution. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5411&r=rmg |
| By: | John Cotter; Kevin Dowd |
| Abstract: | This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user's risk-aversion function. It compares these to more familiar VaR and Expected Shortfall (ES) measures of risk, and also compares the precision and discusses the relative usefulness of each of these risk measures in setting variation margins that incorporate time-varying market conditions. The goodness of fit of the model is confirmed by a variety of backtests. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5408&r=rmg |
| By: | Kevin Dowd; John Cotter |
| Abstract: | Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how they can be estimated using numerical quadrature methods, and how confidence intervals for them can be estimated using a parametric bootstrap. Illustrative results suggest that estimated exponential spectral risk measures obtained using such methods are quite precise in the presence of normally distributed losses. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5409&r=rmg |
| By: | john cotter |
| Abstract: | This letter uses the Block Maxima Extreme Value approach to quantify catastrophic risk in international equity markets. Risk measures are generated from a set threshold of the distribution of returns that avoids the pitfall of using absolute returns for markets exhibiting diverging levels of risk. From an application to leading markets, the letter finds that the Nikkei is more prone to catastrophic risk than the FTSE and Dow Jones Indexes. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5656&r=rmg |
| By: | John Cotter; Jim Hanly |
| Abstract: | Risk aversion is a key element of utility maximizing hedge strategies; however, it has typically been assigned an arbitrary value in the literature. This paper instead applies a GARCH-in-Mean (GARCH-M) model to estimate a time-varying measure of risk aversion that is based on the observed risk preferences of energy hedging market participants. The resulting estimates are applied to derive explicit risk aversion based optimal hedge strategies for both short and long hedgers. Out-of-sample results are also presented based on a unique approach that allows us to forecast risk aversion, thereby estimating hedge strategies that address the potential future needs of energy hedgers. We find that the risk aversion based hedges differ significantly from simpler OLS hedges. When implemented in-sample, risk aversion hedges for short hedgers outperform the OLS hedge ratio in a utility based comparison. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5968&r=rmg |
| By: | Michiel Bijlsma; Sander Muns |
| Abstract: | This research compares systemic risk in the banking sector, the insurance sector, the construction sector, and the food sector. To measure systemic risk, we use extreme negative returns in stock market data for a time-varying panel of the 20 largest U.S. firms in each sector. |
| JEL: | G11 G21 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:cpb:discus:175&r=rmg |
| By: | John Cotter; Fran\c{c}ois Longin |
| Abstract: | Value at risk (VaR) is a risk measure that has been widely implemented by financial institutions. This paper measures the correlation among asset price changes implied from VaR calculation. Empirical results using US and UK equity indexes show that implied correlation is not constant but tends to be higher for events in the left tails (crashes) than in the right tails (booms). |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5655&r=rmg |
| By: | John Cotter |
| Abstract: | Accurate volatility modelling is paramount for optimal risk management practices. One stylized feature of financial volatility that impacts the modelling process is long memory explored in this paper for alternative risk measures, observed absolute and squared returns for high frequency intraday UK futures. Volatility series for three different asset types, using stock index, interest rate and bond futures are analysed. Long memory is strongest for the bond contract. Long memory is always strongest for the absolute returns series and at a power transformation of k < 1. The long memory findings generally incorporate intraday periodicity. The APARCH model incorporating seven related GARCH processes generally models the futures series adequately documenting ARCH, GARCH and leverage effects. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5651&r=rmg |
| By: | John Cotter |
| Abstract: | The use of absolute return volatility has many modelling benefits says John Cotter. An illustration is given for the market risk measure, minimum capital requirements. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5976&r=rmg |
| By: | Kevin Dowd; John Cotter; Ghulam Sorwar |
| Abstract: | Spectral risk measures (SRMs) are risk measures that take account of user riskaversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative approaches based on exponential and power utility functions. A number of problems are identified with both types of spectral risk measure. The general lesson is that users of spectral risk measures must be careful to select utility functions that fit the features of the particular problems they are dealing with, and should be especially careful when using power SRMs. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5674&r=rmg |
| By: | kevin dowd; john cotter |
| Abstract: | Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their risk-aversion functions. To date there has been very little guidance on the choice of risk-aversion functions underlying spectral risk measures. This paper addresses this issue by examining two popular risk aversion functions, based on exponential and power utility functions respectively. We find that the former yields spectral risk measures with nice intuitive properties, but the latter yields spectral risk measures that can have perverse properties. More work therefore needs to be done before we can be sure that arbitrary but respectable utility functions will always yield 'well-behaved' spectral risk measures. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5668&r=rmg |
| By: | John Cotter |
| Abstract: | Key to the imposition of appropriate minimum capital requirements on a daily basis requires accurate volatility estimation. Here, measures are presented based on discrete estimation of aggregated high frequency UK futures realisations underpinned by a continuous time framework. Squared and absolute returns are incorporated into the measurement process so as to rely on the quadratic variation of a diffusion process and be robust in the presence of fat tails. The realized volatility estimates incorporate the long memory property. The dynamics of the volatility variable are adequately captured. Resulting rescaled returns are applied to minimum capital requirement calculations. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5416&r=rmg |
| By: | John Cotter; Simon Stevenson |
| Abstract: | One stylized feature of financial volatility impacting the modeling process is long memory. This paper examines long memory for alternative risk measures, observed absolute and squared returns for Daily REITs and compares the findings for a non- REIT equity index. The paper utilizes a variety of tests for long memory finding evidence that REIT volatility does display persistence, in contrast to the actual return series. Trading volume is found to be strongly associated with long memory. The results do however suggest differences in the findings with regard to REITs in comparison to the broader equity sector which may be due to relatively thin trading during the sample period. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5414&r=rmg |
| By: | John Cotter; Jim Hanly |
| Abstract: | A key issue in the estimation of energy hedges is the hedgers' attitude towards risk which is encapsulated in the form of the hedgers' utility function. However, the literature typically uses only one form of utility function such as the quadratic when estimating hedges. This paper addresses this issue by estimating and applying energy market based risk aversion to commonly applied utility functions including log, exponential and quadratic, and we incorporate these in our hedging frameworks. We find significant differences in the optimal hedge strategies based on the utility function chosen. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5973&r=rmg |
| By: | Laeven, R.J.A.; Stadje, M.A. (Tilburg University, Center for Economic Research) |
| Abstract: | We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences, respectively, upon requiring the certainty equivalents to be translation invariant. In addition, we study the properties of entropy coherent and entropy convex measures of risk, derive their dual conjugate function, and prove their distribution invariant representation. Some financial applications and examples of entropy coherent and entropy convex measures of risk are also investigated. |
| Keywords: | Multiple priors;Variational and homothetic preferences;Robustness;Convex risk measures;Exponential utility;Relative entropy;Translation invariance;Convexity;Indifference valuation. |
| JEL: | D81 G10 G20 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2011031&r=rmg |
| By: | John Cotter |
| Abstract: | This paper empirically analyses risk in the Euro relative to other currencies. Comparisons are made between a sub period encompassing the final transitional stage to full monetary union with a sub period prior to this. Stability in the face of speculative attack is examined using Extreme Value Theory to obtain estimates of tail exchange rate changes. The findings are encouraging. The Euro's common risk measures do not deviate substantially from other currencies. Also, the Euro is stable in the face of speculative pressure. For example, the findings consistently show the Euro being less risky than the Yen, and having similar inherent risk to the Deutsche Mark, the currency that it is essentially replacing. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5418&r=rmg |
| By: | Chevallier, Julien; Etner, Johanna; Jouvet, Pierre-André |
| Abstract: | This article proposes a theory of banking of emission permits under conditions of regulatory uncertainty. Based on a two-period partial equilibrium framework, we examine the effects of increasing risk - in the sense of a mean-preserving spread - regarding a future permits allocation at the firm-level. We also examine the role of an agency to pool risks by re-allocating permits for a group of firms. Our results are twofold. First, an increase in risk may lead to changes in a firm’s banking strategy, depending on the third partial derivative of its production function with respect to pollution. Second, we define an optimal risk-sharing rule between agents to respond to political decision changes. Our results overall suggest that the bankability of permits may be used as a risk-management tool. |
| Keywords: | Banking; Emission permits; Policy risk; Uncertainty; |
| JEL: | Q58 D80 D21 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ner:dauphi:urn:hdl:123456789/5385&r=rmg |
| By: | John Cotter; Simon Stevenson |
| Abstract: | This paper examines volatility in REITs using a multivariate GARCH based model. The Multivariate VAR-GARCH technique documents the return and volatility linkages between REIT sub-sectors and also examines the influence of other US equity series. The motivation is for investors to incorporate time-varyng volatility and correlations in their portfolio selection. The results illustrate the differences in results when higher frequency daily data is tested in comparison to the monthly data that has been commonly used in the existing literature. The linkages both within the REIT sector and between REITs and related sectors such as value stocks are weaker than commonly found in monthly studies. The broad market would appear to be more influential in the daily case. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5660&r=rmg |
| By: | Ongena, S.; Popov, A.; Udell, G.F. (Tilburg University, Center for Economic Research) |
| Abstract: | This paper provides the first empirical evidence on how home-country regulation and supervision affects bank risk-tailing in host-country markets. We analyze lending by 136 banks to 8,253 firms in 1,513 different localities across 13 countries. We find strong evidence that laxer regulatory restrictions in the home country are associated with higher loan rejection rates by banks in host-country markets, but that the resulting loans are mostly to small, unaudited, nonexporting, and innovative firms. The results are stronger when banks are less efficiently supervised at home, and they are observed independently from the effect that bank balance sheet have on lending. These findings imply that loose home-country regulation and supervision are associated with important negative externalities for the host-country in terms of more risk-taking by cross-border banks. |
| Keywords: | bank regulation;cross-border financial institutions;financial risk. |
| JEL: | G21 G28 G32 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2011032&r=rmg |
| By: | John Cotter |
| Abstract: | We present a novel procedure for scaling relatively high frequency tail probability and quantile estimates for the conditional distribution of returns. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5965&r=rmg |
| By: | Elena Di Bernadino (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429); Thomas Laloë (JAD - Laboratoire Jean Alexandre Dieudonné - CNRS : UMR6621 - Université de Nice Sophia-Antipolis); Véronique Maume-Deschamps (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429); Clémentine Prieur (INRIA Rhône-Alpes / LJK Laboratoire Jean Kuntzmann - MOISE - CNRS : UMR5224 - INRIA - Laboratoire Jean Kuntzmann - Université Joseph Fourier - Grenoble I - Institut Polytechnique de Grenoble, (Méthodes d'Analyse Stochastique des Codes et Traitements Numériques) - GdR MASCOT-NUM - CNRS : GDR3179) |
| Abstract: | This paper deals with the problem of estimating the level sets of an unknown distribution function $F$. A plug-in approach is followed. That is, given a consistent estimator $F_n$ of $F$, we estimate the level sets of $F$ by the level sets of $F_n$. In our setting no compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by applications in multivariate risk theory. In this sense we also present simulated and real examples which illustrate our theoretical results. |
| Keywords: | Level sets ; Distribution function ; Plug-in estimation ; Hausdorff distance ; Conditional Tail Expectation |
| Date: | 2011–03–28 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00580624&r=rmg |
| By: | Einmahl, J.H.J.; Krajina, A.; Segers, J. (Tilburg University, Center for Economic Research) |
| Abstract: | Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method. |
| Keywords: | asymptotic statistics;factor model;M-estimation;multivariate extremes;tail dependence. |
| JEL: | C13 C14 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2011013&r=rmg |
| By: | John Cotter; Jim Hanly |
| Abstract: | This paper examines the volatility and covariance dynamics of cash and futures contracts that underlie the Optimal Hedge Ratio (OHR) across different hedging time horizons. We examine whether hedge ratios calculated over a short term hedging horizon can be scaled and successfully applied to longer term horizons. We also test the equivalence of scaled hedge ratios with those calculated directly from lower frequency data and compare them in terms of hedging effectiveness. Our findings show that the volatility and covariance dynamics may differ considerably depending on the hedging horizon and this gives rise to significant differences between short term and longer term hedges. Despite this, scaling provides good hedging outcomes in terms of risk reduction which are comparable to those based on direct estimation. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5966&r=rmg |
| By: | john cotter; kevin dowd |
| Abstract: | This paper measures and compares the tail risks of limit and market orders using Extreme Value Theory. The analysis examines realised tail outcomes using the Dealing 2000-2 electronic broking system based on completed transactions rather than the more common analysis of indicative quotes. In general, limit and market orders exhibit broadly similar tail behaviour, but limit orders have significantly heavier tails and larger tail quantiles than market orders. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5661&r=rmg |
| By: | John Cotter; Fran\c{c}ois Longin |
| Abstract: | Both in practice and in the academic literature, models for setting margin requirements in futures markets classically use daily closing price changes. However, as well documented by research on high-frequency data, financial markets have recently shown high intraday volatility, which could bring more risk than expected. This paper tries to answer two questions relevant for margin committees in practice: is it right to compute margin levels based on closing prices and ignoring intraday dynamics? Is it justified to implement intraday margin calls? The paper focuses on the impact of intraday dynamics of market prices on daily margin levels. Daily margin levels are obtained in two ways: first, by using daily price changes defined with different time-intervals (say from 3 pm to 3 pm on the following trading day instead of traditional closing times); second, by using 5-minute and 1-hour price changes and scaling the results to one day. Our empirical analysis uses the FTSE 100 futures contract traded on LIFFE. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5412&r=rmg |
| By: | John Cotter; Simon Stevenson |
| Abstract: | Using a time-varying approach, this paper examines the dynamics of volatility in the REIT sector. The results highlight the attractiveness and suitability of using GARCH based approaches in the modeling of daily REIT volatility. The paper examines the influencing factors on REIT volatility, documenting the return and volatility linkages between REIT sub-sectors and also examines the influence of other US equity series. The results contrast with previous studies of monthly REIT volatility. Linkages within the REIT sector and with related sectors such as value stocks are diminished, while the general influence of market sentiment, coming through the large cap indices is enhanced. This would indicate that on a daily basis general market sentiment plays a more fundamental role than more intuitive relationships within the capital markets. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5417&r=rmg |
| By: | Raynaud, Franck; Lautier, Delphine |
| Abstract: | This article presents an empirical study of thirteen derivative markets for commodity and financial assets. This paper goes beyond statistical analysis by including the maturity as a variable for futures contracts’s daily returns, from 1998 to 2010 and for delivery dates up to 120 months. We observe that the mean and variance of the commodities follow a scaling behavior in the maturity dimension with an exponent characteristic of the Samuelson effect. The comparison of the tails of the probability distribution according to the expiration dates shows that there is a segmentation in the fat tails exponent term structure above the Lévy stable region. Finally, we compute the average tail exponent for each maturity and we observe two regimes of extreme events for derivative markets, reminding of a phase diagram with a sharp transition at the 18th delivery month. |
| Keywords: | Derivatives; Econophysics; Tail exponents; Term structures; |
| JEL: | G1 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ner:dauphi:urn:hdl:123456789/5528&r=rmg |
| By: | Kevin Dowd; John Cotter; Chris Humphrey; Margaret Woods |
| Abstract: | One of the more memorable moments of last summer's credit crunch came when the CFO of Goldman Sachs, David Viniar, announced in August that Goldman's flagship GEO hedge fund had lost 27% of its value since the start of the year. As Mr. Viniar explained, "We were seeing things that were 25-standard deviation moves, several days in a row." |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1103.5672&r=rmg |