Pricing and Hedging Credit Derivatives with Copulas

In this paper, we apply a copula function pricing technique to the evaluation of credit derivatives, namely a vulnerable default put option and a credit switch. Also in this case, copulas enable one to separate the specification of marginal default probabilities from their dependence structure. Their use is based here on no–arbitrage arguments, which provide pricing bounds and easy–to–implement super–replication strategies.
At a second stage, we specify the copula function to be a mixture one. In this case, we obtain closed form prices and hedges, which we calibrate on real market data. For the sake of comparison, we add a Clayton calibration.
(J.E.L: G11, G12).     

Relationship between oil price and exchange rate by FDA and copula

This article investigates the relationship between daily crude oil prices and exchange rates. Functional data analysis is used to show the clustering pattern of exchange rates and oil prices over the time period through high dimensional visualizations. We select exchange rates for important currencies related to crude oil prices by using the objective Bayesian variable selection method. The selected sample data exhibits non-normal distribution with fat tails and skewness. Under the non-normality of the return series, we use copula functions that do not require to assume the bivariate normality to consider marginal distribution. In particular, our study applies the popular and powerful statistical methods such as Gaussian copula partial correlations and Gaussian copula marginal regression. We find evidence of significant dependence for all considered pairs, except for the Mexican peso-Brent. Our empirical results also show that the rise in the West Texas Intermediate (WTI) oil price returns is associated with a depreciation of the US dollar.     

A new approach to modeling co-movement of international equity markets: evidence of unconditional copula-based simulation of tail dependence

Analyzing equity market co-movements is important for risk diversification of an international portfolio. Copulas have several advantages compared to the linear correlation measure in modeling co-movement. This paper introduces a copula ARMA-GARCH model for analyzing the co-movement of international equity markets. The model is implemented with an ARMA-GARCH model for the marginal distributions and a copula for the joint distribution. After goodness of fit testing, we find that the Student’s t copula ARMA(1,1)-GARCH(1,1) model with fractional Gaussian noise is superior to alternative models investigated in our study where we model the simultaneous co-movement of nine international equity market indexes. This model is also suitable for capturing the long-range dependence and tail dependence observed in international equity markets. Rachev’s research was supported by grants from Division of Mathematical, Life and Physical Science, College of Letters and Science, University of California, Santa Barbara, and the Deutschen Forschungsgemeinschaft (DFG). Sun’s research was supported by grants from the Deutschen Forschungsgemeinschaft (DFG) and Chinese Government Award for Outstanding Ph.D Students Abroad 2006, No. 2006-180. Kalev’s research was supported with a NCG grant from the Faculty of Business and Economics, Monash University. Data are supplied by Securities Industry Research Center of Asia-Pacific (SIRCA) on behalf of Reuters. The constructive comments of two anonymous referees, the Associate Editor, A.S. Wirjanto, and the Editor-in-charge, Baldev Raj, are gratefully acknowledged. The reviewers and editors are not responsible for any residual errors and omissions.     

Asymmetric Contributions to Research Joint Ventures

We show that ex ante identical oligopolists may find it optimal to contribute asymmetrically to a research joint venture. The reason is found in the trade-off between the desire to increase the variance of the distribution of unit costs within the oligopoly (which increases gross profit, though not necessarily net profit, of the group) and the incentive to efficiently carry out R&D activities by equalizing marginal R&D costs across firms. Conditions for non-existence of symmetric contributions are given. We also propose a profit sharing rule for asymmetric research joint ventures.
JEL Classification Numbers: L13, L23.     

Privatization,Underpricing, and Welfare in the Presence of Foreign Competition

We analyze privatization in a differentiated oligopoly setting with a domestic public firm and foreign profit‐maximizing firms. In particular, we examine pricing below marginal cost by the public firm, the optimal degree of privatization, and the relationship between privatization and foreign ownership restrictions. When market structure is exogenous, partial privatization of the public firm improves welfare by reducing public sector losses. Surprisingly, even at the optimal level of privatization, the public firm's price lies strictly below marginal cost, resulting in losses. Our analysis also reveals a potential conflict between privatization and investment liberalization (i.e., relaxing restrictions on foreign ownership) in the short run. With endogenous market structure (i.e., free entry of foreign firms), partial privatization improves welfare through an additional channel: more foreign varieties. Furthermore, at the optimal level of privatization, the public firm's price lies strictly above marginal cost and earns positive profits.     

我国省份之间的要素流动和边际生产率的差异分析

本文讨论了我国各省份之间的生产要素配置的有效性问题。首先 ,在估计各省份的生产函数的基础上 ,给出了各省份资本存量和劳动的边际回报率的大小。其次 ,本文引入了刻划边际回报差异程度的指标———离差指标。通过分析发现 ,从 1 970— 1 989年 ,资本存量的边际生产率的差异水平在缩小 ,从 1 989年起 ,边际生产率的差异水平保持在一个稳定水平 ;劳动的边际生产率的差异从 1 970— 1 993年也在缩小 ,但是 ,从 1 994年开始 ,劳动的边际生产率的差异水平反而开始上升。最后 ,本文对出现的资本存量和劳动的边际回报率差异的变化趋势进行了初步的解释。     

Compensating Variation and Hicksian Choice Probabilities in Random Utility Models that are Nonlinear in Income

In this paper we discuss Hicksian demand and compensating variation in the context of discrete choice. We first derive Hicksian choice probabilities and the distribution of the (random) expenditure function in the general case when the utilities are nonlinear in income. We subsequently derive exact and simple formulae for the expenditure and choice probabilities under price (policy) changes conditional on the initial utility level. This is of particular interest for welfare measurement because it enables the researcher to compute the distribution of compensating variation in a simple way. We also derive formulae for the joint distribution of expenditure, the choice before and after a policy change has been introduced.     

Factor Mobility and Dispersion in Marginal Products: A Case on China

This paper examines the efficiency in resource allocation in China. We estimate production functions at the provincial level and use these functions to compute time series for marginal products of capital and labor. We found that dispersion in the marginal product of capital declined from 1970 to 1984 and then became stable afterward, whereas the dispersion in the marginal product of labor declined initially but the trend has been reversed since 1993. We argue that this reversal may indicate any of the following: (1) policy-driven labor migration adding to labor market inefficiency; (2) the presence of increasing returns in labor; and (3) both capital and labor having become mobile since 1993. Translated from the Economic Research Journal, 2004, (1) (in Chinese)     

Measuring and Optimizing Portfolio Credit Risk: A Copula‐based Approach*

In this work, we present a methodology for measuring and optimizing the credit risk of a loan portfolio taking into account the non‐normality of the credit loss distribution. In particular, we aim at modelling accurately joint default events for credit assets. In order to achieve this goal, we build the loss distribution of the loan portfolio by Monte Carlo simulation. The times until default of each obligor in portfolio are simulated following a copula‐based approach. In particular, we study four different types of dependence structure for the credit assets in portfolio: the Gaussian copula, the Student's t‐copula, the grouped t‐copula and the Clayton n‐copula (or Cook–Johnson copula). Our aim is to assess the impact of each type of copula on the value of different portfolio risk measures, such as expected loss, maximum loss, credit value at risk and expected shortfall. In addition, we want to verify whether and how the optimal portfolio composition may change utilizing various types of copula for describing the default dependence structure. In order to optimize portfolio credit risk, we minimize the conditional value at risk, a risk measure both relevant and tractable, by solving a simple linear programming problem subject to the traditional constraints of balance, portfolio expected return and trading. The outcomes, in terms of optimal portfolio compositions, obtained assuming different default dependence structures are compared with each other. The solution of the risk minimization problem may suggest us how to restructure the inefficient loan portfolios in order to obtain their best risk/return profile. In the absence of a developed secondary market for loans, we may follow the investment strategies indicated by the solution vector by utilizing credit default swaps.     

Energy portfolio risk management using time-varying extreme value copula methods

This work is concerned with the statistical modeling of the dependence structure between three energy commodity markets (WTI crude oil, natural gas and heating oil) using the concept of copulas and proposes a method for estimating the Value at risk (VaR) of energy portfolio based on the combination of time series models with models of the extreme value theory before fitting a copula. Each return series is modeled by AR-(FI) GARCH univariate model. Then, we fit the GPD distribution to the tails of the residuals to model marginal residuals distributions. The extreme value copula to the iid residuals is fitted and we simulate from it to construct N portfolios and estimate VaR. As a first step, the method is applied to a two-dimensional energy portfolio. In second step, we extend method in trivariate context to measure VaR of three-dimensional energy portfolio. Dependences between residuals are modeled using a trivariate nested Gumbel copulas. Methods proposed are compared with various univariate and multivariate conventional VaR methods. The reported results demonstrate that GARCH-t, conditional EVT and FIGARCH extreme value copula methods produce acceptable estimates of risk both for standard and more extreme VaR quantiles. Generally, copula methods are less accurate compared with their predictive performances in the case of portfolio composed of exchange market indices.     

股票资产组合VaR研究基于混合D藤Copula模型

本文在对上证市场五种股票资产组合的风险分析中以VaR作为风险度量指标,采用基于Pair Copula高维建模理论的混合D藤Copula模型,建立了反应多个资产组合相关结构的联合分布模型。该模型对传统D藤Copula建模方法作了进一步的改进,通过一定的选择标准,确定了D藤中每个Pair Copula函数的最优函数族,这样使得所建立的模型不仅考虑到了资产维数的影响,而且还能捕捉到组合内部因子间相关结构的差异性,从而改进后的模型能更好地描述资产组合的相关结构,并且能更精确地反映资产组合收益的实际分布。最后,以混合D藤Copula模型为基础,利用Monte Carlo方法计算了上证市场五种股票资产组合的VaR,并通过实证研究进一步证明了该模型的有效性。     

Estimating the Marginal Contribution to Systemic Risk by A CoVaR‐model Based on Copula Functions and Extreme Value Theory

In this paper, we quantify the contribution to systemic risk of a single financial institution by utilizing a analytical framework based on the principles of Extreme Value Theory (EVT) for modelling the marginal distributions and on the properties of copula functions for describing the dependence structure between the financial system and the single financial institution. Among the several systemic risk measures proposed nowadays by academics and estimated by public data, we choose to adopt as systemic risk metric the Conditional Value‐at‐Risk (CoVaR). We select a co‐risk measure like the CoVaR because of its macro‐dimension that allows us to integrate the dependence structure of the single financial institution and of the whole financial system in the systemic risk measurement. While the copula functions have been utilized in some pioneer studies on this area, the EVT principles have not yet been implemented in such a context of systemic risk contribution measurement.     

Using Copulas to Model Switching Regimes with an Application to Child Labour*

The copula approach to econometric modelling involves the specification of the separate components of the joint distribution of the random variables of interest: models built for each margin are bound together using a copula function. In this paper, the copula approach is used to construct models for switching regimes. The construct is illustrated by fitting a wage earnings model for child workers in the early 1900s, with regimes governed according to literacy. The results improve on earlier modelling efforts by Poirier and Tobias (2003), finding that a child worker may on average expect a reduction in earnings from being literate.     

Liquidity, Trading Size, and the Co-existence of Dealership and Auction Markets

This paper analyses the co-existence of two markets for the same shares, a quote-driven market and an order-driven market, as observed for example for the trading of continental shares on the London SEAQ International. The focus is on the trade-off between the uncertain execution price faced by investors on an auction market and the implicit transaction cost represented by the spread in a dealer market. We obtain that those investors who desire to make large trades will prefer to trade with the dealer, while trades of smaller size will be carried out on the auction market. Moreover, we explicitly investigate the interrelations between the two markets showing that the pricing policy followed by a dealer depends on the conditions prevailing on the auction market.
(J.E.L: G10, D40)     

Fuzzy Value-at-risk: Accounting for Market Liquidity

In this paper we present a value-at-risk measure which accounts for market liquidity. We show that taking into account market liquidity implies a decoupling of valuation of long and short positions. We present a pricing model, named fuzzy measure model, that yields different values for positions of different sign and that can be usefully exploited to account for liquidity risk. This methodology is well-suited to price options when the distribution of the underlying asset is not known precisely, as in the case of implied options in corporate claims or real options. As an example, we apply our pricing technique to an option based model of value-at-risk, in line with the Merton and Perold approach, and we recover different value-at-risk figures for long and short positions.
(J.E.L.: C00, D81, G12).     

Deviations from optimal corporate cash holdings and the valuation from a shareholder’s perspective

The trade-off theory of corporate cash holdings predicts that there is an optimal level of cash. We test the trade-off theory by investigating the relation between deviations from optimal cash holdings and the valuation of cash from a shareholder’s perspective. We decompose corporate cash holdings into the optimal level of cash and the deviations from the optimum. We find that the marginal value of cash for shareholders is higher when a change in cash moves corporate cash holdings towards the optimal level and that this relationship holds for both the above-optimal deviations and the below-optimal deviations. We conclude that the results are consistent with the prediction of the trade-off theory of corporate cash holdings.     

大宗股权定价的实证检验

本文结合现有金融理论,研究大宗股权的定价问题。大宗股权的重要特征是其具有控制权收益,同时由于交易规则的限制,它往往带有流动性约束。大宗股权的这些特征是散股所不具备的,因此也将在定价中反映出来。本文将二者的影响在一个统一的框架下进行分析,并对其做了定量的估计。通过对2002和2003年间我国上市公司协议转让的233笔非流通股的研究,本文发现:流动性约束对非流通股定价有负面作用,而控制权收益对非流通股定价有正面作用。     

Tacit Coordination in a Decentralized Market Entry Game with Fixed Capacity

We focus on a class of market entry games in which a newly emergent market opportunity may be fruitfully exploited by no more than a commonly known, exogenously determined number of firms. Our results show significant effects of the parameters manipulated in the study, namely, the market capacity, entry fee, and method of subject assignment to groups (fixed vs. random). In contrast to previous market entry games with linear payoff functions, we find no evidence of convergence to equilibrium play on the aggregate level. Shifting the focus of the analysis from the aggregate to the individual level, four clusters of subjects are identified. The patterns are: (1) choice of the same action that is independent of the parameters of the game or the outcome of previous presentations of the same game; (2) random choices with probabilities prescribed by the equilibrium solution for risk-neutral players; (3) random choices with probabilities equal to the individual observed overall proportion of entry; and (4) sequential dependencies that violate any model that assumes randomization. Subjects in the fourth and largest category are shown to adjust their choices in accordance with a simple principle of strategic reasoning.     

Why progressive redistribution can hurt the poor

Recent macroeconomic research discusses credit market imperfections as a key channel through which inequality retards growth: With convex technologies, progressive transfers increase aggregate output because marginal returns become more equalized across investment opportunities. We argue that this reasoning may not hold in general equilibrium. Since the investment functions are concave in wealth, reducing inequality increases capital demand and the interest rate. Hence, through the impact on capital costs, shifting wealth from the rich to the middle class depletes the poorest investors' access to credit. But because the poor face the highest marginal returns, the net effect on output may be negative. We find, however, that redistributing towards the bottom-end of the distribution has a clear positive impact. Finally, we discuss the implications of our theoretical findings for future empirical research.     

DEMOGRAPHIC CHANGE AND INEQUALITY IN THE SIZE DISTRIBUTIONS OF LABOR AND NONLABOR INCOME

This paper utilizes a joint distribution model of labor and nonlabor income that allows us to analyze the impact of demographic change in the U.S. on the marginal distributions of these two income components over time. The beta distribution of the second kind is the hypothetical statistical distribution used in this study to approximate the observed income graduation. This distribution is sum stable which allows us to compare and contrast the marginal distributions in a consistent manner, a property most hypothesized functional forms of income distribution do not possess. We are in effect using a hyperparameter model to do our estimation. We examined the impact of changes over time in labor force participation and population on the marginal distributions of labor and nonlabor income. We disaggregated the variables by sex and age cohorts and found that changes in the age distribution and in the labor supply behavior of women in particular has had a significant effect on the marginal income distributions over time. We also found that the results vary when we examined overall changes in the labor force participation rate vis a vis changes in women's labor force participation separately. The findings are consistent for both income components.