A mixed C-vine copula model for hedging price and volumetric risk in wind power trading

When energy trading companies enter into long-term agreements with wind power producers, where a fixed price is paid for the fluctuating production, they are facing a joint price and volumetric risk. Since the pay-off of such agreements is non-linear, a hedging portfolio would ideally consist of not only forwards, but also a basket of e.g. call and put options. Illiquidity and an almost non-existent market for options challenge however the optimal hedging of joint price and volumetric risk in many market places. Here, we consider the case of the Danish power market, and exploit its strong positive correlation with the much more liquid German market to construct a proxy hedge. We propose a three-dimensional mixed vine copula to model the evolution of the Danish and German spot electricity prices and the Danish wind power production. We construct a realistic hedging portfolio by identifying various instruments available in the market, such as real options in the form of the right to transfer electricity across the border and the right to convert electricity to heat. Using the proposed vine copula to determine optimal hedging decisions, we show that significant benefits are to be drawn by extending the hedging portfolio with the proposed instruments.     

Commodity futures hedging,risk aversion and the hedging horizon

This paper examines the impact of management preferences on optimal futures hedging strategy and associated performance. Applying an expected utility hedging objective, the optimal futures hedge ratio is determined for a range of preferences on risk aversion, hedging horizon and expected returns. Empirical results reveal substantial hedge ratio variation across distinct management preferences and are supportive of the hedging policies of real firms. Hedging performance is further shown to be strongly dependent on underlying preferences. In particular, hedgers with high risk aversion and short horizon reduce hedge portfolio risk but achieve inferior utility in comparison to those with low aversion.     

Multivariate models for operational risk

Böcker and Klüppelberg [Risk Mag., 2005, December, 90–93] presented a simple approximation of OpVaR of a single operational risk cell. The present paper derives approximations of similar quality and simplicity for the multivariate problem. Our approach is based on the modelling of the dependence structure of different cells via the new concept of a Lévy copula.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.     

Dynamic programming and mean-variance hedging with partial execution risk

In this paper I consider a hedging problem in an illiquid market where there is a risk that the hedger’s order to buy or sell the underlying asset may be executed only partially. In this setting, I find a mean-variance optimal hedging strategy by the dynamic programming method. The solution contains a new endogenous state variable representing the current position in the underlying. The exogenous coefficients in the solution are given by recursive formulas which can be calculated efficiently in Markov models. I illustrate effects of the partial execution risk in several examples.      

Looking for risk premium and contagion in Asia-Pacific foreign exchange markets

This article tests pure contagion effects among four Asian foreign exchange markets, namely, Japan, Hong Kong, Singapore, and Taiwan during the 1997 Asian crisis. A conditional version of international capital asset pricing model (ICAPM) in the absence of purchasing power parity (PPP) is used to control for economic fundamentals or systematic risks. The empirical results show strong contagion effects in both conditional means and volatilities of those markets after systematic risks have been accounted for. Specifically, the contagion-in-mean effects are mainly driven by the past return shocks in Hong Kong, Singapore, and Taiwan. As for contagion in volatility, the lead/lag relationships appear to be multidirectional among Japan, Singapore, and Taiwan, but between Hong Kong and Singapore, and between Hong Kong and Taiwan, they are unidirectional, with Hong Kong playing the dominant role in generating negative volatility shocks. In addition, the conditional ICAPM with asymmetric multivariate general autoregressive conditional heteroscedastic in mean (MGARCH(1,1)-M) structure is able to explain/predict on average 17.28% of the return variations in those markets. Therefore, this study provide a further evidence that the time-varying risk premium is a very strong candidate in explaining the predictable excess return puzzle [Lewis, K. K. (1994). Puzzles in international financial markets. NBER Working Paper No. 4951] since the risk premia founded in this article are not only statistically significant but also economically significant.     

Can modeling the natural gas futures market as a threshold cointegrated system improve hedging and forecasting performance?

The calculation of the hedge ratio, and therefore the effectiveness of the hedge, is dependent upon the correct specification of the relationship between the futures and spot price. Likewise, a forecast of the future spot or futures price is dependent upon the model specification. This article investigates the appropriateness of using a threshold cointegrated model of the natural gas markets as the basis for hedging and forecasting. The findings suggest that the threshold model is more appropriate for longer contract length and that the threshold model does not offer much improvement in hedging or forecasting efficiency.     

Futures prices and inflation information

This study examines the timing and speed with which inflation futures prices absorb inflation information. Results of the study show that inflation futures prices already reflect the expected inflation. Moreover, 71% of unexpected inflation has been reflected in futures prices about 25 business days prior to the Consumer Price Index (CPI) announcement, which usually coincides with the end of the CPI measurement period. Reaction to the remaining 29% occurs on and shortly after the CPI announcement date, especially on day 0 and day 2. The inflation risk premium that investors are willing to pay to avoid uncertain inflation is estimated to be 1.41% per annum.     

Rare disaster risk and the expected equity risk premium

Consistent with the predictions of rare disaster models, we find that a proxy for the time‐varying probability of rare disasters helps to explain fluctuations in expectations of the equity risk premium. Our proxy for disaster risk is a recently developed measure of global political instability, and the expected market risk premium is from Value Line analysts' expected stock returns. Consistent with long‐run risk models, uncertainty about expected GDP growth and expected consumption growth is also significantly positively related to the expected market risk premium. We obtain similar results when we use the earnings–price ratio and the dividend–price ratio as proxies for the expected market risk premium.     

Pricing and hedging European options with discrete-time coherent risk

The aim of the paper is to provide as explicit as possible expressions for upper/lower prices and for superhedging/subhedging strategies based on discrete-time coherent risk measures. This is done on three levels of generality. For a general infinite-dimensional model, we prove the fundamental theorem of asset pricing. For a general multidimensional model, we provide expressions for prices and hedges. For a wide class of models, in particular, including GARCH, we give more concrete formulas, a sufficient condition for the uniqueness of a hedging strategy, and a numerical algorithm.      

PDE approach to valuation and hedging of credit derivatives

This paper presents a PDE approach in a Markovian setting to hedge defaultable derivatives. The arbitrage price and the hedging strategy for an attainable contingent claim are described in terms of solutions of a pair of coupled PDEs. For some standard examples of defaultable claims, we provide explicit formulae for prices and hedging strategies.     

Multivariate risks and depth-trimmed regions

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship. I. Molchanov supported by Swiss National Science Foundation Grant 200020-109217.     

Multivariate risk aversion and uninsurable risks: Theory and applications

The objective of this paper is to develop conditions for global multivariate comparative risk aversion in the presence of uninsurable, or background, risks, and thus generalize Kihlstrom and Mirman [1974] and Karni [1979,1989]. We analyze von Neumann-Morgenstern (VNM) utility functionsas well as smooth preference functionals which are nonlinear in distribution but locally linear in probabilities. In each case we provide an economic application which illustrates how our theorems can be used. We analyze a risk sharing, a portfolio choice, and a labor supply problem for VNM utility functions, and the optimal allocation of effort to risky technologies in the presence of a random supply (or quality) of a public good for nonlinear preference functionals. We consider thecase where the random variables are mean-independent as well as the case where they are independent. In the labor supply application for VNM utility functions, we show that if the two risks are independent, the comparative statics effect of greater risk aversion on labor supply in the presence of a background non-wage income risk is determined by a monotonic relationship between labor supply and the wage rate under certainty. That is, we extend the applicability of the Diamond-Stiglitz [1974]-Kihlstrom-Mirman [1974]single-crossing property to the case where an independent background risk is present.     

Displacement risk and asset returns

We study asset-pricing implications of innovation in a general-equilibrium overlapping-generations economy. Innovation increases the competitive pressure on existing firms and workers, reducing the profits of existing firms and eroding the human capital of older workers. Due to the lack of inter-generational risk sharing, innovation creates a systematic risk factor, which we call “displacement risk.” This risk helps explain several empirical patterns, including the existence of the growth-value factor in returns, the value premium, and the high equity premium. We assess the magnitude of displacement risk using estimates of inter-cohort consumption differences across households and find support for the model.     

News sentiment and sovereign credit risk

We explore the impact of media content on sovereign credit risk. Our measure of media tone is extracted from the Thomson Reuters News Analytics database. As a proxy for sovereign credit risk we consider credit default swap (CDS) spreads, which are decomposed into their risk premium and default risk components. We find that media tone explains and predicts CDS returns and is a mixture of noise and information. Its effect on risk premium induces a temporary change in investors’ appetite for credit risk exposure, whereas its impact on the default component leads to reassessments of the fundamentals of sovereign economies.     

基于藤结构Copula的多元信用风险相关性度量模型及其比较

在信贷组合管理的框架下,以行业信用风险为基础,构建了基于藤结构Copula的多元信用风险相关性度量模型,并以2006年6月～2010年12月中国上市公司数据对模型进行了参数估计,发现Canoni-cal藤结构更适合度量行业信用风险相关性,以电力煤气及水的生产为代表的强周期性行业对信用风险起着引导作用。     

Hazard rate for credit risk and hedging defaultable contingent claims

We provide a concise exposition of theoretical results that appear in modeling default time as a random time, we study in details the invariance martingale property and we establish a representation theorem which leads, in a complete market setting, to the hedging portfolio of a vulnerable claim. Our main result is that, to hedge a defaultable claim one has to invest the value of this contingent claim in the defaultable zero-coupon.Received: April 2003Mathematics Subject Classification: 91B24, 91B29, 60G46JEL Classification: G10The authors would like to thank D. Becherer and J.N. Hugonnier for interesting discussions and the anonymous referee whose pertinent questions on the first version of this paper help them to clarify the proofs. All remaining errors are ours.     

Information content and the contractual nature of hedging derivative incomes

In a sample of 87 banks representing 631 bank-years for the period 1996–2003, we examine whether information content of hedging derivative incomes is predicated on the contractual nature of the derivative. Of particular interest are the different abnormal trading volume reactions to incomes arising from executory contracts (i.e., cash flow and net investment hedges) and incomes arising from nonexecutory contracts (i.e., fair value hedges). We find a positive and significant relationship between two alternative measures of abnormal trading volume and incomes arising from cash flow and net investment hedges. The results are robust in an equity valuation framework. Our findings suggest that derivative incomes are informative, notably those incomes that are related to executory contracts. An implication for standard setters is that the complex rules for disaggregating incomes on hedging derivatives provide valuable information to the market.     

Hedging jump risk,expected returns and risk premia in jump-diffusion economies

This article presents a pure exchange economy that extends Rubinstein [Bell J. Econ. Manage. Sci., 1976, 7, 407–425] to show how the jump-diffusion option pricing model of Black and Scholes [J. Political Econ., 1973, 81, 637–654] and Merton [J. Financ. Econ., 1976, 4, 125–144] evolves in gamma jumping economies. From empirical analysis and theoretical study, both the aggregate consumption and the stock price are unknown in determining jumping times. By using the pricing kernel, we determine both the aggregate consumption jump time and the stock price jump time from the equilibrium interest rate and CCAPM (Consumption Capital Asset Pricing Model). Our general jump-diffusion option pricing model gives an explicit formula for how the jump process and the jump times alter the pricing. This innovation with predictable jump times enhances our analysis of the expected stock return in equilibrium and of hedging jump risks for jump-diffusion economies.