Valuation of futures and commodity options with information costs

In this article, futures and commodity options are analyzed in the context of Merton's (1987) model of capital market equilibrium with incomplete information. First, following Dusak (1973) and Black (1976), the conditions under which Merton's model can be applied to the valuation of forward and futures contracts are proposed. Then an application to futures markets is given. We provide a partial differential equation and the formulas for European commodity options, futures contracts, and American options in the same context. The models are simulated and compared to standard models with no information costs. We find that model prices are not significantly different from standard model prices. However, our models correct for some pricing biases in standard models. In particular, they reduce the overvaluation bias for European and American commodity options. It seems that the costs of gathering and processing information regarding the option and its underlying asset play a role in explaining the biases observed in standard models. This work can be applied to other futures markets. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 645–664, 1999     

Speculative pressure

The paper investigates the information content of speculative pressure across futures classes. Long-short portfolios of futures contracts sorted by speculative pressure capture a significant premium in commodity, currency, and equity markets but not in fixed income markets. Exposure to commodity, currency, and equity index futures’ speculative pressure is priced in the broad cross-section after controlling for momentum, carry, global liquidity, and volatility risks. The findings are confirmed by robustness tests using alternative speculative pressure signals, portfolio construction techniques, and subperiods interalia. We argue that there is an efficient hedgers-speculators risk transfer in commodity, currency, and equity index futures markets.     

Commodity tail risks

In this study, we investigate the cross-section of option-implied tail risks in commodity markets. In contrast to findings from equity markets, left and right tail risks implied by option markets are both large. Commodity-specific variables exert the largest influence on tail risk, while there is no evidence of systematic commodity factors that are linked to tail risk. Additionally, we find strong links to the equity markets, but also comovements to macroeconomic factors. Left or right tail risks are largely independent of variance risk premiums. Finally, both left and right tail risks are priced in the cross-section of commodity futures returns.     

Cross‐commodity analysis and applications to risk management

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. Although this is a well‐discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this study we are concerned with describing the joint return distribution of energy‐related commodities futures, namely power, oil, gas, coal, and carbon. The objective of the study is threefold. First, we conduct a careful analysis of empirical returns and show how the class of multivariate generalized hyperbolic distributions performs in this context. Second, we present how risk measures can be computed for commodity portfolios based on generalized hyperbolic assumptions. And finally, we discuss the implications of our findings for risk management analyzing the exposure of power plants, which represent typical energy portfolios. Our main findings are that risk estimates based on a normal distribution in the context of energy commodities can be statistically improved using generalized hyperbolic distributions. Those distributions are flexible enough to incorporate many characteristics of commodity returns and yield more accurate risk estimates. Our analysis of the market suggests that carbon allowances can be a helpful tool for controlling the risk exposure of a typical energy portfolio representing a power plant. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:197–217, 2009     

Principal components analysis for correlated curves and seasonal commodities: The case of the petroleum market

This article presents a family of term structure models that can be applied to value contingent claims in multicommodity and seasonal markets. We apply the framework to the futures contracts on crude and heating oils trading on NYMEX. We show how to deal with the problem of having to value products depending on the “whole” market, such as spread options on contracts on a single commodity maturing at different times (time‐spreads) or spread options on the added value of the products derived from the raw commodity (crack spreads). Also, we show how to build term structure models for a commodity that experiences seasonality, such as heating oil. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:1019–1035, 2002     

Price discovery in commodity derivatives: Speculation or hedging?

We investigate whether commodity futures or options markets play a more important role in the price discovery process in the six most actively traded markets: crude oil, natural gas, gold, silver, corn, and soybeans. Using new information leadership techniques, we report new evidence and report that both markets make a meaningful contribution to price discovery in recent times; however, on average, options lead futures in reflecting new information for a majority of these commodities. We find that increased speculation, rather than hedging activity, in commodity derivatives is a key determinant of price discovery in the options markets.     

中国亿元商品交易市场发展的特点及其成因

改革开放以来,我国的商品交易市场在经历了数量增长和规模扩张之后,逐渐实现了从量的变化向质的飞跃,从外延扩张到内涵提升的转变。亿元商品交易市场的成交额占全部商品交易市场总成交额的比重逐年上升,其在商品交易市场体系中的地位和作用也日益显现,辐射力不断增强,已成为我国城乡经济发展的重要推动力。     

Relationship between portfolio diversification and value at risk: Empirical evidence

This research explores the risk associated with the stocks prices in the seventeen selected companies that are listed in Indian BSE (100) National as well as portfolios of investment that are constructed from these seventeen companies employed. Additionally, for considering the possibility of international diversification, construction of portfolios of investment form stock price indexes in various emerging markets and developed countries of the world is considered. Correlations for domestically as well as internationally diversified portfolios are computed to unveil the relationship between stock prices of various firms as well as domestic and internationally diversified portfolios of investments. Further, to understand the effect of diversification on the risk associated with each of the portfolios of investments employed, value at risk analysis (VaR) is undertaken for studying the benefits associated with domestic as well as international diversification (if any).The study results show that domestic diversification lowers the expected losses associated with each of the domestic portfolios of investment employed where the international diversification substantially mitigates the portfolio risks. Results from VaR analysis reveal that diversification lowers the portfolio risks and additional reduction in portfolio risks is realized by international diversification.     

Dependence of stock and commodity futures markets in China: Implications for portfolio investment

We examine the recent trends in dependence structure between the fast-growing commodity markets and the stock markets in China. We address this issue by using copula functions that allow for measuring both average and tail dependence. Our results provide evidence of low and positive correlations between these markets, suggesting that commodity futures are a desirable asset class for portfolio diversification. By comparing the market risks of alternative portfolio strategies, we show that Chinese investors can take advantage of commodity futures during different times to realize risk diversification and downside risk reduction benefits.     

Home bias and high turnover: Dynamic portfolio choice with incomplete markets

Why do investors trade a lot in foreign assets and hold so little of them in their portfolios? This paper shows that both observations can arise naturally in the presence of nondiversifiable nontraded consumption risk when each country specializes in production, preferences exhibit consumption home bias, and asset markets are incomplete. Using a general equilibrium two-country, two-sector (tradable and nontradable) model of the world economy with production I show that low diversification occurs because variations in relative prices (i) increase the riskiness of foreign assets and (ii) facilitate risk-sharing across countries. Large and volatile capital flows are necessary to take advantage of international risk premia differentials that occur in response to productivity changes in the nontradable sector. I characterize the optimal portfolio holdings, the evolution of the investment opportunity set, the risk premium, and the dynamics of capital flows using a new methodology for solving dynamic general equilibrium models with incomplete markets and portfolio choice.     

Exchange risk and asset returns: A theoretical and empirical study of an open economy asset pricing model

This study develops a consumption-based asset pricing model in which domestic consumers can buy goods from domestic and foreign markets but can only invest in domestic markets. In this model, the exchange rate influences asset prices through the marginal utility of consumption and increases the risks investors face. We find that our model can successfully price the 25 Fama–French portfolios and industry portfolios in the Chinese market, and the exchange rate is an important pricing factor in the unconditional linear model. We also find that the exchange risk is time-varying and countercyclical, which can help to explain the countercyclicality in equity premium.     

Valuation and applications of compound basket options

This study investigates compound basket options, which are options on portfolios of options. Although they may be new to financial markets, they are available as equity basket options, equity spread options, stocks of holding companies, and collateralized debt obligations. Using moments of portfolio values, we provide formulas for pricing compound basket options. According to numerical analysis, a lower bound and a weighted average of bounds yield relatively small errors. Additionally, ignoring the compound feature increases the pricing error of equity basket options because the feature captures the capital structure and leverage effect of stock prices.     

在商品大市场建设与培育中要深入解决的几个问题

改革开放20年来,我国各类商品市场空前发展,我国商品市场建设总体上已经进入了由量的建设向质的提升的阶段。但是,要将各商品市场进一步做大做强,真正拉动区域经济增长,还应深入研究解决好几个问题。     

Managed commodity funds

The performance of managed commodity fund investments during the years l982 through 1996 is examined, both as stand-alone investments and as assets in diversified stock and bond portfolios. Nine stylized commodity fund investments are examined: randomly-selected, single-CTAs, pool, and fund portfolios; equally weighted market portfolios (EWMPs) of CTAs, pools, and funds; and value-weighted portfolios (VWMP) of CTAs, pools, and funds. Further, two subperiods are examined: 1982–1988 and 1989–1996. Based on an analysis using Sharpe ratios as the performance criterion, several types of managed commodity funds make both good stand-alone investments and good portfolio assets; an EWMP of CTAs and a VWMP of pools receive the highest ranking among the alternative commodity fund investments. It is also shown that commodity indexes are not a substitute for a managed commodity fund investment. A number of issues warrant further study: Can investors still earn consistently attractive risk-adjusted returns on managed commodity fund investments if they do not hold diversified portfolios of CTAs and pools? Also: How can such high speculative returns be earned in efficient commodity markets? And: Are CTA and pool returns high because commodity fund managers have superior trading skill? An important issue for future research is to determine whether in fact CTAs do possess such skill. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 377–411, 1999     

MEAN–VARIANCE PORTFOLIO CHOICE: QUADRATIC PARTIAL HEDGING

In this paper we investigate the problem of mean–variance portfolio choice with bankruptcy prohibition. For incomplete markets with continuous assets' price processes and for complete markets, it is shown that the mean–variance efficient portfolios can be expressed as the optimal strategies of partial hedging for quadratic loss function. Thus, mean–variance portfolio choice, in these cases, can be viewed as expected utility maximization with non-negative marginal utility.     

Efficient use of commodity futures in diversified portfolios

We provide evidence on the role of commodity futures in portfolios comprised of stocks, bonds, T‐bills, and real estate. Over the period investigated (1973–1997), Markowitz optimization over a range of risk levels gives substantial weight to commodity futures, thereby enhancing the portfolios’ returns. We find dramatically different results when we use a simple ex ante measure of monetary stringency to dichotomize the sample into expansive‐versus‐restrictive monetary‐policy periods. In periods characterized by restrictive monetary policy, commodity futures are shown to have substantial weight in the efficient portfolios, with significant return enhancement at all levels of risk. In periods characterized by expansive monetary policy, commodity futures are shown to have little or no weight in the efficient portfolios, with no return enhancement at all levels of risk. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:489–506, 2000     

Intermediary asset pricing in commodity futures returns

This paper assesses the extent to which intermediary capital (IC) risk contributes toward explaining commodity futures returns. We find that the IC effect is substantially positive and continues to grow as the financialization of commodities deepens. Positive and negative IC risks play asymmetric roles, with the effect of negative IC strengthening in recent subperiods. We further confirm the heterogeneous roles of IC across individual commodities by cross-section analyses. Overall, the effect of the positive IC risk factor varies significantly. Portfolios with low basis, low open interest, low momentum, and low liquidity earn significantly higher returns than counterparty portfolios.     

Risk Management in Agricultural Markets: A Review

This article surveys and evaluates the current state of knowledge about producers' marketing strategies to manage price and revenue risk for farm commodities. The review highlights gaps between concepts and their implementation. Many well‐developed models of price behavior exist, but appropriate characterization and estimation of the probability distributions of commodity prices remain elusive. Hence, the preferred measure of price risk is ambiguous. Numerous models of optimal marketing portfolios for farmers have been specified, but their behavior appears to be inconsistent with most, if not all, of these models. In addition, some research suggests that farmers can earn speculative profits, which is inconsistent with notions of efficient markets. The conclusions discuss what academic research can and cannot accomplish in relation to assisting producers with risk‐management decisions. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:953–985, 2001     

Do trend following strategies work in Chinese futures markets?

We examine the performance of trend following strategies in Chinese commodity futures markets. We provide evidence that trend following‐based technical trading rules yield better performance than the buy and hold strategy on both individual contracts and sorted portfolios. The outperformance is robust to transaction costs, data frequency, sub‐prime crisis, shorting constraint, delayed execution, liquidity and parameters. Finally, the profitability of the trend following strategy may be subject to data snooping bias.