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.     

Risk measure pricing and hedging in incomplete markets

This article attempts to extend the complete market option pricing theory to incomplete markets. Instead of eliminating the risk by a perfect hedging portfolio, partial hedging will be adopted and some residual risk at expiration will be tolerated. The risk measure (or risk indifference) prices charged for buying or selling an option are associated to the capital required for dynamic hedging so that the risk exposure will not increase. The associated optimal hedging portfolio is decided by minimizing a convex measure of risk. I will give the definition of risk-efficient options and confirm that options evaluated by risk measure pricing rules are indeed risk-efficient. Relationships to utility indifference pricing and pricing by valuation and stress measures will be discussed. Examples using the shortfall risk measure and average VaR will be shown. The work of Mingxin Xu is supported by the National Science Foundation under grant SES-0518869. I would like to thank Steven Shreve for insightful comments, especially his suggestions to extend the pricing idea from using shortfall risk measure to coherent ones, and to study its relationship to utility based derivative pricing. The comments from the associate editor and the anonymous referee have reshaped the paper into its current version. The paper has benefited from discussions with Freddy Delbaen, Jan Večeř, David Heath, Dmitry Kramkov, Peter Carr, and Joel Avrin.     

The relative pricing of European dividend futures and their predictive abilities for index returns

We use dividend futures prices to derive a dividend future discount model. Arbitrage arguments postulate that the sum of discounted dividend futures prices should equal the index price, i.e. the sum of discounted dividends. We analyze whether this relation holds and find that the two valuation approaches lead to a different valuation of expected dividends. These observations indicate that dividend futures and index prices seem to provide the investor with different information on future dividends. We further show that the difference in valuation can be used to forecast index returns and show how an investment strategy can exploit this predictability.     

Pursuit of complete markets: the missing perspectives

India's financial sector reform path has been a measured, cautious and steady process, aiming to attain standards of international best practice, but fine-tuning the process keeping the context in view. Although much has been achieved, this paper focuses on the remaining gaps. But post-crisis the pursuit of complete markets is no longer the holy grail of regulation. In particular, underlying needs and systemic risk assessment should drive the regulatory framework for cash markets, not the elusive search for market completion and efficient derivatives markets.     

The interrelatedness of global equity markets, money markets, and foreign exchange markets

This article investigates different aspects of global financial markets, specifically relationships among equity markets, money markets, and foreign exchange markets across countries. To represent the three major financial markets of the world, Japan is the proxy for Asia, Germany is the proxy for Europe, and the United States is the proxy for North America. Strong evidence exists that international money markets and international equity markets are becoming increasingly integrated over time. This article incorporates foreign exchange values as partial determinants of equity returns and money market returns and investigates the interactions among these three asset markets from a global perspective.     

Daily volatility behavior in Chinese futures markets

This study examines the daily volatility of four futures contracts on Chinese futures exchanges (copper, mungbeans, soybeans and wheat). We find that returns have asymmetric effects on volatility, meaning that negative returns have a greater effect on volatility than positive returns do. Volume is positively related to volatility, open interest is negatively related to volatility, and the extent of large-volume traders’ participation is also positively related to volatility. We conjecture that the global patterns of volatility relationship, which have become more pronounced in Chinese markets in more recent years, are attributable to the results of ongoing government attempts to achieve transparency and better disclosure.     

The price of power: The valuation of power and weather derivatives

Pricing contingent claims on power presents numerous challenges due to (1) the unique behavior of power prices, and (2) time-dependent variations in prices. We propose and implement a model in which the spot price of power is a function of two state variables: demand (load) and fuel price. In this model, any power derivative price must satisfy a PDE with boundary conditions that reflect capacity limits and the non-linear relation between load and the spot price of power. Moreover, since power is non-storable and demand is not a traded asset, the power derivative price embeds a market price of risk. Using inverse problem techniques and power forward prices from the PJM market, we solve for this market price of risk function. During 1999–2001, the upward bias in the forward price was as large as $50/MWh for some days in July. By 2005, the largest estimated upward bias had fallen to $19/MWh. These large biases are plausibly due to the extreme right skewness of power prices; this induces left skewness in the payoff to short forward positions, and a large risk premium is required to induce traders to sell power forwards. This risk premium suggests that the power market is not fully integrated with the broader financial markets.     

Option pricing with random volatilities in complete markets

This article presents the theory of option pricing with random volatilities in complete markets. As such, it makes two contributions. First, the newly developed martingale measure technique is used to synthesize results dating from Merton (1973) through Eisenberg, (1985, 1987). This synthesis illustrates how Merton's formula, the CEV formula, and the Black-Scholes formula are special cases of the random volatility model derived herein. The impossibility of obtaining a self-financing trading strategy to duplicate an option in incomplete markets is demonstrated. This omission is important because option pricing models are often used for risk management, which requires the construction of synthetic options.Second, we derive a new formula, which is easy to interpret and easy to program, for pricing options given a random volatility. This formula (for a European call option) is seen to be a weighted average of Black-Scholes values, and is consistent with recent empirical studies finding evidence of mean-reversion in volatilities.Helpful comments from an anonymous referee are greatly appreciated.     

A valuation algorithm for indifference prices in incomplete markets

A probabilistic iterative algorithm is constructed for indifference prices of claims in a multiperiod incomplete model. At each time step, a nonlinear pricing functional is applied that isolates and prices separately the two types of risk. It is represented solely in terms of risk aversion and the pricing measure, a martingale measure that preserves the conditional distribution of unhedged risks, given the hedgeable ones, from their historical counterparts.Received: 1 September 2003, Mathematics Subject Classification: 93E20, 60G40, 60J75JEL Classification: C61, G11, G13The second author acknowledges partial support from NSF Grants DMS 0102909 and DMS 0091946.     

Sequential information arrival in the Finnish stock index derivatives markets

This paper investigates the hypothesis of sequential information arrival in the Finnish stock index futures and options markets. With no short selling restrictions in the derivatives markets, no causality relationships between returns and trading volume are observed. However, by using the so-called call-put signal, based on call and put volumes, causality between returns and volume is found supporting the hypothesis of sequential information arrival. In addition, it is discovered that the increased volume in stock index options relative to index futures has significantly increased their importance in the intermarket price discovery process.     

Risk and return in residential spatial markets: An empiric and theoretic model

The paper is concerned with price and rent fluctuations in predominantly owner-occupied residental real estate. It presents the owner-occupier household as a housing consumer as well as an investor. It conjectures that since risk and return are known to be positively related in financial markets, they might also be thus related in residential real estate markets. If that is so, neighborhoods that are known to yield high returns will be the ones less price and rent stable than low yielding ones.The Capital Asset Pricing Model is not helpful in explaining a possible risk/return relationship in housing markets. Its major assumption about portfolio diversification is contrary to the nature of owner-occupied residential real estate. An owner occupier household, by definition, holds one unit of the asset and acts simultaneously as an investor and consumer of housing. For the capital market investor, investment and consumption decisions are separable. Therefore, a new theoretical model of consumer choice is proposed. Tel-Aviv price and rent data during a volatile market period are used for testing the main risk/return conjecture as well as other related hypotheses stemming from the model. The findings lend support to the conjecture and shed light on possible spatial determinants of owners' risk.     

Non-synchronous trading and testing for market integration in Central European emerging markets

The paper contributes to the literature on integration of stock markets by addressing the issue of non-synchronous trading. We argue that controlling for time differences in trading hours of stock markets is important and show that time-adjustment improves estimates of market integration. We also show that using weekly frequency does not sidestep the consequences of the time-match problem but leads to significant loss of information. We show that the nature of integration of stock exchanges operating in the Czech Republic, Hungary, and Poland with the stock markets of Germany, UK and US in the period 1994–2004 is very dynamic. Finally, the study shows that the autocorrelation of returns on the main market indices of these emerging markets have declined over time.     

Price discovery in spot and futures markets: a reconsideration

We reconsider the issue of price discovery in spot and futures markets. We use a threshold error correction model to allow for arbitrage opportunities to have an impact on the return dynamics. We estimate the model using quote midpoints, and we modify the model to account for time-varying transaction costs. We find that (a) the futures market leads in the process of price discovery and (b) the presence of arbitrage opportunities has a strong impact on the dynamics of the price discovery process.     

Pacific Basin stock markets and international capital asset pricing

In this paper, we follow Harvey (1991) to investigate whether rates of return on Pacific Basin stock markets can be explained by conditional version of International Capital Asset Pricing Model (ICAPM), which allows for time-varying expected returns, variances, and covariances. The results show that most individual Pacific Basin markets can be described by the conditional ICAPM. However, the multiple markets' tests do not support the conditional ICAPM formulation, and the estimates of world reward to risk ratio are not the same across these markets. Furthermore, the Ghysels and Hall test (Ghysels & Hall, 1990a, 1990b) shows that the estimates of parameter are also unstable in the conditional ICAPM formulation. This implies that it is difficult to use world return to describe the relationship between expected return and risk for the Pacific Basin stock markets.     

Stochastic volatility and time-varying country risk in emerging markets

This study suggests an alternative method to estimate time-varying country risk. We first apply a new multivariate stochastic volatility (SV) model to a set of emerging stock markets. To estimate the SV model, we use a Bayesian Markov chain Monte Carlo simulation procedure. By applying the deviance information criterion, we show that the new model performs well relative to alternative multivariate SV models. We then compute the conditional betas for the different markets and compare the results with an often-used procedure based on multivariate GARCH models. We show that the new multivariate SV model more accurately captures the time-varying nature of country risk. The conditional betas show signs of large variations, indicating the importance of taking time-varying country risk into consideration when managing emerging market portfolios.     

Investigating efficiency in betting markets: Evidence from the Greek 6/49 Lotto

In this paper we investigate the existence of profit opportunities in the Greek market for the 6/49 Lotto. Under the assumption of random number selection we find evidence suggesting that the market is efficient. Because number selection is found to deviate from randomness, we further investigate the existence of profit opportunities due to number unpopularity. The evidence suggests that although unpopular numbers exist, they are not sufficiently unpopular so as to generate positive expected payoffs.     

New entry,strategic diversity and efficiency in soccer betting markets: the creation and suppression of arbitrage opportunities

ABSTRACT

We find that prices offered by competing bookmakers within the same quote-driven soccer (football) betting market provide arbitrage opportunities. However, the management practices of bookmakers prevent informed bettors exploiting these in practice. We identify two groups of bookmakers, ‘position-takers’ and ‘book-balancers’. Position-takers alter their odds infrequently, while actively restricting informed traders. Book-balancers actively manage inventory by adjusting odds, and place few restrictions on their customers. We identify 545 arbitrage portfolios, and find that around 50% would require a bet on the favourite at the position-taking bookmaker. The management practices of position-takers generally prevent these opportunities being exploited in practice.     

Stock index dynamics and derivatives pricing with stochastic interest rates

The paper analyzes the equilibrium valuation of stock index derivatives in an economy with stochastic interest rates and with a representative agent having time-additive power utility. The equilibrium short interest rate dynamics and the equilibrium term structure of interest rates are described by an affine one-factor term structure model. In equilibrium the value of the stock index is a non-trivial function of the short interest rate. The paper investigates the consequences of the induced stock index dynamics for the theoretical spreads between index forward prices and index futures prices and the consequences for the valuation of options on stock index futures.The paper was written while the author was a visiting scholar at Department of Finance, Kellogg Graduate School of Management, Northwestern University. I thank for helpful comments and suggestions from Gurdip Bakshi, Avi Bick, Menachem Brenner (the editor), Zhiwu Chen, San-Lin Chung, Mark Fisher, Andreas Höger, Marti Subrahmanyam, two anonymous referees, and participants at the Western Finance Association meeting in San Diego, the European Financial Management Association meeting in Istanbul, the European Finance Association meeting in Vienna, and the Center of Analytical Finance workshop at University of Aarhus. Financial support from the Danish Natural Science and Social Science Reasearch Councils is gratefully acknowledged.