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 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.     

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 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.     

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.     

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.     

Round-the-clock market efficiency and home bias: Evidence from the international Japanese government bonds futures markets

This paper examines how information is processed between almost identical international futures markets: London (LIFFE) and Tokyo (TSE) JGB futures. In these markets, variations in open-to-open changes are virtually the same as those of close-to-close changes, suggesting that information is transmitted efficiently across markets with small opening pricing errors. The overall results confirm market efficiency around the clock, yet the intraday U-shaped patterns in volume/volatility of the London JGB futures suggest home bias in international investments, indicating a less global view of trading than expected. Specifically, at the LIFFE open, London investors rush to rebalance portfolios instead of doing so at the TSE close, which is only one hour before the LIFFE opens.     

现货市场波动与商品期货合约定价

通过构建商品期货合约定价模型,证明商品期货合约价格由资本市场系统风险溢价和标的现货市场特有(非市场)风险溢价两个部分构成.商品期货市场价格影响标的商品期货价格的前提条件是存在足够多的参与商品期货市场的交易者.当标的商品现货市场需求增加.在预期商品期货合约价格为正值的情况下,都将会使商品期货合约的价格上升,扩大交易风险并增加多头收益.相反,在预期商品期货合约价格为负值的情况下,需求增长引起初级产品价格上升将使商品期货合约价格的绝对值下降,减少交易风险和引起多头损失.如果标的商品现货市场需求减少,在预期商品期货合约价格为正值的情况下,将引起商品期货合约的价格下降,减少交易风险并降低空头损失.相反,在预期商品期货合约价格为负值的情况下,商品期货合约价格的绝对值增加,扩大交易风险和增加空头收益.     

The pricing of sentiment risk in European stock markets

This paper studies whether sentiment is rewarded with a significant risk premium in the European stock markets. We examine several sentiment proxies and identify the Economic Sentiment Indicator from the EU Commission as the most relevant sentiment proxy for our sample. The analysis is performed for the contemporaneous excess returns of EA-11 stock markets in the period from February 1999 to September 2015. We apply a conditional multi-beta pricing model in order to track the variation of the sentiment risk premium over time. The results demonstrate a positive significant relationship between sentiment and contemporaneous excess returns which is consistent with previous studies. The calculated sentiment risk premium is significant as well but negative implying that an investment in EA-11 countries over the examined time period – that is bearing sentiment risk – would have been unattractive to the investors on average.     

Price discovery and volatility spillovers in index futures markets: Some evidence from Mexico

This paper investigates the hypotheses that the recently established Mexican stock index futures market effectively serves the price discovery function, and that the introduction of futures trading has provoked volatility in the underlying spot market. We test both hypotheses simultaneously with daily data from Mexico in the context of a modified EGARCH model that also incorporates possible cointegration between the futures and spot markets. The evidence supports both hypotheses, suggesting that the futures market in Mexico is a useful price discovery vehicle, although futures trading has also been a source of instability for the spot market. Several managerial implications are derived and discussed.     

Pricing of non-redundant derivatives in a complete market

We consider a complete financial market with primitive assets and derivatives on these primitive assets. Nevertheless, the derivative assets are non-redundant in the market, in the sense that the market is complete,only with their existence. In such a framework, we derive an equilibrium restriction on the admissible prices of derivative assets. The equilibrium condition imposes a well-ordering principle restricting the set of probability measures that qualify as candidate equivalent martingale measures. This restriction is preference free and applies whenever the utility functions belong to the general class of Von-Neumann Morgenstern functions. We provide numerical examples that show the applicability of the restriction for the computation of option prices.We are indebted to the editor Marti Subrahmanyam and two anonymous referees for very constructive comments. We have also benefitted from conversations with Nour Meddahi. We would like to thank seminar participants at Université de Montréal, Washington University, HEC Montréal, Ecole Polytechnique de Tunisie, Institut Henri Poincaré, Trento Mathematical Finance Conference (1997), Aspet (FIQUAM) Conference (1998) as well as the participants at the Quantitative Methods of Finance Conference, Australia, 1997.This author gratefully acknowledges the financial support of INQUIRE-Europe.     

Nonlinear serial dependence and the weak-form efficiency of Asian emerging stock markets

The objective of this paper is to re-examine the weak-form efficiency of 10 Asian emerging stock markets. Using a battery of nonlinearity tests, the statistical results reveal that all the returns series still contain predictable nonlinearities even after removing linear serial correlation from the data. The next stage of sub-sample analysis using the Hinich [Hinich, M., 1996. Testing for dependence in the input to a linear time series model. Journal of Nonparametric Statistics 6, 205–221] bicorrelation test shows that the 10 Asian series follow a pure noise process for long periods of time, only to be interspersed with brief periods of strong nonlinear dependence. The exploratory investigation found that the cross-country differences in nonlinear departure from market efficiency can be explained by market size and trading activity, while the transient burst of nonlinear periods in each individual market can be attributed largely to the occurrence of economic and political events.     

Stock and Bond Liquidity and its Effect on Prices and Financial Policies

An asset is liquid if it can be traded at the prevailing market price quickly and at low cost. We show that in addition to risk, liquidity affects asset prices and returns. Theories of asset pricing suggest that the expected return of an asset is increasing in its risk, because risk-averse investors require compensation for bearing more risk. Because investors are also averse to the costs of illiquidity and want to be compensated for bearing them, asset returns are increasing in illiquidity. Thus, asset prices should depend on two asset characteristics: risk and liquidity. This paper surveys research on the effects of liquidity on asset prices and returns, showing that liquidity is an important factor in capital asset pricing.     

Liquidity risk and arbitrage pricing theory

Classical theories of financial markets assume an infinitely liquid market and that all traders act as price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders or for modelling transaction costs. We extend the classical approach by formulating a new model that takes into account illiquidities. Our approach hypothesizes a stochastic supply curve for a securitys price as a function of trade size. This leads to a new definition of a self-financing trading strategy, additional restrictions on hedging strategies, and some interesting mathematical issues.Received: 1 November 2003, Mathematics Subject Classification: 60G44, 60H05, 90A09JEL Classification: G11, G12, G13Umut Çetin: This work was performed while Dr. Çetin was at the Center for Applied Mathematics, Cornell UniversityPhilip Protter: Supported in part by NSF grant DMS-0202958 and NSA grant MDA-904-03-1-0092 The authors wish to thank M. Warachka and Kiseop Lee for helpful comments, as well as the anonymous referee and Associate Editor for numerous helpful suggestions, which have made this a much improved paper.     

The relation between implied and realised volatility in the Danish option and equity markets

We show that the conclusions to be drawn concerning the informational efficiency of illiquid options markets depend critically on whether one carefully recognises and appropriately deals with the econometrics of the errors‐in‐variables problem. This paper examines the information content of options on the Danish KFX share index. We consider the relation between the volatility implied in an option's price and the subsequently realised index return volatility. Since these options are traded infrequently and in low volumes, the errors‐in‐variables problem is potentially large. We address the problem directly using instrumental variables techniques. We find that when measurement errors are controlled for, call option prices even in this very illiquid market contain information about future realised volatility over and above the information contained in historical volatility.     

Index arbitrage and the pricing relationship between Australian stock index futures and their underlying shares

This paper examines the mispricing of Australian stock index futures. Exogenous and endogenous price volatility is confirmed to have a positive impact on the mispricing spread, after filtering out predictable time series components. More accurate pricing associated with surprise trading volume in the underlying stocks is consistent with arbitrageurs acting to narrow price disparities relative to the futures market. Ex‐ante interest rate volatility is the primary source of risk faced by arbitrageurs and fluctuations in the transaction cost of opening index arbitrage positions influence the extent to which they drive prices towards theoretical fair values.