Do S&P 500 index options violate the martingale restriction?

The study tests Longstaff's martingale restriction on S&P 500 index options over the period 1990–1994. Assuming the S&P index follows a lognormal distribution results in systematic violations of the martingale restriction, the implied index value from options consistently overestimating the market value. Adopting a generalized distribution, allowing for nonnormal third and fourth moments, produces economically insignificant rejections of the martingale restriction. A simulation analysis supports the empirical results from the lognormal model in the presence of nonnormal skewness and kurtosis. Overall, the results support the conclusion that the no-arbitrage assumption coupled with the generalized distribution offers a good working model for S&P index options over the period studied. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 499–521, 1999     

Futures price limit moves as options

This note demonstrates that an asset's price in an environment with price limit rules can be replicated by the price of a portfolio consisting of a riskless asset and two synthetic options. A procedure is developed to unbundle the unobservable option values imbedded in the actual futures price and impute a theoretical true futures price. Using this framework, evidence from the Treasury Bond futures market suggests that theoretical true futures prices diverge from actual futures prices, on average, 3 h prior to the activation of price limit rules, indicating that price limit moves might be predictable. The reversal of both the actual futures prices and the theoretical futures prices back within the limit range after a limit move provides support for the possibility that traders tend to overreact when market prices are near price limits. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:901–913, 2002     

What moves option‐implied bond market expectations?

This article examines the impact of macroeconomic news announcements on bond market expectations, as measured by option‐implied probability distributions of future bond returns. The results indicate that expected bond market volatilities increase in response to higher‐than‐expected inflation and unemployment announcements. Furthermore, the asymmetries in bond market expectations are found to be affected mostly by surprises in inflation and economic production figures. In particular, it is found that higher‐than‐expected inflation announcements cause optionimplied bond return distributions to become more negatively skewed or less positively skewed, implying a shift in market participants' perceptions toward future increases in interest rates. Finally, the results indicate that market expectations of future extreme movements in bond prices are virtually unaffected by macroeconomic news releases. Some evidence is found, however, that suggests that after extreme surprises in inflation announcements market participants attach higher probabilities for extreme movements in bond prices. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:817–843, 2005     

The realized volatility of FTSE‐100 futures prices

Five‐minute returns from FTSE‐100 index futures contracts are used to obtain accurate estimates of daily index volatility from January 1986 to December 1998. These realized volatility measures are used to obtain inferences about the distributional and autocorrelation properties of FTSE‐100 volatility. The distribution of volatility measured daily is similar to lognormal while the volatility time series has persistent positive autocorrelation that displays long‐memory effects. The distribution of daily returns standardized using the measures of realized volatility is shown to be close to normal, unlike the unconditional distribution. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:627–648, 2002     

THEORY AND CALIBRATION OF SWAP MARKET MODELS

This paper introduces a general framework for market models, named Market Model Approach, through the concept of admissible sets of forward swap rates spanning a given tenor structure. We relate this concept to results in graph theory by showing that a set is admissible if and only if the associated graph is a tree. This connection enables us to enumerate all admissible models for a given tenor structure. Three main classes are identified within this framework and correspond to the co-terminal, co-initial, and co-sliding model. We prove that the LIBOR market model is the only admissible model of a co-sliding type. By focusing on the co-terminal model in a lognormal setting, we develop and compare several approximating analytical formulae for caplets, while swaptions can be priced by a simple Black-type formula. A novel calibration technique is introduced to allow simultaneous calibration to caplet and swaption prices. Empirical calibration of the co-terminal model is shown to be faster, more robust, and more efficient than the same procedure applied to the LIBOR market model. We then argue that the co-terminal approach is the simplest and most convenient market model for pricing and hedging a large variety of exotic interest-rate derivatives.     

Modeling seasonality in agricultural commodity futures

The stochastic behavior of agricultural commodity prices is investigated using observations of the term structures of futures prices over time. The continuous time dynamics of (log‐) commodity prices are modeled as a sum of a deterministic seasonal component, a non‐stationary state‐variable, and a stationary state‐variable. Futures prices are established by standard no‐arbitrage arguments and the Kalman filter methodology is used to estimate the model parameters for corn futures, soybean futures, and wheat futures based on weekly data from the Chicago Board of Trade for the period 1972–1997. Furthermore, in a discussion of the estimated seasonal patterns in agricultural commodity prices, the paper provides empirical evidence on the theory of storage that predicts a negative relationship between stocks of inventory and convenience yields; in particular, convenience yields used in this analysis are extracted using the Kalman filter. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:393–426, 2002     

Approximating Large Diversified Portfolios

This paper considers a financial market with asset price dynamics modeled by a system of lognormal stochastic differential equations. A one‐dimensional stochastic differential equation for the approximate evolution of a large diversified portfolio formed by these assets is derived. This identifies the asymptotic dynamics of the portfolio as being a lognormal diffusion. Consequentially an efficient way for computing probabilities, derivative prices, and other quantities for the portfolio are obtained. Additionally, the asymptotic strong and weak orders of convergence with respect to the number of assets in the portfolio are determined.     

An analysis of the relationship between electricity and natural‐gas futures prices

This article analyzes the relationship between electricity futures prices and natural‐gas futures prices. We find that the daily settlement prices of New York Mercantile Exchange's (NYMEX's) California–Oregon Border (COB) and Palo Verde (PV) electricity futures contracts are cointegrated with the prices of its natural‐gas futures contract. The coefficient of natural‐gas futures prices in our model of COB electricity futures prices is not significantly different from the coefficient of gas prices in our model of PV electricity although there are differences in the production of electricity in these two service areas. The coefficients in our model do reflect differences in the consumption of electricity in the COB and PV service areas, however. Our trading‐rule simulations indicate that the statistically significant mean reversion found in the relationship between electricity and natural‐gas futures prices also is economically significant in both in‐sample and out‐of‐sample tests. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:95–122, 2002     

EXACT SOLUTION OF A MARTINGALE STOCHASTIC VOLATILITY OPTION PROBLEM AND ITS EMPIRICAL EVALUATION

Exact explicit solution of the log-normal stochastic volatility (SV) option model has remained an open problem for two decades. In this paper, I consider the case where the risk-neutral measure induces a martingale volatility process, and derive an exact explicit solution to this unsolved problem which is also free from any inverse transforms. A representation of the asset price shows that its distribution depends on that of two random variables, the terminal SV as well as the time average of future stochastic variances. Probabilistic methods, using the author's previous results on stochastic time changes, and a Laplace–Girsanov Transform technique are applied to produce exact explicit probability distributions and option price formula. The formulae reveal interesting interplay of forces between the two random variables through the correlation coefficient. When the correlation is set to zero, the first random variable is eliminated and the option formula gives the exact formula for the limit of the Taylor series in Hull and White's (1987) approximation. The SV futures option model, comparative statics, price comparisons, the Greeks and practical and empirical implementation and evaluation results are also presented. A PC application was developed to fit the SV models to current market prices, and calculate other option prices, and their Greeks and implied volatilities (IVs) based on the results of this paper. This paper also provides a solution to the option implied volatility problem, as the empirical studies show that, the SV model can reproduce market prices, better than Black–Scholes and Black-76 by up to 2918%, and its IV curve can reproduce that of market prices very closely, by up to within its 0.37%.     

Local costs of distribution,international trade costs and micro evidence on the law of one price

This paper connects trade flows to deviations from the law of one price (LOOP) in a structural model of trade and retailing. It accounts for the observed cross-country dispersion in prices of goods, based on retail price survey data, by focusing on two sources of goods market segmentation — (i) international trade costs, and (ii) non-traded input costs of distribution. I find that a multi-sector Ricardian trade model, ala Eaton–Kortum, augmented with a distribution sector, can account for the average price dispersion for a basket of goods fully and generates 70% of the variation in price dispersion across goods within the basket. While tradability of goods is important in explaining the average price dispersion for the basket of goods, distribution costs are important in explaining why, within the basket, some goods show more price dispersion than others.     

A Study of Arbitrage Efficiency Between the FTSE‐100 Index Futures and Options Contracts

Despite the importance of the London markets and the significance of the relationship for market makers, little published research is available on arbitrage between the FTSE‐100 Index futures and the FTSE‐100 European index options contracts. This study uses the put–call–futures parity condition to throw light on the relationship between options and futures written against the FTSE Index. The arbitrage methodology adopted in this study avoids many of the problems that have affected prior research on the relationship between options or futures prices and the underlying index. The problems that arise from nonsynchroneity between options and futures prices are reduced by the matching of options and futures prices within narrow time intervals with time‐stamped transaction data. This study allows for realistic trading and market‐impact costs. The feasibility of strategies such as execute‐and‐hold and early unwinding is examined with both ex‐post and ex‐ante simulation tests that take into consideration possible execution time lags for the arbitrage trade. This study reveals that the occurrence of matched put–call–futures trios exhibits a U‐shaped intraday pattern with a concentration at both open and close, although the magnitude of observed mispricings has no discernible intraday pattern. Ex‐post arbitrage profits for traders facing transaction costs are concentrated in at‐the‐money options. As in other major markets, despite important microstructure differences, opportunities are generally rapidly extinguished in less than 3 min. The results suggest that arbitrage opportunities for traders facing transaction costs are small in number and confirm the efficiency of trading on the London International Financial Futures and Options Exchange. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:31–58, 2002     

Time‐varying market price of risk in the crude oil futures market

In this study, a three‐factor model of crude oil prices is estimated, which incorporates a time‐varying market price of risk. The model is able to accurately capture the term structure of futures prices with evidence suggesting that risk premiums in the crude oil market are time‐varying. Using the cross‐section of futures prices, we estimate a time‐series of the market price of risk in the crude oil market implied by the model. We find that the risk premiums in the crude oil market are driven by the same risk factors as equity and bond markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:779–807, 2011     

Pricing and hedging S&P 500 index options with Hermite polynomial approximation: empirical tests of Madan and Milne's model

The universal use of the Black and Scholes option pricing model to value a wide range of option contracts partly accounts for the almost systematic use of Gaussian distributions in finance. Empirical studies, however, suggest that there is an information content beyond the second moment of the distribution that must be taken into consideration.This article applies a Hermite polynomial-based model developed by Madan and Milne (1994) to an investigation of S&P 500 index option prices from the CBOE when the distribution of the underlying index is unknown. The model enables us to incorporate the non-normal skewness and kurtosis effects empirically observed in option-implied distributions of index returns. Out-of-sample tests confirm that the model outperforms Black and Scholes in terms of pricing and hedging. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 735–758, 1999     

Economic and political risks of world oil markets

The present easing on the world oil market could foster the illusion that energy problems are now resolved. During 1981 various oil-producing countries (OPEC and non-OPEC alike) found they had to cut their prices. OPEC production has had to be reduced by about one-third from the 1979 level of 31 mbd¹. Last September’s OPEC output of 20 mbd was the lowest monthly figure for 12 years and has by year-end 1981 recovered to just 22 mbd. “The OPEC is no longer able to dictate prices; there is more oil than the market can take.” These are typical recent comments, but they reflect too short-term and superficial a view. The real issue is the question whether energy supplies are secure in thelong term, too, and whether energy itself presents a danger for general economic and political developments.     

Option pricing under extended normal distribution

This article proposes a closed pricing formula for European options when the return of the underlying asset follows extended normal distribution, that is, any different degrees of skewness and kurtosis relative to the normal distribution induced by the Black‐Scholes model. The moment restriction is suggested, so that the pricing model under any arbitrary distribution for an underlying asset must satisfy the arbitrage‐free condition. Numerical experiments and comparison of empirical performance of the proposed model with the Black‐Scholes, ad hoc Black‐Scholes, and Gram‐Charlier distribution models are carried out. In particular, an estimation of implied parameters such as standard deviation, skewness, and kurtosis of the return on the underlying asset from the market prices of the KOSPI 200 index options is made, and in‐sample and out‐of‐sample tests are performed. These results not only support the previous finding that the actual density of the underlying asset shows skewness to the left and high peaks, but also demonstrate that the present model has good explanatory power for option prices. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:845–871, 2005     

What moves the tail? The determinants of the option‐implied probability density function of the DAX index

In this article a study of the option‐implied probability density function (PDF) of German stock returns is presented. The use of option prices allows for the quantification of the risk‐neutral probability of large movements in the DAX index. Using daily data for the period from December 1995 to May 2002, the mixture of log‐normals specification with a constant maturity of 49 days is estimated. The time series behavior of the option‐implied PDF during episodes of market turbulence is discussed at the outset. The main purpose of the study is to consider the relationship of summary measures of the option‐implied PDF to macroeconomic news, information from the U.S. stock market, and risk premia. The results suggest the existence of a significant spillover from the U.S. stock market. Returns and the volatility of U.S. stock prices have a strong effect on changes in the lower DAX tail probability, but also on the higher moments of the option‐implied PDF. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:515–536, 2005     

The new market for volatility trading

This study analyses the new market for trading volatility; VIX futures. We first use market data to establish the relationship between VIX futures prices and the index itself. We observe that VIX futures and VIX are highly correlated; the term structure of average VIX futures prices is upward sloping, whereas the term structure of VIX futures volatility is downward sloping. To establish a theoretical relationship between VIX futures and VIX, we model the instantaneous variance using a simple square root mean‐reverting process with a stochastic long‐term mean level. Using daily calibrated long‐term mean and VIX, the model gives good predictions of VIX futures prices under normal market situation. These parameter estimates could be used to price VIX options. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 30:809–833, 2010     

Price Differences in Consumer Goods in Retail Markets

Abstract

This study analyses the effects that competition causes on the dispersion of prices in the mass market products. Therefore, a model is proposed that integrates the vertical, spatial and market environment factors that make up the competitive structure of the retail trade distribution sector. The results obtained, after processing a database of more than 19,000 records, indicate that various indicators of these three levels of competition exercise a decisive influence on determining the final prices of the analysed products. Likewise, the research allows verifying that there are significant differences in the effect caused by the analysed factors on the dispersion of prices, thereby depending on the considered product category (packaged goods versus fresh food).     

The forward pricing function of the shipping freight futures market

This article investigates the unbiasedness hypothesis of futures prices in the freight futures market. Being the only market whose underlying asset is a service, it sets it apart from other markets investigated so far in the literature. Cointegration techniques, employed to examine this hypothesis, indicate that futures prices one and two months before maturity are unbiased forecasts of the realized spot prices, whereas a bias exists in the three-months futures prices. This mixed evidence is in agreement with studies in other markets and suggests that the acceptance or rejection of unbiasedness depends on the idiosyncrasies of the market under investigation and on the time to maturity of the contract. Despite the existence of a bias in the three-months prices, futures prices for all maturities are found to provide forecasts of the realized spot prices that are superior to forecasts generated from error correction, ARIMA, exponential smoothing, and random walk models. Hence it appears that users of the BIFFEX market receive accurate signals from the futures prices (regarding the future course of cash prices) and can use the information generated by these prices to guide their physical market decisions. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 353–376, 1999     

On estimating an asset's implicit beta

A.F. Siegel (1995) has developed a technique with which the systematic risk of a security (beta) can be estimated without recourse to historical capital market data. Instead, beta is estimated implicity from the current market prices of exchange options that enable the exchange of a security against shares on the market index. Because this type of exchange options is not currently traded on the capital markets, Siegel's technique cannot yet be used in practice. This study will show that beta can also be estimated implicitly from the current market prices of plain vanilla options, based on the capital asset pricing model. Empirical evidence on implicit betas is provided using prices of exchange options from the European Derivatives Exchange Market (EUREX) over years 2000 to 2004. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:961–979, 2007