Pricing efficiency and market success of the BFP futures and options

During the past decade, the United States dairy industry has begun a significant restructuring toward a market-driven system. This shift brings greater milk price volatility and risk to the cash market. The recent development of dairy futures and options markets on the Chicago Mercantile Exchange (CME) could prove to be an important source of price discovery and risk management for this industry in transition. This study examines the efficiency of the CME basic formula price (BFP) futures and options markets as well as the usefulness of various option pricing models in pricing these fluid milk contracts. Several characteristics of the maturing CME BFP futures market are examined according to Black\u27s (1986) criteria for a successful market. These characteristics include: trading volume and open interest, spot price forecasting ability, and residual risk. These characteristics together do not point conclusively to long-term market failure or indicate any market inefficiency. Rather, the characteristics indicate the potential for CME BFP futures market success. Three alternative option pricing models are compared in this study: 1) the traditional Black model with historical 30-day volatilities; 2) the GARCH option pricing model with trading volume; and 3) the GARCH-in-mean option pricing model with trading volume. These models are compared to their performance in pricing BFP options in contrast to actual market premiums. Six option contracts are analyzed, including both in-the-money and out-of-the-money put and call options for January, April, and July 1999. The GARCH models lead to two approximations of predicted conditional volatility used in an option pricing formula. Using root mean square error as a comparison criterion, the Black model outperformed both GARCH models and their approximations in pricing most options. All models generally priced calls more accurately than puts. All models also priced out-of-the-money options more accurately than in-the-money options. The results indicate that the BFP futures and options markets are efficient and effective risk management tools for dairy producers. The results also indicate that the traditional Black option pricing model may price a maturing market more accurately than GARCH models or their variants. Mispricing of in-the-money options is a consistent result of all models and may be related to the unique characteristics of a maturing market

Garch Option Pricing, Valuing the Target Price Support Program, and a New Efficiency Criterion

Commodity futures price changes are not distributed normally. Their distribution is leptokurtic and asymmetric. Volatility of price changes is not constant over time. Black's option pricing model which is based on normality and constant volatility is known to systematically misprice actual option premiums. The biases in Black's model may result from not considering stochastic volatility and non-normality. A GARCH option pricing model using Monte Carlo integration meets this objective. However, a limitation of the GARCH process is that it does not model skewness. This paper introduces an asymmetric GARCH model that considers skewness. Results show that the asymmetric GARCH(2, 1 )-t process fits the data better than alternative models of Kansas City wheat futures prices. The GARCH Monte Carlo integration shows that Black's model underprices deep out-of-the-money put and call options relative to GARCH option pricing model when the true underlying process is a GARCH process. Differences between Black's model and the GARCH option model increase as time to maturity increases. When used to forecast actual option premiums, the mean squared error of the GARCH option pricing model for deep out-of-the-money put option is significantly smaller than that of Black's model. However, Black's model is sometimes better for at-the money or in-the-money options.The U.S. government deficiency payment program stabilizes farm income by transferring income from taxpayers to farmers. When revenue lost due to the acreage restriction exceeds the revenue gained from participating in the program, farmers would lose money by participating. Therefore, measuring the expected revenue from the government program is important for farmers to decide whether to participate in the program or not. This essay uses a GARCH average option pricing model to predict the implicit premium of the U.S. government deficiency payment program. The GARCH average option pricing model combines the GARCH process that considers both stochastic volatility and a nonnormal distribution with the average option pricing model that considers the average price of the underlying asset over a fixed period. A regression model based on the simulation results is provided for the GARCH average option model to be easily used to project deficiency payments. The results can be used by extension economist to help producers decide whether to participate in the program and by USDA to project participation, government cost, and to calculate advance deficiency payments.This paper develops a new risk efficiency model, Mean - Separated Target Deviations {MSD). MSD can be an interval analysis that orders risky choices for a decision maker whose monotonically increasing utility function lies within a specified range. Conventional measures of risk do not distinguish between below-target and above-target outcomes, or else impose risk neutrality for above-target outcomes. The model is motivated by the intuition that although decision makers in an investment environment are comfortable with expected value as a measure of return, they respond in different ways to potential outcomes below a target return than to potential outcomes above a target return. The measure of risk is a weighted sum of below-target deviations and above-target deviations. The weights are determined by decision maker's risk attitude. MSD is a special case of a van Neumann-Morgenstern expected utility function and of stochastic dominance. Unlike the mean-variance criterion, the MSD model considers skewness in ranking alternatives. An empirical evaluation of a decision maker's choice of wheat marketing strategies shows that the criterion yields a smaller efficient set than alternative efficiency criteria.This paper develops a new risk efficiency model, Mean - Separated Target Deviations {MSD). MSD can be an interval analysis that orders risky choices for a decision maker whose monotonically increasing utility function lies within a specified range. Conventional measures of risk do not distinguish between below-target and above-target outcomes, or else impose risk neutrality for above-target outcomes. The model is motivated by the intuition that although decision makers in an investment environment are comfortable with expected value as a measure of return, they respond in different ways to potential outcomes below a target return than to potential outcomes above a target return. The measure of risk is a weighted sum of below-target deviations and above-target deviations. The weights are determined by decision maker's risk attitude. MSD is a special case of a van Neumann-Morgenstern expected utility function and of stochastic dominance. Unlike the mean-variance criterion, the MSD model considers skewness in ranking alternatives. An empirical evaluation of a decision maker's choice of wheat marketing strategies shows that the criterion yields a smaller efficient set than alternative efficiency criteria.Agricultural Economic

Volatility forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1

A Stochastic Volatility Model With Realized Measures for Option Pricing

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options

Forecasting volatility in commodity markets

Commodity prices have historically been among the most volatile of international prices. Measured volatility (the standard deviation of price changes) has not been below 15 percent and at times has been more than 50 percent. Often the volatility of commodity prices has exceeded that of exchange rates and interest rates. The large price variations are caused by disturbances in demand and supply. Stockholding leads to some price smoothing, but when stocks are low, prices can jump sharply. As a result, commodity price series are not stationary and in some periods they jump abruptly to high levels or fall precipitously to low levels relative to their long-run average. Thus it is difficult to determine long-term price trends and the underlying distribution of prices. The volatility of commodity prices makes price forecasting difficult. Indeed, realized prices often deviate greatly from forecasted prices, which has led to the practice of giving forecasts probability ranges. But assigning probability ranges requires forecasting future price volatility, which, given uncertainties about true price distribution, is difficult. One potentially useful source of information for forecasting volatility is the volatility forecasts imbedded in the prices of options written on commodities traded in exchanges. Options give the holder the right to buy (call) or sell (put) a certain commodity at a certain date at a fixed (exercise) price. Options prices depend on several variables, one of which is the expected volatility up to the maturity date. Given a specific theoretical model, the market prices of options can be used to derive the market's expectations about price volatility and the price distribution. The authors systematically analyze different methods'abilities to forecast commodity price volatility (for several commodities). They collected the daily prices of commodity options and other variables for seven commodities (cocoa, corn, cotton, gold, silver, sugar, and wheat). They extracted the volatility forecasts implicit in options prices using several techniques. They compared several volatility forecasting methods, divided into three categories: (1) forecasts using only expectations derived form options prices; (2) forecasts using only time-series modeling; (3) forecasts that combine market expectations and time-series modeling (a new method devised for this purpose). They find that the volatility forecasts produced by method 3 outperform the first two as well as the naive forecast based on historical volatility. This result holds both in and out of sample for almost all commodities considered.Markets and Market Access,Access to Markets,Economic Theory&Research,Economic Forecasting,Science Education

Option Pricing with Orthogonal Polynomial Expansions

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the nested affine cases. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.Comment: forthcoming in Mathematical Finance, 38 pages, 3 tables, 7 figure

Arbitrage-free prediction of the implied volatility smile

This paper gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional time series of option prices corresponding to $n$ strikes (with $n$ large, e.g. $n\geq 40$) and the same maturity, is a difficult task due to the fact that option prices at any moment in time satisfy non-linear and non-explicit no-arbitrage restrictions. Hence any $n$-dimensional time series model also has to satisfy these implicit restrictions at each time step, a condition that is impossible to meet since the model innovations can take arbitrary values. We solve this problem for any n\in\NN in the context of Foreign Exchange (FX) by first encoding the option prices at each time step in terms of the parameters of the corresponding risk-neutral measure and then performing the time series analysis in the parameter space. The option price predictions are obtained from the predicted risk-neutral measure by effectively integrating it against the corresponding option payoffs. The non-linear transformation between option prices and the risk-neutral parameters applied here is \textit{not} arbitrary: it is the standard mapping used by market makers in the FX option markets (the SABR parameterisation) and is given explicitly in closed form. Our method is not restricted to the FX asset class nor does it depend on the type of parameterisation used. Statistical analysis of FX market data illustrates that our arbitrage-free predictions outperform the naive random walk forecasts, suggesting a potential for building management strategies for portfolios of derivative products, akin to the ones widely used in the underlying equity and futures markets.Comment: 18 pages, 2 figures; a shorter version of this paper has appeared as a Technical Paper in Risk (30 April 2014) under the title "Smile transformation for price prediction