A test of the beta model on Eurodollar futures options

The paper reports empirical tests of the beta model for pricing fixed-income options. The beta model resembles the Black–Scholes model with the lognormal probability distribution replaced by a beta probability distribution. The test is based on 32 817 daily prices of Eurodollar futures options and concludes that the beta model is more accurate than alternative option pricing models.     

Futures Options and the Volatility of Futures Prices

Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at-the-money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.     

Black–Scholes versus artificial neural networks in pricing FTSE 100 options

This paper compares the performance of Black–Scholes with an artificial neural network (ANN) in pricing European‐style call options on the FTSE 100 index. It is the first extensive study of the performance of ANNs in pricing UK options, and the first to allow for dividends in the closed‐form model. For out‐of‐the‐money options, the ANN is clearly superior to Black–Scholes. For in‐the‐money options, if the sample space is restricted by excluding deep in‐the‐money and long maturity options (3.4% of total volume), then the performance of the ANN is comparable to that of Black–Scholes. The superiority of the ANN is a surprising result, given that European‐style equity options are the home ground of Black–Scholes, and suggests that ANNs may have an important role to play in pricing other options for which there is either no closed‐form model, or the closed‐form model is less successful than is Black–Scholes for equity options. Copyright © 2005 John Wiley & Sons, Ltd.     

A Pricing Model for Quantity Contracts

An economic model is proposed for a combined price futures and yield futures market. The innovation of the article is a technique of transforming from quantity and price to a model of two genuine pricing processes. This is required in order to apply modern financial theory. It is demonstrated that the resulting model can be estimated solely from data for a yield futures market and a price futures market. We develop a set of pricing formulas, some of which are partially tested, using price data for area yield options from the Chicago Board of Trade. Compared to a simple application of the standard Black and Scholes model, our approach seems promising.     

Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?

We show in any economy trading options, with investors havingmean-variance preferences, that there are arbitrage opportunitiesresulting from negative prices for out of the money call options.The theoretical implication of this inconsistency is that mean-varianceanalysis is vacuous. The practical implications of this inconsistencyare investigated by developing an option pricing model for aCAPM type economy. It is observed that negative call pricesbegin to appear at strikes that are two standard deviationsout of the money. Such out-of-the money options often trade.For near money options, the CAPM option pricing model is shownto permit estimation of the mean return on the underlying asset,its volatility and the length of the planning horizon. The model is estimated on S&P 500 futures options data coveringthe period January 1992–September 1994. It is found thatthe mean rate of return though positive, is poorly identified.The estimates for the volatility are stable and average 11%,while those for the planning horizon average 0.95. The hypothesisthat the planning horizon is a year can not be rejected. Theone parameter Black–Scholes model also marginally outperformsthe three parameter CAPM model with average percentage errorsbeing respectively, 3.74% and 4.5%. This out performance ofthe Black–Scholes model is taken as evidence consistentwith the mean-variance analysis being vacuous in a practicalsense as well.     

Commodity derivatives valuation with autoregressive and moving average components in the price dynamics

In this paper, we develop a continuous time factor model of commodity prices that allows for higher-order autoregressive and moving average components. We document the need for these components by analyzing the convenience yield’s time series dynamics. The model we propose is analytically tractable and allows us to derive closed-form pricing formulas for futures and options. Empirically, we estimate a parsimonious version of the general model for the crude oil futures market and demonstrate the model’s superior performance in pricing nearby futures contracts in- and out-of-sample. Most notably, the model substantially improves the pricing of long-horizon contracts with information from the short end of the futures curve.     

The volatility linkage between energy and agricultural futures markets with external shocks

This paper investigates the volatility linkage between energy and agricultural futures returns and how this linkage responds to external macroeconomic shocks. A framework combining the VARMA-BEKK-GARCH model and the Permanent-Transitory decomposition technology is employed to detect the volatility transmission, to decompose the volatility linkage into permanent and transitory components, and to examine the underlying determinants of the transitory volatility linkage. We have the following findings. A bidirectional volatility linkage between energy and agricultural futures returns exists and becomes more pronounced in recent years. The bidirectional linkage results from the co-movement effect induced by external shocks rather than from the substitution effect induced by the biofuel industry, and is not weakened by the shale gas revolution. Serving as proxies for external shocks from the world economy, trade, and financial markets, the CRB, BDI, and USDX indices provide strong explanatory power for the transitory volatility linkage, and the futures of these indices can be used to effectively and inexpensively hedge against the risks of the portfolios involving energy and agricultural futures.     

Interest Rate Futures Options and Interest Rate Options

This paper derives pricing models of interest rate options and interest rate futures options. The models utilize the arbitrage-free interest rate movements model of Ho and Lee. In their model, they take the initial term structure as given, and for the subsequent periods, they only require that the bond prices move relative to each other in an arbitrage-free manner. Viewing the interest rate options as contingent claims to the underlying bonds, we derive the closed-form solutions to the options. Since these models are sufficiently simple, they can be used to investigate empirically the pricing of bond options. We also empirically examine the pricing of Eurodollar futures options. The results show that the model has significant explanatory power and, on average, has smaller estimation errors than Black's model. The results suggest that the model can be used to price options relative to each other, even though they may have different expiration dates and strike prices.     

Common asset pricing factors in volatilities and returns in futures markets

Factor-based asset pricing models have been used to explain the common predictable variation in excess asset returns. This paper combines means with volatilities of returns in several futures markets to explain their common predictable variation. Using a latent variables methodology, tests do not reject a single factor model with a common time-varying factor loading. The single common factor accounts for up to 53% of the predictable variation in the volatilities and up to 14% of the predictable variation in the means. S&P500 futures volatility predicted by the factor model is highly correlated with volatility implied in S&P500 futures options. But both the factor and implied volatilities are significant in predicting future volatility. In derivatives pricing, both implied volatility from options and factors extracted from asset pricing models should be employed.     

PRICING AND HEDGING SHORT STERLING OPTIONS USING NEURAL NETWORKS

This paper compares the performance of artificial neural networks (ANNs) with that of the modified Black model in both pricing and hedging short sterling options. Using high‐frequency data, standard and hybrid ANNs are trained to generate option prices. The hybrid ANN is significantly superior to both the modified Black model and the standard ANN in pricing call and put options. Hedge ratios for hedging short sterling options positions using short sterling futures are produced using the standard and hybrid ANN pricing models, the modified Black model, and also standard and hybrid ANNs trained directly on the hedge ratios. The performance of hedge ratios from ANNs directly trained on actual hedge ratios is significantly superior to those based on a pricing model, and to the modified Black model. Copyright © 2012 John Wiley & Sons, Ltd.     

Is Volatility Risk for the British Pound Priced in U.S. Options Markets?

This paper estimates the premium for volatility risk for European currency options written on British pounds. The average annualized premium for volatility risk is neither statistically different from zero nor invariant to the option's moneyness. However, the risk premium is positively and nonproportionaly related to the level of volatility, except for out‐of‐the‐money options. Finding a zero premium for volatility risk does not undermine the assumption of a zero‐price volatility risk in many extant stochastic‐volatility option pricing models and the option pricing formulas in those models.     

Valuation of American Futures Options: Theory and Empirical Tests

This paper reviews the theory of futures option pricing and tests the valuation principles on transaction prices from the S&P 500 equity futures option market. The American futures option valuation equations are shown to generate mispricing errors which are systematically related to the degree the option is in-the-money and to the option's time to expiration. The models are also shown to generate abnormal risk-adjusted rates of return after transaction costs. The joint hypothesis that the American futures option pricing models are correctly specified and that the S&P 500 futures option market is efficient is refuted, at least for the sample period January 28, 1983 through December 30, 1983.     

Efficient Analytic Approximation of American Option Values

This paper provides simple, analytic approximations for pricing exchange-traded American call and put options written on commodities and commodity futures contracts. These approximations are accurate and considerably more computationally efficient than finite-difference, binomial, or compound-option pricing methods.     

PRICING CURRENCY OPTIONS UNDER STOCHASTIC INTEREST RATES AND JUMP‐DIFFUSION PROCESSES

We investigate the effects of stochastic interest rates and jumps in the spot exchange rate on the pricing of currency futures, forwards, and futures options. The proposed model extends Bates's model by allowing both the domestic and foreign interest rates to move around randomly, in a generalized Vasicek term‐structure framework. Numerical examples show that the model prices of European currency futures options are similar to those given by Bates's and Black's models in the absence of jumps and when the volatilities of the domestic and foreign interest rates and futures price are negligible. Changes in these volatilities affect the futures options prices. Bates's and Black's models underprice the European currency futures options in both the presence and the absence of jumps. The mispricing increases with the volatilities of interest rates and futures prices. JEL classification: G13     

The Pricing of Futures and Options Contracts on the Value Line Index

This paper considers the problems peculiar to the Value Line Index, because of its use of geometric averaging, as regards the pricing of options and futures on that index. The Value Line Composite Index (VLCI) is an equally weighted geometric average index of nearly 1700 stocks. The VLCI futures market has existed since 1982 while the VLCI options market was established in 1985. This paper provides valuation formulas and analyzes the economic properties of these contracts. Because of the geometric averaging in the VLCI, its contingent claims have special properties. For example, the futures price may fall short of the spot price and the value of a VLCI call option may decline when the volatility of the index is increased. VLCI futures are shown to provide a direct means for duplicating an equally weighted portfolio of the underlying stocks.     

Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence

American options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2009) from 1983 to 2006 are identified as potentially profitable trades. Call bid prices more frequently violate their upper bound than put bid prices do, while violations of the lower bounds by ask prices are infrequent. In out‐of‐sample tests of stochastic dominance, the writing of options that violate the upper bound increases the expected utility of any risk‐averse investor holding the market and cash, net of transaction costs and bid‐ask spreads. The results are economically significant and robust.     

中国大宗商品期货市场定价机制研究

大宗商品期货市场是我国资本市场的重要组成部分,其定价有效性关系到投资者套期保值和价格发现等功能的实现。本文对国际前沿研究中常用的定价因子进行全面系统梳理,并对这些因子对我国商品期货合约收益率的解释和预测能力进行检验。在此基础上,本文构建了适用于我国大宗商品期货市场的包含市场、基差以及基差动量的三因子定价模型。进一步研究表明,基于大宗商品存储理论和现货存货数据构建的投资组合收益率可以被本文三因子模型有效解释,验证了经典的存储理论在我国的适用性。此外,本文对基差与基差动量两个重要因子的经济学意义进行了阐释。本文研究为进一步厘清大宗商品期货市场定价机制提供了一定参考。     

An Event Option Pricing Model with Scheduled and Unscheduled Announcement Effects

There is considerable evidence supporting the time-varying distribution of asset returns. There is also ample evidence that scheduled announcement events such as money supply announcements (in the case of foreign exchange), earnings announcements (in the case of stocks), and crop reports (in the case of commodities), as well as random unscheduled events, can affect the level and volatility of asset returns. This study provides an Event Model for European call options which explicitly addresses effects of these two classes of events. This specification requires estimation of more parameters, but it could provide a more accurate basis for pricing options than previous Poisson jump-diffusion models. Parametric analysis shows that the standard models under price the options relative to the Event Model. The Event Model may be particularly useful in pricing short-term deep out-of-the-money options when scheduled events are present in the market.     

Are They Hedgers or Speculators? Evidence from South Korea's Political Elections

This study uses a simultaneous equation model based on a three-stage least squares estimation to offer new empirical evidence that investors are hedgers or speculators during South Korea's elections. Major investor groups include individuals, securities companies, and foreigners in the Korea Composite Stock Price Index (KOSPI 200) market. The results show that cash market volatility and futures market activity have lead behaviors with one another. However, the contemporaneous variables of cash market volatility and options market activity have only unidirectional causality. Most investors will trade futures and options contracts for speculating within the entire sample period. During political election periods, investors prefer to trade options contracts for hedging rather than futures contracts.