Price Expectation and the Pricing of Stock Index Futures

Capital markets are not perfect or frictionless, and arbitrage mechanism cannot be complete, particularly for index arbitrage. This study constructs a theoretical foundation to explain why the price expectation of the underlying asset should be entered into the pricing formula of stock index futures. The price expectation and incompleteness of arbitrage then are taken into account to develop a pricing model of stock index futures in imperfect markets. This study also presents three approaches for estimating the model parameter. Finally, the concept of the degree of market imperfection is defined and the valuation model is provided.     

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.     

Pricing rainfall futures at the CME

Many business people such as farmers and financial investors are affected by indirect losses caused by scarce or abundant rainfall. Because of the high potential of insuring rainfall risk, the Chicago Mercantile Exchange (CME) began trading rainfall derivatives in 2011. Compared to temperature derivatives, however, pricing rainfall derivatives is more difficult. In this article, we propose to model rainfall indices via a flexible type of distribution, namely the normal-inverse Gaussian distribution, which captures asymmetries and heavy-tail behaviour. The prices of rainfall futures are computed by employing the Esscher transform, a well-known tool in actuarial science. This approach is flexible enough to price any rainfall contract and to adjust theoretical prices to market prices by using the calibrated market price of risk. The empirical analysis is conducted with US precipitation data and CME futures data providing first results on the market price of risk for rainfall derivatives.     

Stochastic Convenience Yield and the Pricing of Oil Contingent Claims

This paper develops and empirically tests a two-factor model for pricing financial and real assets contingent on the price of oil. The factors are the spot price of oil and the instantaneous convenience yield. The parameters of the model are estimated using weekly oil futures contract prices from January 1984 to November 1988, and the model's performance is assessed out of sample by valuing futures contracts over the period November 1988 to May 1989. Finally, the model is applied to determine the present values of one barrel of oil deliverable in one to ten years time.     

沪深300指数期货价格随机利率效应研究

经典持有成本模型在非随机利率假设无法满足的条件下仅仅是远期合约而非期货的定价模型。本文采用拟合SHIBOR曲线的方法生成无风险纯折现债券模拟价格序列,对沪深300指数期货价格的随机利率效应进行了实证检验。研究结果表明,由于利率管制、股指期货市场和货币市场发展不成熟等因素的共同作用,沪深300指数期货价格中不含随机利率效应,指数远期和期货理论价格相等;如果持有成本模型其他假设条件也得到满足,则该模型可以用于沪深300指数期货定价。     

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。     

A Pricing Framework for Real Estate Derivatives

New methods are developed here for pricing the main real estate derivatives — futures and forward contracts, total return swaps, and options. Accounting for the incompleteness of this market, a suitable modelling framework is outlined that can produce exact formulae, assuming that the market price of risk is known. This framework can accommodate econometric properties of real estate indices such as predictability due to autocorrelations. The term structure of the market price of risk is calibrated from futures market prices on the Investment Property Databank index. The evolution of the market price of risk associated with all five futures curves during 2009 is discussed.     

基于人工神经网络的沪锌期货价格预测研究

分析沪锌期货的特征,发现沪锌期货价格存在非线性和波动集聚性的特点.选择沪锌期货的相关指标作为参数,运用人工神经网络训练数据,进行价格涨跌预测,构建BP神经网络和卷积神经网络沪锌期货预测模型.实证研究结果表明:模型预测准确率高,预测效果良好,在盘整行情中可获得较高收益,为投资决策提供重要参考,并可在期货市场中进行广泛应用.     

THE PRICING OF FUTURES CONTRACTS AND THE ARBITRAGE PRICING THEORY

When interest rates are stochastic, the cash flows of futures and forward contracts differ because of the marking-to-market requirement of futures contracts. The price effect of this difference is examined here by applying the risk and return model of the arbitrage pricing theory. The resulting futures pricing equation is preference free, and is obtainable using other no-arbitrage approaches. The pricing equation suggests that the price difference is due to the covariance of spot asset returns and interest rates. An empirical study is conducted on the Major Market Index futures from October 1, 1984 to September 27, 1985. Results indicate that the covariance, extracted by the Kalman filter according to the pricing equation, is significant in the pricing of futures contracts.     

Mean-variance hedging with oil futures

We analyze mean-variance-optimal dynamic hedging strategies in oil futures for oil producers and consumers. In a model for the oil spot and futures market with Gaussian convenience yield curves and a stochastic market price of risk, we find analytical solutions for the optimal trading strategies. An implementation of our strategies in an out-of-sample test on market data shows that the hedging strategies improve long-term return-risk profiles of both the producer and the consumer.     

Informational linkage and price discovery between China's futures and spot markets: Evidence from the US–China trade dispute

This study examines the effects of the US–China trade dispute on the informational linkages and price discovery between China's futures and spot markets. Using the daily price data of four assets representing the real and financial sectors in China during 2016–2019, empirical findings suggest that the futures–spot correlations for the stock index, copper, and corn markets have increased significantly during the trade dispute. In contrast, sharp declines in the dynamic correlations between gold futures and spot markets, as gold is a safe haven asset, are observed during the event window. During uncertainty disturbance (i.e., the trade dispute), the futures–spot cointegrated relationships in the gold and corn markets are found to adjust more quickly and efficiently, whereas the correction speeds of the market deviations for the stock index and copper market are moderately slower. With the intensive integration of market expectations with uncertainty shocks, the economic shocks of trade disputes tend to remarkably improve the pricing efficiency of China's futures markets, except for the gold futures market. China's spot markets, however, seem to be more sensitive to the noise trades and information disturbances arising from the trade dispute.     

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.     

Optimal portfolio choice of gold assets in the differential market and differential game structures

Portfolio choices of gold-related assets for market investors and dealers may not only depend on price differences and the inflation rate, but may also react to the market participants’ strategic behavior and risk attitude. This study develops a two-agent stochastic differential game model to solve the portfolio choice problem of the asset allocations of gold spot, futures, and cash for market participators who are exposed to inflation risks. The equilibrium prices of spot and futures driven by the volatility rate and co-variances that reflect various risk sources are also determined. Specifically, regarding the choice of hedging tools, market participators may prefer gold spot to futures for the purpose of hedging inflation risk. By capturing the stylistic facts of differential market and multiple agent structures, the article can develop a more reasonable and practical model to usefully explain the gold portfolio choices and pricing in the gold markets.     

Lower tick sizes and futures pricing efficiency: evidence from the emerging Malaysian market

We provide robust evidence of the impact on spot market liquidity and the pricing efficiency of FBM-FKLI index futures following the introduction of lower tick sizes for the stocks listed in the Bursa Malaysia. Our findings show a significant increase in unexpected trading volume and the speed of mean reversion of the futures mispricing. We find that the increase in the unexpected trading volume of the underlying stocks helps in reducing inter-market price discrepancies. The findings offer new evidence that lowering of tick sizes improves pricing efficiency in the Malaysian futures market.

     

No-arbitrage conditions for storable commodities and the modeling of futures term structures

One distinguishable feature of storable commodities is that they relate to two markets: cash market and storage market. This paper proves that, if no arbitrage exists in the storage-cash dual markets, the commodity convenience yield has to be non-negative. However, classical reduced-form models for futures term structures could allow serious arbitrages due to the high volatility of the convenience yield. To avoid negative convenience yield, this paper proposes a semi-affine arbitrage-free model, which prices futures analytically and fits futures term structures reasonably well. Importantly, our model prices commodity-related contingent claims (such as calendar spread options) quite differently with classical models.     

Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets

We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61–73] allows us to derive a closed-form formula for the fair value of discretely monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion.     

Speculative Futures Trading under Mean Reversion

This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein–Uhlenbeck, Cox–Ingersoll–Ross, or exponential Ornstein–Uhlenbeck model. The futures term structure is derived and its connection to futures price dynamics is examined. For each futures contract, we describe the evolution of the roll yield, and compute explicitly the expected roll yield. For the futures trading problem, we incorporate the investor’s timing option to enter or exit the market, as well as a chooser option to long or short a futures upon entry. This leads us to formulate and solve the corresponding optimal double stopping problems to determine the optimal trading strategies. Numerical results are presented to illustrate the optimal entry and exit boundaries under different models. We find that the option to choose between a long or short position induces the investor to delay market entry, as compared to the case where the investor pre-commits to go either long or short.     

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.     

Asymmetric Volatility,Skewness, and Downside Risk in Different Asset Classes: Evidence from Futures Markets

This study examines the cross‐sectional variation of futures returns from different asset classes. The monthly returns are positively correlated with downside risk and negatively correlated with coskewness. The asymmetric volatility effect generates negatively skewed returns. Assets with high coskewness and low downside betas provide hedges against market downside risk and offer low returns. The high returns offered by assets with low coskewness and high downside betas are a risk premium for bearing downside risk. The asset pricing model that incorporates downside risk partially explains the futures returns. The results indicate a unified risk perspective to jointly price different asset classes.     

Futures and forward price differential and the effect of marking‐to‐market: Australian evidence

The objective of this paper is to examine the effects of marking‐to‐market of futures contracts on the price differential between futures and forward contracts based on the predictions of the Cox, Ingersoll and Ross (1981) (CIR) model. Cox et al ., (1981) derive a series of propositions with respect to the relationship between futures and forward prices and a set of testable implications. These are tested empirically in this paper using Australian data from November 1991 to June 1997. The results provide evidence of the presence of significant futures and forward price differences, where the futures price is consistently below the forward price. Only partial support is found for the Cox et al ., (1981) propositions, implying that the effect of marking‐to‐market is not able to fully account for the price differential. Therefore, it is not possible to rule out the influence of other institutional factors on the futures‐forward price difference.