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.     

多标的资产期权定价的Monte Carl模拟方法及其应用研究

鉴于一般的偏微分解析方法和传统数值方法处理高维期权定价问题存在很大困难,本文在单标的资产价格随机模型的基础上,推导了具相关性的多标的资产价格的随机过程公式,以此构造蒙特卡罗模拟高维欧式期权定价的随机模型,给出模拟算法,并分析了影响蒙特卡罗模拟效果的几个关键因素,模拟算例的结果显示模拟效果较好.     

基于Copula GARCH的多资产期权定价

自从Black和Scholes在1976年开创性的提出了BS期权定价公式以来,期权定价理论得到了极大的发展,而在其后的研究中发展基于BS公式的隐含波动率对于执行价格具有类似微笑的曲线,其原因是标的资产的过程并不是BS公式所假设的几何布朗运动。Engle提出的ARCH模型和Bollerslev提出的GARCH模型能对标的资产的收益率序列进行很好的描述,因此将GARCH模型引入期权定价。在多资产期权定价研究当中,最为关键的是标的资产之间的依赖关系,关于依赖关系的最有力的就是Copula理论,而Copula的一大优势就是可以将边缘分布和联合分布分开,可以分别考虑边缘分布和数据的相关结构。本文设想将多元GARCH引入多资产期权定价中,但是一般的多元GARCH的系数过多而不易估计,另一方面模型的灵活程度较小,所以用一元的GARCH模型分别对各个标的资产的收益率序列进行建模,再用Copula将各个资产的分布联接起来,这便是Copula based MGARCH模型。接下来便可以通过Monte Carlo模拟对期权进行定价。     

基于Copula GARCH的多资产期权定价

自从Black和Scholes在1976年开创性的提出了BS期权定价公式以来,期权定价理论得到了极大的发展,而在其后的研究中发展基于BS公式的隐含波动率对于执行价格具有类似微笑的曲线,其原因是标的资产的过程并不是BS公式所假设的几何布朗运动。Engle提出的ARCH模型和Bollerslev提出的GARCH模型能对标的资产的收益率序列进行很好的描述,因此将GARCH模型引入期权定价。在多资产期权定价研究当中,最为关键的是标的资产之间的依赖关系,关于依赖关系的最有力的就是Copula理论,而Copula的一大优势就是可以将边缘分布和联合分布分开,可以分别考虑边缘分布和数据的相关结构。本文设想将多元GARCH引入多资产期权定价中,但是一般的多元GARCH的系数过多而不易估计,另一方面模型的灵活程度较小,所以用一元的GARCH模型分别对各个标的资产的收益率序列进行建模,再用Copula将各个资产的分布联接起来,这便是Copula based MGARCH模型。接下来便可以通过Monte Carlo模拟对期权进行定价。     

期权交易能提高标的资产的定价效率吗?——基于上证50ETF套利视角的实证研究

随着上证50ETF期权的推出,期权交易能否提高标的资产定价效率的问题显得愈发重要。本文从对定价效率影响最大的套利机制入手,研究上证50ETF期权推出前后,其对应标的——华夏上证50ETF市场价格和净值的偏差所带来套利机会的多少,进而得出期权交易对标的资产定价效率的影响。研究发现:期权交易在刚推出的一定时间内降低了标的资产的定价效率,但是随着时间的推移,标的资产的定价效率会重新提高并且超过初期。因此从长期看,期权交易能够提高标的资产的定价效率,期权交易对标的资产的定价效率的影响是一条"J"形曲线。     

基于GARCH模型的股票期权定价方法研究

本文应用GARCH模型估计股票期权标的股票的收益波动率,并将估计出的收益波动率代入Black-Schole期权定价公式,以期提高Black-Scholes期权定价公式的精确度.为验证该方法的有效性,本文以首创JBTI为例进行了实证研究,结果表明在期权交易价格上升的期间内,基于GARCH模型的期权定价方法可以提高Black-Scholes期权定价公式的精确度.     

基于受约束正则方法的奇异期权定价

本文研究一种对奇异期权定价的非参数方法,避开了传统期权定价方法对资产价格分布假设和波动率假设等难题,并且不同于其他非参数方法从期权历史交易价格出发为新期权定价,本文直接用标的资产的价格为期权定价。因此,即使在期权市场不完善,期权价格不可靠、不可得,甚至不存在的情况下,也能为期权有效定价。此外,本文将正则定价方法和隐含二叉树方法有效结合,扩展到为奇异期权的定价问题上,并在传统的正则定价方法中加入了价格敏感因素作为约束条件,以提高该方法的定价精度。     

股价波动源模型下可转换债券的鞅定价

衍生证券是指其价格或投资回报最终取决于另一种资产(即标的资产)的价格的一类新型的金融工具,从1973年出现至今已有30多个年头了.其间,期权市场得到了迅猛发展,在标准期权的基础上,衍生出了各种各样的奇异期权,障碍期权就是其中的一种.对其合理适当地定价是金融数学中一个既具有理论意义又具有实际应用价值的重要问题.     

基于蒙特卡罗模拟的多标的资产期权定价研究

在单标的资产价格随机模型的基础上,推导了具相关性的多标的资产价格的随机过程公式,以此构造蒙特卡罗模拟高维欧式期权定价的随机模型,给出模拟算法,并分析了影响蒙特卡罗模拟效果的几个关键因素。模拟算例的结果显示模拟效果较好。     

权证上市对标的股票的影响——基于中国股市的分析与实证

本文基于连续时间动态资产定价模型,推导出权证作为一种新的、依赖于标的股票的风险资产上市交易后,标的股票均衡价格变动的一般性结果,揭示出标的股票资产定价机制必然发生根本性改变;通过建立标的股票收益率与波动率的计量模型验证理论结果;实证考察,在中国,权证上市交易后对标的股票收益率及其波动性的影响,最后得出关于标的股票收益率各方面特征变化的完整结论,作为监管部门与投资者决策的参考依据。     

The stochastic behavior of commodity prices with heteroskedasticity in the convenience yield

We document a new stylized fact regarding the dynamics of the commodity convenience yield: the volatility of the convenience yield is heteroskedastic for industrial commodities; specifically, the volatility (variance) of the convenience yield depends on the convenience yield level. To explore the economic and statistical significance of the improved specification of the convenience yield process, we propose an affine model with three state variables (log spot price, interest rate, and the convenience yield). Our model captures three important features of commodity futures—the heteroskedasticity of the convenience yield, the positive relationship between spot-price volatility and the convenience yield and the dependence of futures risk premium on the convenience yield. Moreover our model predicts an upward sloping implied volatility smile, commonly observed in commodity option market.     

Commodity price modelling that matches current observables: a new approach

We develop a stochastic model of the spot commodity price and the spot convenience yield such that the model matches the current term structure of forward and futures prices, the current term structure of forward and futures volatilities, and the inter-temporal pattern of the volatility of the forward and futures prices. We let the underlying commodity price be a geometric Brownian motion and we let the spot convenience yield have a mean-reverting structure. The flexibility of the model, which makes it possible to simultaneously achieve all these goals, comes from allowing the volatility of the spot commodity price, the speed of mean-reversion parameter, the mean-reversion parameter, and the diffusion parameter of the spot convenience yield all to be time-varying deterministic functions.     

Pricing Commodity Spread Options with Stochastic Term Structure of Convenience Yields and Interest Rates

The purpose of this research is to provide a valuation formula for commodity spread options. Commodity spread options are options written on the difference of the prices (spread) of two commodities. From the aspect of commodity contingent claims, it is considered that commodity spread options are difficult to evaluate with accuracy because of the existence of the convenience yield. Hence, the model of the convenience yield is the key factor to price commodity spread options. We use the concept of future convenience yields to develop the model that enriches the stochastic behavior of convenience yield. We also introduce Heath-Jarrow-Morton interest rate model to the valuation framework. This general model not only captures the mean reverting feature of the convenience yield, but also allows us to handle a very wide range of shape that the term structure of convenience yield can take. Therefore our model provides various types of models. The numerical analysis presented in this paper provides some unique features of commodity spread options in contrast to normal options. These characteristics have never been addressed in previous studies. Moreover, it suggests that the existing model overprice commodity spread options through neglecting the effect of interest rates.     

A continuous time equilibrium model of forward prices and futures prices in a multigood economy

This paper is a theoretical investigation of equilibrium forward and futures prices. We construct a rational expectations model in continuous time of a multigood, identical consumer economy with constant stochastic returns to scale production. Using this model we find three main results. First, we find formulas for equilibrium forward, futures, discount bond, commodity bond and commodity option prices. Second, we show that a futures price is actually a forward price for the delivery of a random number of units of a good; the random number is the return earned from continuous reinvestment in instantaneously riskless bonds until maturity of the futures contract. Third, we find and interpret conditions under which normal backwardation or contango is found in forward or futures prices; these conditions reflect the usefulness of forward and futures contracts as consumption hedges.     

Seasonal and stochastic effects in commodity forward curves

In this paper we develop a new model for the dynamics of forward curves of commodities exhibiting seasonalities, such as natural gas, electricity or agricultural commodities. In the existing literature on the subject, the first state variable in multi-factor models is the commodity price, which combines seasonal and stochastic features and may be unobservable. We propose to use instead the average forward price, which is devoid of seasonality and conveys a more robust representation of the current forward curve level. The second factor in the model is a quantity analogous to the stochastic convenience yield, which accounts for the random changes in the forward curve shape. The well-known cost-of-carry relationship is significantly improved by introducing a deterministic seasonal premium within the convenience yield. We develop model estimation procedures and apply them to a number of energy markets.     

Pricing commodity-linked bonds with stochastic convenience yield,interest rate and counterparty credit risk: application of Mellin transform methods

Review of Derivatives Research - This paper investigates the effects of the spot underlying commodity price, stochastic convenience yield, interest rate and counterparty credit risk on the pricing...     

The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging

In this article we compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets. The first model is a simple one-factor model in which the logarithm of the spot price of the commodity is assumed to follow a mean reverting process. The second model takes into account a second stochastic factor, the convenience yield of the commodity, which is assumed to follow a mean reverting process. Finally, the third model also includes stochastic interest rates. The Kalman filter methodology is used to estimate the parameters of the three models for two commercial commodities, copper and oil, and one precious metal, gold. The analysis reveals strong mean reversion in the commercial commodity prices. Using the estimated parameters, we analyze the implications of the models for the term structure of futures prices and volatilities beyond the observed contracts, and for hedging contracts for future delivery. Finally, we analyze the implications of the models for capital budgeting decisions.     

Option Approach to Search for Threshold Rice Price Toward Sustainable Paddy Field Management

This paper applies an option approach to search for the threshold rice price toward the sustainable paddy field management under rice price stochasticity. Rice price is assumed to follow geometric Brownian motion. The management model for paddy fields is a discrete stochastic dynamic programming model with binomial approximation for geometric Brownian motion, where a control variable is a decision to sustain or terminate paddy yield management. Our computational experiments indicate that an increase in rice price volatility could lower the threshold rice price for farmers to continue rice production. It is also shown that depending on the degree of rice price volatility, even under a lower price level than production costs, maintaining the management could become beneficial. Considering an option to terminate production could make the higher expected value of rice production than without it. Using 12 sets of time series data on voluntarily marketed rice produced in Hokkaido, Aomori, Iwate, Miyagi, Akita, Yamagata, Fukui, Ibaragi, Chiba, Niigata, Toyama and Nagano, the minimum threshold rice price of 6,700 Yen/60 kg was found in Chiba with the largest volatility, and the maximum of 7,250 Yen/60 kg in Ibaragi with the smallest volatility. If the market price becomes lower than the threshold rice price, some policy measures would be necessary toward sustainable paddy field management by covering the difference between them.     

Optimal delta hedging for options

As has been pointed out by a number of researchers, the normally calculated delta does not minimize the variance of changes in the value of a trader's position. This is because there is a non-zero correlation between movements in the price of the underlying asset and movements in the asset's volatility. The minimum variance delta takes account of both price changes and the expected change in volatility conditional on a price change. This paper determines empirically a model for the minimum variance delta. We test the model using data on options on the S&P 500 and show that it is an improvement over stochastic volatility models, even when the latter are calibrated afresh each day for each option maturity. We also present results for options on the S&P 100, the Dow Jones, individual stocks, and commodity and interest-rate ETFs.     

Good-Deal Option Price Bounds for a Non-Traded Event with Stochastic Return: A Note

Cochrane and Sa'a-Requejo (2000, Journal of Political Economy) proposed the good-deal price bounds for the European call option on an event that is not a traded asset, but is correlated with a traded asset that can be used as an approximate hedge. One remarkable feature of their model is that the return on an event process explicitly appears in the option price bounds formula, which offered a contrast with the standard option pricing model. We show that the good-deal option price bounds on a non-traded event are obtained as a closed-form formula, when the return on an event is governed by a mean reverting process.