The Shapley value,the Proper Shapley value,and sharing rules for cooperative ventures

In this note, we discuss two solutions for cooperative transferable utility games, namely the Shapley value and the Proper Shapley value. We characterize positive Proper Shapley values by affine invariance and by an axiom that requires proportional allocation of the surplus according to the individual singleton worths in generalized joint venture games. As a counterpart, we show that affine invariance and an axiom that requires equal allocation of the surplus in generalized joint venture games characterize the Shapley value.     

Efficiency and equity in private and public education: A nonparametric comparison

We present a nonparametric approach for (1) efficiency and (2) equity evaluation in education. Firstly, we use a nonparametric (Data Envelopment Analysis) model that is specially tailored to assess educational efficiency at the pupil level. The model accounts for the fact that typically minimal prior structure is available for the behavior (objectives and feasibility set) under evaluation. It allows for uncertainty in the data, while it corrects for exogenous ‘environmental’ characteristics that are specific to each pupil. Secondly, we propose two multidimensional stochastic dominance criteria as naturally complementary aggregation criteria for comparing the performance of different school types (private and public schools). While the first criterion only accounts for efficiency, the second criterion also takes equity into consideration. The model is applied for comparing private (but publicly funded) and public primary schools in Flanders. Our application finds that no school type robustly dominates another type when controlling for the school environment and taking equity into account. More generally, it demonstrates the usefulness of our nonparametric approach, which includes environmental and equity considerations, for obtaining ‘fair’ performance comparisons in the public sector context.     

证券价格长期波动控制系统的最优控制策略

探讨证券价格长期波动控制系统的最优控制问题.建立了在有效市场条件下证券价格长期波动的控制系统模型.为了使证券价格和内在价值按照人们预期的目标变化,探讨了对它们服从的系统采用经典信息结构下的随机最优控制策略问题.设计了使系统的输出跟踪证券内在价值的估计值,同时使调节控制的幅度尽可能小的性能指标,给出了最优控制策略的求解公式和计算过程,并给出了考虑系统性能的计算过程,对相应结果进行了分析.主要结论是:当价值对价格的均衡回归调整不足,或投资者对前期价值的增值预期乐观时,最优控制策略所起的作用在加强;而当价值对价格的均衡回归调整过度,或投资者对前期价值的增值预期悲观时,最优控制策略所起的作用在减弱.这些结果可以为完善证券市场和上市公司的监管提供理论依据     

基于卡尔曼滤波的期货价格期限结构模型

为准确对商品期货合约进行定价和预测,本文在短期-长期模型的基础上,提出以短期偏离、中期偏离和长期均衡为状态变量的三因素模型。本文根据状态变量的假设建立相关微分方程,并推导出模型的解,再运用卡尔曼滤波和极大似然法得到模型的参数和状态变量。最后,通过比较多种误差统计量证明,本文的短期-中期-长期模型的拟合与预测能力优于短期-长期模型。     

Strategic Pricing of Commodities

Abstract

We consider a setting where a large number of agents are trading commodity bundles. Assuming that agents of the same type have a certain utility attached to each transaction, we construct a statistical equilibrium which in turn implies prices on the different commodities. Our basic question is then the following. Assuming that some commodities come out with prices that are socially unacceptable, is it possible to change these prices systematically if a new type of agent is paid to enter the market? We will consider explicit examples where this can be done.     

A Control Variate Method for Monte Carlo Simulations of Heath–Jarrow–Morton Models with Jumps

This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process. The pricing framework adapted was developed by Chiarella and Nikitopoulos to provide an extension of the Heath, Jarrow and Morton model to jump‐diffusions and achieves Markovian structures under certain volatility specifications. Fourier Transform solutions for the price of a bond option under deterministic volatility specifications are derived and a control variate numerical method is developed under a more general state dependent volatility structure, a case in which closed form solutions are generally not possible. In doing so, a novel perspective is provided on control variate methods by going outside a given complex model to a simpler more tractable setting to provide the control variates.     

Closed Formula for Options with Discrete Dividends and Its Derivatives

Abstract

We present a closed pricing formula for European options under the Black–Scholes model as well as formulas for its partial derivatives. The formulas are developed making use of Taylor series expansions and a proposition that relates expectations of partial derivatives with partial derivatives themselves. The closed formulas are attained assuming the dividends are paid in any state of the world. The results are readily extensible to time-dependent volatility models. For completeness, we reproduce the numerical results in Vellekoop and Nieuwenhuis, covering calls and puts, together with results on their partial derivatives. The closed formulas presented here allow a fast calculation of prices or implied volatilities when compared with other valuation procedures that rely on numerical methods.     

Stock price dynamics and option valuations under volatility feedback effect

According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price–dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations under the volatility feedback effect by modeling the joint dynamics of stock price, dividends, and volatility in continuous time. Most importantly, our model predicts the negative effect of an increase in squared return volatility on the value of deep-in-the-money call options and, furthermore, attempts to explain the volatility puzzle. We theoretically demonstrate a mechanism by which the market price of diffusion return risk, or an equity risk-premium, affects option prices and empirically illustrate how to identify that mechanism using forward-looking information on option contracts. Our theoretical and empirical results support the relevance of the volatility feedback effect. Overall, the results indicate that the prevailing practice of ignoring the time-varying dividend yield in option pricing can lead to oversimplification of the stock market dynamics.     

Calibration of a multifactor model for the forward markets of several commodities

We propose a model for the evolution of forward prices of several commodities, which is an extension of the factor forward model in [1, 2], to a market where multiple commodities are traded. We calibrate this model in a market where forward contracts on multiple commodities are present, using historical forward prices. First, we calibrate separately the four coefficients of each individual commodity, using an approach based on quadratic variation/covariation of forward prices. Then, with the same technique, we pass to the estimation of the mutual correlation among the Brownian motions driving the different commodities. This calibration is compared to a calibration method used by practitioners, which uses rolling time series and requires a modification of the model, but turns out to be more accurate in practice, especially with a low frequency of observed transaction. We present efficient methods to perform the calibration with both methods, as well as the calibration of the intercommodity correlation matrix. Then we calibrate our model to WTI, ICE Brent and ICE Gasoil forward prices. Finally we present a method for estimating spot volatility from forward parameters, with an application to the WTI spot volatility.     

基于ARIMA模型的我国大宗农产品价格指数预测

以2006年6月至2015年12月我国大宗农产品价格指数月度时间序列作为研究对象.构建ARIMA(1,1,1)模型对我国大宗农产品价格指数进行了拟合和预测,并对模型拟合效果和预测准确度进行了检验,效果均良好.预测结果表明,从长期变化趋势看,我国大宗农产品价格指数上涨是大势所趋.从短期变化趋势看,大宗农产品面对较大的价格下行压力.