Measure preserving derivatives and the pricing kernel puzzle

Recent empirical studies have found evidence of nonmonotonicity in the pricing kernels for a variety of market indices. This phenomenon is known as the pricing kernel puzzle. The payoff distribution pricing model of Dybvig predicts that the payoff distribution of a direct investment of $1 in a market index may be replicated by investing less than $1 in some derivative written on that market index whenever the associated pricing kernel is nondecreasing. Using the Hardy–Littlewood rearrangement inequality, we obtain an explicit solution for the cheapest replicating derivative, which we refer to as the optimal measure preserving derivative. The optimal measure preserving derivative is the permutation appearing in Ryff’s decomposition of the pricing kernel with respect to the market payoff measure. We compute optimal measure preserving derivatives corresponding to the estimated physical and risk neutral distributions in the paper by Jackwerth (2000) that first brought attention to the pricing kernel puzzle.     

On pricing and hedging options in regime-switching models with feedback effect

We study the pricing and hedging of European-style derivative securities in a Markov, regime-switching, model with a feedback effect depending on the economic condition. We adopt a pricing kernel which prices both financial and economic risks explicitly in a dynamically incomplete market and we provide an equilibrium analysis. A martingale representation for a European-style index option's price is established based on the price kernel. The martingale representation is then used to construct the local risk-minimizing strategy explicitly and to characterize the corresponding pricing measure.     

The market for crash risk

This paper examines the equilibrium when stock market crashes can occur and investors have heterogeneous attitudes towards crash risk. The less crash averse insure the more crash averse through options markets that dynamically complete the economy. The resulting equilibrium is compared with various option pricing anomalies: the tendency of stock index options to overpredict volatility and jump risk, the Jackwerth [Recovering risk aversion from option prices and realized returns. Review of Financial Studies 13, 433–451] implicit pricing kernel puzzle, and the stochastic evolution of option prices. Crash aversion is compatible with some static option pricing puzzles, while heterogeneity partially explains dynamic puzzles. Heterogeneity also magnifies substantially the stock market impact of adverse news about fundamentals.     

An Empirical Test of Pricing Kernel Monotonicity

A large class of asset pricing models predicts that securities which have high payoffs when market returns are low tend to be more valuable than those with high payoffs when market returns are high. More generally, we expect the projection of the stochastic discount factor on the market portfolio—that is, the discounted pricing kernel evaluated at the market portfolio—to be a monotonically decreasing function of the market portfolio. Numerous recent empirical studies appear to contradict this prediction. The non‐monotonicity of empirical pricing kernel estimates has become known as the pricing kernel puzzle. In this paper we propose and apply a formal statistical test of pricing kernel monotonicity. We apply the test using 17 years of data from the market for European put and call options written on the S&P 500 index. Statistically significant violations of pricing kernel monotonicity occur in a substantial proportion of months, suggesting that observed non‐monotonicities are unlikely to be the product of statistical noise. Copyright © 2014 John Wiley & Sons, Ltd.     

Extracting market information from equity options with exponential Lévy processes

Lévy processes have been successfully applied in the modeling of financial assets. Useful information such as implied volatility, skewness, and risk-preferences can be derived from market option prices. In this paper, we advocate using Esscher conjugate Lévy processes to estimate risk-neutral and empirical densities. More specifically, we employ the exponential Meixner and NIG processes to calculate in closed form the pricing kernel in the equity market and then study the evolution of equity market behavior between 2002 and 2010. Our empirical analysis using S&P 500 options shows that the risk preferences of equity investors were signalling an anomaly in the market well before the subprime prime mortgage crisis (August 2007) and the crisis of confidence that followed, anticipating the downfall in equity markets in 2008, but then returning to normal levels in 2009.     

Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach

This paper contributes to the literature on the estimation of the Risk Neutral Density (RND) function by proposing a log-semi-nonparametric (log-SNP) distribution as the implicit RND when the Gram-Charlier model is used for option pricing. The performance of the model is compared to the lognormal (Black Scholes) benchmark for a sample of option prices for West Texas Intermediate (WTI) crude oil that were traded in the period between January 2016 and December 2017. Results show that the lognormal specification tends to systematically undervalue option prices and that the proposed log-SNP distribution, which explicitly adjusts for negative skewness and excess kurtosis, results in markedly improved accuracy, especially in periods of market instability. As a result, the implied skewness and excess kurtosis are relevant sources of information on market expectations that should be used for hedging and risk management purposes.     

中国企业债券特征与风险补偿

利率风险、信用风险、流动性风险是债券市场上常见的风险类型,而债券的特征可以直接或间接地反映这些风险。本文通过分析中国企业债券市场上的债券发行量、已发行时间、债券期限、息票利率、收益率波动性、久期、凸性、到期收益率等债券特征对债券定价的影响,实证检验这些债券特征与债券风险及风险补偿的关系。本文的分析结论认为,这些债券特征显著地影响企业债券的定价,它们与利率风险、信用风险和流动性风险有显著关系,其中对企业债券信用风险的影响最大。流动性风险未被合理定价,低流动性债券未能获得显著的风险补偿。     

中国无风险利率之谜与股权溢价

按照传统的消费资本资产定价理论,中国股市的高股权溢价只能由投资者的高相对风险厌恶系数来解释。但是这又会产生所谓的无风险利率之谜,因为投资者相对风险厌恶系数高时,其时间偏好率为负,明显不合情理。     

A unified entropic pricing framework of option: Using Cressie-Read family of divergences

The entropy valuation of option (Stutzer, 1996) provides a risk-neutral probability distribution (RND) as the pricing measure by minimizing the Kullback–Leibler (KL) divergence between the empirical probability distribution and its risk-neutral counterpart. This article establishes a unified entropic framework by developing a class of generalized entropy pricing models based upon Cressie-Read (CR) family of divergences. The main contributions of this study are: (1) this unified framework can readily incorporate a set of informative risk-neutral moments (RNMs) of underlying return extracted from the option market which accurately captures the characteristics of the underlying distribution; (2) the classical KL-based entropy pricing model is extended to a unified entropic pricing framework upon a family of CR divergences. For each of the proposed models under the unified framework, the optimal RND is derived by employing the dual method. Simulations show that, compared to the true price, each model of the proposed family can produce high accuracy for option pricing. Meanwhile, the pricing biases among the models are different, and we hence conduct theoretical analysis and experimental investigations to explore the driving causes.     

Optimal Two‐part Pricing under Cost Uncertainty

This paper examines the optimal two‐part pricing under cost uncertainty. We consider a risk‐averse monopolistic firm that is subject to a cost shock to its constant marginal cost of production. The firm uses two‐part pricing to sell its output to a continuum of heterogeneous consumers. We show that the global and marginal effects of risk aversion on the firm's optimal two‐part pricing are to raise the unit price and lower the fixed payment. We further show that an increase in the fixed cost of production induces the firm to raise (lower) the unit price and lower (raise) the fixed payment under decreasing (increasing) absolute risk aversion. The firm's optimal two‐part pricing is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving spread increase in cost uncertainty induces the firm to raise the unit price and lower the fixed payment under either decreasing or constant absolute risk aversion. Copyright © 2011 John Wiley & Sons, Ltd.     

欧洲股票市场的规模和动因:基于不同β系数的资本资产定价模型实证研究

我们选用在13个欧洲股市上市的证券,形成规模和动因组合。我们不仅发现规模溢价的证据,还发现8个样本市场存在重大动因收益率。这些收益率可能不构成异常现象,因为它们与不同β值的资本资产定价模型一致。我们还发现,系统风险与经济周期有关。此外,研究结果显示,虽然规模和动因收益率显著,但是难以在中、短期利用它们,因为在我们的样本中只有极少年份它们的数值为正且很大。     

金融资产厚尾分布及常用的风险度量

本文首先运用正态分布、带有位置-尺度参数的t分布、logistic分布、极值分布、-stable分布和核密度估计对上证综指收益率分布进行拟合,结果表明核密度估计优于其他分布。其次,在进行尾部风险拟合和度量风险方面,通过设定相关指标,在显著性水平为1%时,-stable分布更适合衡量风险程度,在此基础上提出了调和-stable分布,并得到一个同构表示解。最后,本文给出了蒙特卡洛-stable分布模拟和经验值下的MDD、DaR和CDaR,并得到了模型值和经验值之间的乘离率。     

Subsampling realised kernels

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.     

信贷资产组合保险策略定价研究

本文探讨了信贷资产组合保险策略在信用风险管理领域的地位。基于CreditMetrics模型，提出了信贷资产组合保险策略的定价算法，这是对主流风险计量模型的一种全新尝试。处理的过程对CreditMetrics的VaR技术做了一些细节上的变换，通过蒙特卡洛模拟得到了较理想的运算结果。最后对模型的实施提出了合理的建议。     

Forecasting risk measures using intraday data in a generalized autoregressive score framework

A new framework for the joint estimation and forecasting of dynamic value at risk (VaR) and expected shortfall (ES) is proposed by our incorporating intraday information into a generalized autoregressive score (GAS) model introduced by Patton et al., 2019 to estimate risk measures in a quantile regression set-up. We consider four intraday measures: the realized volatility at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized volatilities. In a forecasting study, the set of newly proposed semiparametric models are applied to four international stock market indices (S&P 500, Dow Jones Industrial Average, Nikkei 225 and FTSE 100) and are compared with a range of parametric, nonparametric and semiparametric models, including historical simulations, generalized autoregressive conditional heteroscedasticity (GARCH) models and the original GAS models. VaR and ES forecasts are backtested individually, and the joint loss function is used for comparisons. Our results show that GAS models, enhanced with the realized volatility measures, outperform the benchmark models consistently across all indices and various probability levels.     

作业成本法下的产品定价模型

本文在分析作业成本定价原理的基础上建立了作业成本产品定价模型,并且利用Excel设计了动态的产品定价模型,使得企业产品定价决策实现自动化,解决了实际工作中繁杂的计算问题。     

Rationalizing investors’ choices

Assuming that agents’ preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer with an explicitly derived concave non-decreasing utility function. This result enables us to infer the utility and risk aversion of agents from their investment choice in a non-parametric way. We relate the property of decreasing absolute risk aversion (DARA) to distributional properties of the terminal wealth and of the financial market. Specifically, we show that DARA is equivalent to a demand for a terminal wealth that has more spread than the opposite of the log pricing kernel at the investment horizon.     

现金并购定价分析

现金并购意味着收购股权的支付方式有别于传统的现金支付方式,而现金并购中的关键环节是真实的反映被并购企业的价值。本文对并购企业价值的决定与相关因素及其使用方法进行了分析,认为完善现金收购中的定价体系,有助于资本市场的进一步发展,对并购定价体系给予科学的分析具有实际意义。     

信息不完全的信用风险定价模型及其在我国的应用

基于信息不完全的信用风险定价模型与传统的结构化模型和约化模型的最大区别在于它将信息不完全这一前提引入了以信息完全为前提的结构化模型,同时它又考虑了约化模型中强度的优点,引入短期信用风险的度量,成为当前最切合现实的信用风险定价模型。本文认为,应用基于信息不完全的信用风险定价模型来测度信用风险,将具有十分重要的现实意义。     

基于Morlet小波时频互相关的股指期货价格发现效率研究

本文采用Morlet小波时频互相关分析方法,从"时域"和"频域"两个维度检验了我国以及国际主要市场股指期货和现货价格序列的动态关联性,研究了股指期货价格发现效率的问题。研究表明,沪深300指数和股指期货在低频长周期范围内,呈现长时间高度相关、协同波动的特征;在高频短周期范围内,两者整体仍然具有协同波动特征,但时常出现短暂紊乱的情况,即期货与现货的交错引导现象。我国股指期货市场的价格发现效率较美国、英国成熟市场仍有较大差距,但强于日本。