有交易成本的利率期限结构的分析

本文利用无套利均衡方法对存在着交易费，赋税，以及买卖差价等交易成本的债券市场进行分析．用数学方法严格地证明了一个基本结论：在有交易成本的债券市场上，弱无套利性与相容期限结构的存在性是等价的．     

摩擦市场的最优消费-投资组合选择

本文研究摩擦市场中的最优消费-投资组合选择问题.当金融资产和自然状态个数为有限个以及摩擦局限于成比例的交易费时,可用原始市场或适当转换了的市场的无套利性来刻画最优消费-投资组合策略的存在性或充要条件.     

基于NS混合模型的中国利率期限结构动态估计比较研究

采用NS混合模型动态估计中国利率期限结构,考察动态NS模型,无套利NS模型及广义无套利NS模型等NS混合模型对我国利率期限结构的动态估计效率,比较NS混合模型的样本外预测能力,检验无套利约束对混合模型动态估计的影响.本文的经验分析结果表明:无套利条件的引入增强了NS混合模型的样本内动态估计能力和样本外预测能力;五因素的广义无套利NS模型(AFGNS)无论在利率期限结构样本内动态估计还是在总体预测效率上都要高于其他模型,可将其作为利率期限结构研究的基础模型:     

有摩擦金融市场中的美式未定权益定价

本文研究了高借款利率下投资策略受限制的美式未定权益的定价问题. 文章通过引入反映上述金融市场摩擦的辅助的无摩擦金融市场类给出了美式未定权益的上下套期保值价格$h_{\text{up}}(K)$和$h_{\text{low}}(K)$的定价公式. 进一步, 在基于金融市场无套利的准则下证明了$[h_{\text{low}}(K),h_{\text{up}}(K)]$是美式未定权益的无套利价格区间. 最后在投资策略受到某些具体限制的情形下, 以美式看涨期权为例, 给出了上下套期保值价格的显式表达式或估计式.     

金融危机与一般均衡下的CDO定价

传统的CDO根据无套利原理,将信用风险的保险费和违约后的回收金额两个现金流进行复制得出定价,注重金融市场局部均衡.然而无套利均衡定价的思路只针对存在套利机会的资产市场的局部均衡,使得该均衡与基础资产的联系不强.而一般均衡分析,可以引入实体经济的因素,有利于防止CDO定价的泡沫风险.因此文章在CDO定价中引入实体经济要素,证明一般均衡下CDO定价相比无套利定价有更丰富更敏感的风险刻画能力.实证结果发现,一般均衡定价相当于无套利定价加上修正项,且在高风险时期两者价差高于低风险时期,这是由于无套利定价忽略了实体经济的风险.因此CDO产品的无套利定价很可能存在着泡沫而导致资源配置扭曲.最后,文章认为CDO可以预防定价风险,用于解决地方政府债务问题,并提出相关的风险控制建议.     

摩擦市场中无套利、近似无套利与没有免费午餐

本文研究具有摩擦的证券市场中资产定价,即在局部凸拓扑空间中弱与强无套利、弱与强近似无套利及弱与强没有免费午餐.我们建立了这三个概念之间的关系并且解决了资产定价理论的估值问题.     

利率期限结构与宏观经济变量的相互关系研究

本文研究了利率期限结构与宏观经济变量之间的相互关系。运用利率期限结构与宏观经济变量的无套利模型,对向量自回归模型进行了扩展,将其引入到状态空间模型框架中,基于卡尔曼滤波并结合EM算法对模型参数进行了有效估计,结合实际数据对利率期限结构与宏观经济变量的相互影响关系进行了实证研究。结果表明:利率期限结构与宏观经济变量的双向影响关系显著;宏观经济变量对利率期限结构具有一定的解释力;研究利率期限结构时,宏观经济变量的影响作用不能忽略。     

多叉树模型中鞅测度的刻画与构造

在无套利假设下,讨论了多叉树模型中鞅测度的构造问题.利用二叉树方法,构造了有限个符号测度.证明了-个概率测度为鞅测度的充要条件是它可以表示为这组符号测度的某个满足特定条件的凸线性组合.     

有交易费市场中套利问题的注记

对有交易费的资产模型,本文引入了市场有套利机会的一般定义,并利用辅助鞅和资产折算函数方法,讨论了无套利市场的基本性质,即在可允许投资策略下市场不存在套利机会.     

基于我国期货市场的统计套利研究

不同于股票市场,期货市场存在天然的做空机制,非常方便进行套利。本文以我国的期货市场为研究对象,对期货市场上的统计套利进行实证研究.首先,我们提出了协整模型、误差修正模型和基于协整关系的GARCH等3个统计套利模型,设计了相应的交易策略,然后,对样本外数据进行检验,分析不同开仓位、止盈、止损位置与累计收益率的关系。结果表明,基于协整关系的GARCH模型是三个统计套利模型中最优的.实证结果表明,本文所提出的统计套利模型以及相应的策略在我国的期货市场是可行的。     

Sequential Arbitrage Measurements and Interest Rate Envelopes

This paper proposes new measures that provide us with the level of sequential arbitrage in bond markets. All the measures vanish in an arbitrage-free market and all of them are positive otherwise. Each measure is generated by a dual pair of optimization problems. Primal problems permit us to compute optimal sequential arbitrage strategies, if available. Each dual problem generates a concrete proxy for the term structure of interest rates. The set of proxies allows us to obtain the exact market price of any bond and may measure several effects. For instance, the credit risk spread of nondefault free bonds, or the embedded option price of callable or extendible bonds. The developed theory has been tested empirically.     

基于我国期货市场的跨期套利研究

不同于股票市场,期货市场存在天然的做空机制,非常方便进行套利操作。本文以我国的期货市场为研究对象,主要针对跨期套利进行实证研究。首先介绍了跨期套利,并提出了一套完善的、可操作的套利交易策略。其次,在此基础上,我们选取郑州商品交易所的期货的棉花的15种组合(不同交割月份)所有历史数据进行测试,最后,我们分析了该策略下跨期套利机会出现次数、收益率、对冲平仓次数、实物交割次数、仓位管理、保证金追加等方面。实证结果表明,本文所提出的跨期套利模型以及相应的策略在我国的期货市场是可行的。     

Kernel-Correlated Lévy Field Driven Forward Rate and Application to Derivative Pricing

We propose a term structure of forward rates driven by a kernel-correlated Lévy random field under the HJM framework. The kernel-correlated Lévy random field is composed of a kernel-correlated Gaussian random field and a centered Poisson random measure. We shall give a criterion to preclude arbitrage under the risk-neutral pricing measure. As applications, an interest rate derivative with general payoff functional is priced under this pricing measure.     

Asymptotic arbitrage in large financial markets with friction

In the modern version of arbitrage pricing theory suggested by Kabanov and Kramkov the fundamental financially meaningful concept is an asymptotic arbitrage. The ??real world?? large market is represented by a sequence of ??models?? and, though each of them is arbitrage free, investors may obtain non-risky profits in the limit. Mathematically, absence of the asymptotic arbitrage is expressed as contiguity of envelopes of the sets of equivalent martingale measures and objective probabilities. The classical theory deals with frictionless markets. In the present paper we extend it to markets with transaction costs. Assuming that each model admits consistent price systems, we relate them with families of probability measures and consider their upper and lower envelopes. The main result concerns the necessary and sufficient conditions for absence of asymptotic arbitrage opportunities of the first and second kinds expressed in terms of contiguity. We provide also more specific conditions involving Hellinger processes and give applications to particular models of large financial markets.     

On Gaussian HJM framework for Eurodollar Futures

One of the standard tools for the theoretical analysis of fixed income securities and their associated derivatives is the term structure model of Heath, Jarrow and Morton. In this paper the question, what specific HJM model is consistent with the observed price of an Eurodollar Futures contract? is discussed. Eurodollar Futures, apart from being the most heavily traded futures are connected to London Inter Bank Offered Rate (LIBOR) and to domestic monetary conditions. The answer to the above question will help in pricing any new derivative on Eurodollar Futures or the one that is not heavily traded. A simple tool to measure the adequacy of different HJM structures that may be used to model Eurodollar Futures price process is suggested. Moreover, the question of estimation of parameters of these models by different methods—method of realized volatility, method of maximum likelihood (ML) and a two‐stage method that combines both the realized volatility and ML—is addressed. Although it sounds like a typical statistical procedure, one must be careful in applying standard statistical techniques that are not suitable under arbitrage theory, in particular, ML method. Copyright © 2010 John Wiley & Sons, Ltd.     

Implied volatility and state price density estimation: arbitrage analysis

This paper deals with implied volatility (IV) estimation using no-arbitrage techniques. The current market practice is to obtain IV of liquid options as based on Black–Scholes (BS type hereafter) models. Such volatility is subsequently used to price illiquid or even exotic options. Therefore, it follows that the BS model can be related simultaneously to the whole set of IVs as given by maturity/moneyness relation of tradable options. Then, it is possible to get IV curve or surface (a so called smile or smirk). Since the moneyness and maturity of IV often do not match the data of valuated options, some sort of estimating and local smoothing is necessary. However, it can lead to arbitrage opportunity if no-arbitrage conditions on state price density (SPD) are ignored. In this paper, using option data on DAX index, we aim to analyse the behavior of IV and SPD with respect to different choices of bandwidth parameter h, time to maturity and kernel function. A set of bandwidths which violates no-arbitrage conditions is identified. We document that the change of h implies interesting changes in the violation interval of moneyness. We also perform the analysis after removing outliers, in order to show that not only outliers cause the violation of no-arbitrage conditions. Moreover, we propose a new measure of arbitrage which can be considered either for the SPD curve (arbitrage area measure) or for the SPD surface (arbitrage volume measure). We highlight the impact of h on the proposed measures considering the options on a German stock index. Finally, we propose an extension of the IV and SPD estimation for the case of options on a dividend-paying stock.     

有交易费的无套利资产组合优化性质

针对所给出的有交易费的资产过程模型，引入了资产折算函数以刻划套期保值和套利机会，并利用辅助鞅和凸分析的对偶方法，讨论了该模型下基于无套利分析的资产组合优化可达性的一些性质．     

Mean‐Reverting Market Model: Speculative Opportunities and Non‐Arbitrage

The paper studies arbitrage opportunities and possible speculative opportunities for diffusion mean‐reverting market models. It is shown that the Novikov condition is satisfied for any time interval and for any set of parameters. It is non‐trivial because the appreciation rate has Gaussian distribution converging to a stationary limit. It follows that the mean‐reverting model is arbitrage‐free for any finite time interval. Further, it is shown that this model still allows some speculative opportunities: a gain for a wide enough set of expected utilities can be achieved for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters.