确定波动率的欧式期权鞅定价与利率期限结构

把merton随机利率期权模型扩展到允许基础资产支付红利情形,在一系列假设前提基础上重新运用鞅测度方法可以得到无套利时随机利率下欧式未定权益的一般定价公式,进而得出欧式期权定价的解析表达式。通过对债券价格过程的假设,构造出一个关于确定波动率的债券价格过程、单因素利率期限结构模型和债券价格之间的对应关系的命题,并由此得出了债券期权定价的解析公式。     

利率动态模型研究评述——基于Shibor应用的视角

在利率市场化条件下,各国央行都通过控制或影响基准利率来调节整个利率体系,进而实现对利率的监管功能。构建适合上海银行间同业拆放利率（Shibor）的利率动态模型不仅能够更好地模拟Shibor本身的动态变化特征。让Shibor真正在我国利率市场化改革进程中起到货币政策利率传导的主导与核心作用,而且对我国大力发展以Shibor为标的的金融衍生产品,培养我国金融机构的利率衍生产品的自我定价能力、完善利率风险管理方面具有重要意义。     

基于波动率的期权定价理论及实证研究

金融衍生品价格是否合理是市场是否能够有效进行的保证,本文通过对波动率下的期权定价模型的理论分析与比较,使用港股期权的最新数据,运用BS、GRACH以及Heston模型三种方法分别进行实证研究.     

期权定价模型中的波动率分析

期权定价模型是布莱克的一种典型的相对经济理论,它在金融实践过程中产生巨大的经济影响,这种期权的模型需要输入参数中在市场中无法直接观察取得的重要变量,即波动率数值,也就是说,基于历史数据来计量历史波动。人们通常在期权经济定价中,结合期权的价格,采用定量模型倒推出隐含的波动率,这种隐含的波动率对于投资者未来市场的预期有很重要的作用,对于期权市场和经济市场的避险和套期保值业务来说,为了能够进行更好的风险规避和管理,就必须要了解隐含波动率的波动规律。     

CIR-CKLS-Jump利率波动模型与商业银行隐含期权定价

以经典CIR和CKLS利率波动模型为基础,结合利率跳跃扩散理论,构建出CIR-CKLSJump利率波动模型,采用对偶变量方差减少技术蒙特卡洛模拟方法对商业银行存贷款隐含期权进行定价。结果表明,CIR-CKLS-Jump利率波动模型能较好地模拟现实数据的变化过程,且商业银行存贷款隐含期权值均处于实值状态。在利率完全市场化的情况下,商业银行在开展存贷款业务时若能充分考虑隐含期权价值,将提高银行利率定价能力,减少利率风险。     

利率动态模型研究评述——基于Shibor应用的视角

在利率市场化时期,各国央行都是通过控制或影响基准利率来调节整个利率体系,进而实现对利率的监管功能。Shibor是央行培育的中国货币市场基准利率体系,在利率动态模型的框架内,通过对利率动态模型的国内外相关文献回顾,重点评述了利率动态模型及其相关扩展,并基于对Shibor的应用视角展开了一定的讨论,对于研究Shibor在我国利率市场化背景下的市场基准利率角色与金融衍生品市场的快速发展具有重要意义。     

Shibor与利率市场化

文章回顾了我国利率市场化改革的进程，指出Shibor处于市场最基准的地位，直接关系到利率市场化。从目前运行情况看。Shibor已可以作为货币市场流动性的有效衡量指标，其与货币市场产品的比价关系逐渐显现。下一步，我们要以Shibor为核心推进利率市场化，并在培育基准利率的同时，探索建立中央银行货币政策调控的目标利率和利率调控框架。     

期权定价模型中的波动率分析

布莱克-斯科尔斯的期权定价模型是一个对经济理论、金融实践产生巨大影响的模型。该模型需要输入的参数中唯一无法在市场中直接观察到的重要变量是基础资产的波动率。基于历史数据来计量的历史波动率有严重缺陷,于是人们根据期权的市场价格,利用Black-Scholes定价模型倒推出隐含波动率。隐含波动率反映投资者对未来市场的共同预期;对于避险者的套期保值业务来说,这是进行风险管理的一项重要指标。然而,隐含波动率在使用过程中也存在着＂波动率微笑＂、＂波动率偏斜＂及＂波动率期限结构＂等现象。究其根源,皆源自于Black-Scholes模型所依据的某些假设条件与实际情况不相符合。     

Shibor与利率市场化：前景展望

在Shibor推出的基础上，产品定价市场化、存贷款利率市场化以及央行货币政策调控目标部将以此为基础逐步展开。文章认为应该不断提高Shibor报价的交易性和市场性，提高其独立定价影响其他利率的能力，使Shibor的基准利率地位不断成熟完善；使其能够真实反映市场资金供求状况，并促进央行的货币政策实现由数量型调控转向价格型调控。     

Shibor市场价格短期波动率特征及预测研究——基于GARCH族和TVP-SV-VAR模型的实证分析

Shibor作为一种包含多个期限的利率价格体系,其短期波动具有双重特征：从外部性而言,Shibor是市场上拆借资金供求状况的自然反映,其短期波动趋势会受到拆借资金供求状况的影响;从内部性而言,不同期限Shibor间的波动会彼此影响。研究表明,Shibor波动率外部特征具有很强的波动集聚性和持续性,不同期限Shibor的波动外部特征存在明显差异。Shibor波动率内部特征表现出了时变联动性,期限较短Shibor的波动敏感性较强,期限较长Shibor的波动溢出效应显著。     

Interest rate option pricing with volatility humps

This paper develops a simple model for pricing interest rate options when the volatility structure of forward rates is humped. Analytical solutions are developed for European claims and efficient algorithms exist for pricing American options. The interest rate claims are priced in the Heath-Jarrow-Morton paradigm, and hence incorporate full information on the term structure. The structure of volatilities is captured without using time varying parameters. As a result, the volatility structure is stationary. It is not possible to have all the above properties hold in a Heath Jarrow Morton model with a single state variable. It is shown that the full dynamics of the term structure is captured by a three state Markovian system. Caplet data is used to establish that the volatility hump is an important feature to capture. This revised version was published online in June 2006 with corrections to the Cover Date.     

Target volatility option pricing in the lognormal fractional SABR model

We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula of Itô's calculus yields an approximation formula for the price of a target volatility option in small time by the technique of freezing the coefficient. A decomposition formula in terms of Malliavin derivatives is also provided. Alternatively, we also derive closed form expressions for a small volatility of volatility expansion of the price of a target volatility option. Numerical experiments show the accuracy of the approximations over a reasonably wide range of parameters.     

浅谈Shibor与利率互换市场发展

Shibor已经成为利率互换交易重要的基准利率,且其基准性的确立和以其为基准的互换市场的发展相辅相成,互相促进：我国当前以Shibor为基准的互换交易印证Shibor已经具有一定的基准性;同时,以Shibor为基准互换市场的发展也依赖于Shibor基准性的培育。展望未来,应继续增强其基准性,明确Shibor定价中各因素的风险权重,以促进利率互换市场的进一步发展。     

A new approach for option pricing under stochastic volatility

We develop a new approach for pricing European-style contingent claims written on the time T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic volatility literature, we assume continuous dynamics for the price of the underlying asset. In contrast to most of the stochastic volatility literature, we do not directly model the dynamics of the instantaneous volatility. Instead, taking advantage of the recent rise of the variance swap market, we directly assume continuous dynamics for the time T variance swap rate. The initial value of this variance swap rate can either be directly observed, or inferred from option prices. We make no assumption concerning the real world drift of this process. We assume that the ratio of the volatility of the variance swap rate to the instantaneous volatility of the underlying asset just depends on the variance swap rate and on the variance swap maturity. Since this ratio is assumed to be independent of calendar time, we term this key assumption the stationary volatility ratio hypothesis (SVRH). The instantaneous volatility of the futures follows an unspecified stochastic process, so both the underlying futures price and the variance swap rate have unspecified stochastic volatility. Despite this, we show that the payoff to a path-independent contingent claim can be perfectly replicated by dynamic trading in futures contracts and variance swaps of the same maturity. As a result, the contingent claim is uniquely valued relative to its underlying’s futures price and the assumed observable variance swap rate. In contrast to standard models of stochastic volatility, our approach does not require specifying the market price of volatility risk or observing the initial level of instantaneous volatility. As a consequence of our SVRH, the partial differential equation (PDE) governing the arbitrage-free value of the contingent claim just depends on two state variables rather than the usual three. We then focus on the consistency of our SVRH with the standard assumption that the risk-neutral process for the instantaneous variance is a diffusion whose coefficients are independent of the variance swap maturity. We show that the combination of this maturity independent diffusion hypothesis (MIDH) and our SVRH implies a very special form of the risk-neutral diffusion process for the instantaneous variance. Fortunately, this process is tractable, well-behaved, and enjoys empirical support. Finally, we show that our model can also be used to robustly price and hedge volatility derivatives.     

Shibor利率体系的现实与推进建议

Shibor运行一年多日寸间来，其在提升自身基准利率地位及推进国内利率市场化方面所取得的成绩有目共睹。文章从探讨目前较受关注的中长期Shibor的合理性人手，分析了Shibor定价机理的现实基础及定价分歧的缘由，并从宏观和微观两个层面就完善Shibor利率体系建设提出建议。     

Shibor与金融机构产品定价

Shibor自2007年初正式发布以来，在市场各方参与主体的大力推进下，其在货币市场的基准利率地位已经逐渐被市场所认可，在金融市场的产品定价中也得到了日益广泛的运用。Shibor的进一步发展，需要金融机构不断深化对Shibor重要意义的认识，也需要不断完善Shibor报价的形成机制，各方参与主体部应在Shibor建设中积极发挥自身的作用。     

以Shibor为基准强化金融产品利率市场化

该文分析认为市场化基准利率的缺失已成为利率市场化产品定价的主要困难之一,认为将Shibor建成我国市场化的基准利率体系是人民币利率市场化必由之路,同时将大幅完善产品的市场化定价机制;而通过建立以Shibor为基础的内部资金转移定价体系,可将市场信号传导至业务端,在现行条件下能使管制利率下的存贷款利率部分实现与市场化利率的接轨。     

票据产品以Shibor为基准定价的探索

该文首先分析了票据产品以Shibor为基准定价的重要意义,认为它有利于扩展和验证Shibor的基准性、有利于规范票据产品定价、有利于加速利率市场化改革进程;进而探讨了交通银行在票据产品以Shibor为基准定价方面所作的有益探索,认为Shibor作为市场基准利率,在票据市场运用的广度和深度势必会不断提高,交通银行会继续在票据市场加大Shibor的运用力度,巩固Shibor的市场基准地位。     

Bond and option pricing for interest rate model with clustering effects

This paper analyzes an interest rate model with self-exciting jumps, in which a jump in the interest rate model increases the intensity of jumps in the same model. This self-exciting property leads to clustering effects in the interest rate model. We obtain a closed-form expression for the conditional moment-generating function when the model coefficients have affine structures. Based on the Girsanov-type measure transformation for general jump-diffusion processes, we derive the evolution of the interest rate under the equivalent martingale measure and an explicit expression of the zero-coupon bond pricing formula. Furthermore, we give a pricing formula for the European call option written on zero-coupon bonds. Finally, we provide an interpretation for the clustering effects in the interest rate model within a simple framework of general equilibrium. Indeed, we construct an interest rate model, the equilibrium state of which coincides with the interest rate model with clustering effects proposed in this paper.     

关于上海同业拆借利率定价影响因素及其基准性建设

Shibor作为推进利率市场化的重要基础条件和机制建设内容,将在深化改革过程中发挥重要作用。文章概括了Shibor的总体市场表现,用计量分析的方法筛选确定对3个月Shibor定价有显著影响的相关利率,从市场运行的角度探讨这些金融产品利率对3个月Shibor定价的影响和传导途径,并就进一步加强Shibor基准性建设提出相关政策建议。