Valuation of sinking-fund bonds in the Vasicek and CIR frameworks∗Financial support from Murst Fondo 40% on ‘Modelli di struttura a termine dei tassi d'interesse’ is gratefully acknowledged.

In a sinking-fund bond, the issuer is required to retire portions of the bond prior to maturity, with the option of doing so either by calling the bonds by lottery, or by buying them back at their market value. This paper discusses the valuation of a default-free sinking-fund bond issue in the Vasicek (1977) and, alternatively, the Cox, Ingersoll and Ross (CIR) (1985) frameworks. We show in particular that, calling the bond issue without the delivery option ‘corresponding serial’, and the one without the prepayment feature ‘corresponding coupon’, under no-arbitrage a sinking-fund bond can be priced either in terms of the corresponding coupon bond and a bond call option, or in terms of the corresponding serial and a bond put option. We also present a detailed comparative-statics analysis of our valuation model, where we show that a sinking-fund bond has a stochastic duration intermediate between the ones of the corresponding serial and coupon bonds. We argue that such a feature gives a further rational for the presence of the delivery option. Moreover, we compare our results with the ones of Ho (1985), who has previously discussed the valuation problem under scrutiny.     

A note on first-passage times of continuously time-changed Brownian motion

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, for example, for the pricing of single-barrier and double-barrier options in a Black-Scholes framework. One popular possibility to generalize the Black-Scholes model is to introduce a stochastic time scale. This equips the modelled returns with desirable stylized facts such as volatility clusters and jumps. For continuous time transformations, independent of the Brownian motion, we show that analytical results for the double-barrier problem can be obtained via the Laplace transform of the time change. The result is a very efficient power series representation for the resulting exit probabilities. We discuss possible specifications of the time change based on integrated intensities of shot-noise type and of basic affine process type.     

考虑零售商公平关切的期权合约研究

当供应链中的企业都是完全理性时,一个合理设计的期权合约可使得供应链达到协调。本文考虑一个具有公平关切的零售商的供应链系统,分析期权合约下零售商的订货决策,以及使供应链达到协调的条件。研究发现,零售商的公平关切偏好对期权合约的协调作用有着显著的影响:尽管与完全理性的供应链系统相比,可协调供应链的期权合约的定价规则没有变化,但是随着零售商公平关切程度的提高,供应商可能获得的最大利润减小,协调性期权合约的可选择范围不断缩小,直至消失.算例分析进一步验证了以上结论,并说明了即使存在协调性期权合约,零售商可能会因为对不公平的厌恶而极大降低自身效用,出现负的效用值,导致该合约被拒绝。     

Lattice Boltzmann methods for solving partial differential equations of exotic option pricing

This paper establishes a lattice Boltzmann method (LBM) with two amending functions for solving partial differential equations (PDEs) arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O(N), where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.     

基于分数布朗运动的具有信息影响的投资组合期权定价

假设标的资产价格服从分数布朗散运动,其价格跳跃度服从复合Poisson分布,采用拟鞅定价的方法,得到了具有信息影响的投资组合的期权定价公式.     

跳扩散条件下波动率风险溢价及影响因素研究——基于上证50 ETF期权市场的实证

本文采用上证50 ETF及其期权交易数据,运用SVCJ模型、MCMC及傅里叶变换等方法,从P测度及Q测度中提取波动率风险溢价,并分析了其时变特征及影响因素。实证研究表明:SVCJ模型相较于SV模型及SVJ模型具有更好的市场拟合优度;傅里叶变换法能提高波动率风险溢价的估计效率;波动率风险溢价具有时变特征,在市场急剧动荡时期,波动率风险溢价基本为负,投资者厌恶波动风险,购买期权对冲波动风险的意愿较高;在市场非急剧动荡时期,波动率风险溢价基本为正,投资者偏好波动风险,购买期权对冲波动风险的意愿较低;市场收益率、波动率、换手率及投资者情绪对波动率风险溢价具有显著的影响。     

零售商风险规避条件下基于期权契约的生鲜农产品供应链协调研究

民以食为天,随着生活水平的不断提高,生鲜农产品在消费结构中的重要性越来越突出,本文将期权思想引入生鲜农产品供应链运作当中,针对由一个零售商和一个供应商组成的二级生鲜农产品供应链,结合生鲜农产品的自然属性,考虑在途损耗对产品数量的影响以及保鲜投入对产品新鲜度的影响,运用CVaR模型研究了零售商的风险规避程度对供应链决策的影响以及期权契约协调机制。研究表明,期权机制可实现风险在供需双方之间共担,可解决随机需求下生鲜农产品供应链的协调问题并合理分配整体利润;仅当零售商的风险规避程度较低时系统协调和帕累托改进才能同时达成。     

跳-扩散模型下的再装期权定价

本文建立股票价格的跳过程为Poisson过程,跳跃高度服从对数正态分布时股票价格过程的随机微分方程,在风险中性的假设下找到等价鞅测度,利用鞅方法,用较简单的数学推导得到了股票价格服从跳-扩散过程的欧式再装期权定价公式.     

MCNP程序中一处缺陷的证实及规避方法

当应用MCNP程序的SDEF卡进行固定源问题的源信息描述时,需要对源的分布进行描述,MCNP程序提供了SP卡用以指定源在各个栅元中的分布概率,SP卡中的V选项用于便利用户实现体密度方式的源强分布描述。研究发现,该程序存在一个缺陷,在使用SP卡V选项时可能会导致计算结果的不准确。通过构建典型算例模型,对使用V选项和不使用该选项的计算结果进行对比分析,可以证实该缺陷的存在,并且能够证明可以通过其他源描述方法在具体的程序使用中规避该缺陷。