简单可转换债券的定价——一种鞅方法

可转换债券作为债券和期权的混合体,其定价比债券和期权的定价都要复杂.本文用鞅方法讨论可转换债券的定价问题,给出了便于计算的类似于Black-Scholes模型的定价公式.但我们利用鞅方法使定价模型的推导更自然.基于这一定价模型,可转换债券的价格可分解为转换期权的价格和简单债券的价值之和.     

结构转换条件下债券期权定价研究

从利率动态变化、结构转换和期权定价三个方面进行分析,对结构转换下的债券和债券期权进行定价,考虑了结构转换对利率衍生物定价的影响,利用Ito引理获得债券定价的偏微分方程,并得到债券期权定价的特征函数与递归等式.结构转换下债券期权定价的灵敏度分析表明期权价值与初始状态概率、结构的持续性和结构波动率有关.     

带有违约风险的可转换债券的简约型定价

本文考虑简约模型下带有违约风险的可转换债券的定价问题.假定市场中可转换债券的违约强度满足Vasicek模型,利用鞅方法获得了该模型下可转换债券的定价公式.此外,我们通过数值分析显示了模型参数变化对可转换债券价值影响的敏感性程度,结果也表明违约风险将降低可转换债券的价值.     

跳-扩散结构下内含巴黎期权特征的可转债定价研究

考虑了跳-扩散结构下的可转换债券定价问题.首先分析了回售、赎回等条款,发现可转换债券具有巴黎期权特征.然后,根据期权定价理论,运用近似对冲跳跃风险的方法,建立了可转换债券的定价模型,得到了可转换债券价格所满足的偏微分方程.基于半离散化方法,给出了偏微分方程求解的数值方法,并且对数值方法的稳定性和误差进行了分析.最后,以重工转债和南山转债为例,对可转债市场进行了实证研究.     

基于路径积分方法的可转换债券定价

可转换债券是一种混合金融衍生品,主要特点是在某时刻可以转换成其他金融产品,保障双方收益.假设利率服从Vasicek随机利率模型和股票价格服从几何布朗运动过程,利用Feynman路径积分方法分别重构债券和转股期权的定价函数给出可转债定价体系新的估值模型.通过数值模拟说明解析公式的计算结果更稳定,能够降低可转债高估的风险.     

带有重置条款的可转换债券定价

可转换债券是中国证券市场的热点之一.本文主要研究如何给带有重置条款的可转换债券进行定价.文中采用了等价鞅测度的思想将标的物从风险世界转换到风险中性世界中,然后在风险中性世界中应用鞅评价方法对带有重置条款的可转换债券进行定价.     

可转换债券价值确定的蒙特卡罗方法

首先对可转换债券定价的各种数值方法作了研究综述,并比较了各种方法的优点和缺陷;针对可转换债券品种价值确定过程中的特征,介绍了采用蒙特卡罗仿真算法为可转换债券定价的实施步骤,根据可转换债券持有、转股、赎回和回售等可能发生的状况,分别给出了用该方法实现定价的原理和过程.     

随机利率下可分离交易可转换债券的鞅定价

从定量的角度分析了可分离式可转换债券的价值构成,并在服从Vasicek利率模型的随机利率下,利用Martingle Pricing方法推导出其定价公式.     

风险投资中基于不同退出方式的可转换证券应用研究

风险投资具有巨大的不确定性和风险性,风险投资主体对投资金融工具和退出方式的选择直接影响投资成败.为了分析风险投资中退出方式和金融工具选择问题,本文基于不同退出方式对参加分配可转换证券构建了混合实物期权模型,利用该模型比较研究了一般可转换证券和参加分配可转换证券,证明了参加分配可转换证券的使用将使风险投资主体在首次公开上市和收购两种退出方式中更倾向于后者的结论,并得出了参加分配可转换证券给风险投资主体带来的风险收益.     

有跳-扩散违约风险的可转换债券的定价

本文研究在跳-扩散违约风险模型下可转换债券的定价问题,假定股票价格服从对数正态分布,利用Martingale Pricing方法推导出其定价公式.     

Risk management of a bond portfolio using options

In this paper, we elaborate a formula for determining the optimal strike price for a bond put option, used to hedge a position in a bond. This strike price is optimal in the sense that it minimizes, for a given budget, either Value-at-Risk or Tail Value-at-Risk. Formulas are derived for both zero-coupon and coupon bonds, which can also be understood as a portfolio of bonds. These formulas are valid for any short rate model that implies an affine term structure model and in particular that implies a lognormal distribution of future zero-coupon bond prices. As an application, we focus on the Hull-White one-factor model, which is calibrated to a set of cap prices. We illustrate our procedure by hedging a Belgian government bond, and take into account the possibility of divergence between theoretical option prices and real option prices. This paper can be seen as an extension of the work of Ahn and co-workers [Ahn, D., Boudoukh, J., Richardson, M., Whitelaw, R., 1999. Optimal risk management using options. J. Financ. 54, 359-375], who consider the same problem for an investment in a share.     

A numerical PDE approach for pricing callable bonds

Many debt issues contain an embedded call option that allows the issuer to redeem the bond at specified dates for a specified price. The issuer is typically required to provide advance notice of a decision to exercise this call option. The valuation of these contracts is an interesting numerical exercise because discontinuities may arise in the bond value or its derivative at call and/or notice dates. Recently, it has been suggested that finite difference methods cannot be used to price callable bonds requiring notice. Poor accuracy was attributed to discontinuities and difficulties in handling boundary conditions. As an alternative, a semi-analytical method using Green's functions for valuing callable bonds with notice was proposed. Unfortunately, the Green's function method is limited to special cases. Consequently, it is desirable to develop a more general approach. This is provided by using more advanced techniques such as flux limiters to obtain an accurate numerical partial differential equation method. Finally, in a typical pricing model an inappropriate financial condition is required in order to properly specify boundary conditions for the associated PDE. It is shown that a small perturbation of such a model is free from such artificial conditions.     

The simulation of option prices with application to LIFFE options on futures

We build a framework for modelling the deviation of observed option prices from the Black & Scholes prices. We use a flexible model for a density, a two sided switching Weibull, to capture the implied volatility. The model can be used to generate prices, it can take into account no-arbitrage bounds for option prices and is capable of generating such stylised facts as the smile effect. We apply this methodology to LIFFE options on German government bond futures.     

A Simple Novel Approach to Valuing Risky Zero Coupon Bond in a Markov Regime Switching Economy

We have addressed the problem of pricing risky zero coupon bond in the framework of Longstaff and Schwartz structural type model by pricing it as a Down-and-Out European Barrier Call option on the company’s asset-debt ratio assuming Markov regime switching economy. The growth rate and the volatility of the stochastic asset debt ratio is driven by a continuous time Markov chain which signifies state of the economy. Regime Switching renders market incomplete and selection of a Equivalent martingale measure (EMM) becomes a subtle issue. We price the zero coupon risky bond utilizing the powerful technique of Risk Minimizing hedging of the underlying Barrier option under the so called “Risk Minimal” martingale measure via computing the bond default probability.     

CHANGE OF NUMÉRAIRE AND AMERICAN OPTIONS

The change of numéraire technique is a standard tool in mathematical finance. We apply it to the analysis of the value and the hedging strategies of American options.

The change of numéraire is particularly powerful if the option is written on more assets and has a positively homogeneous payoff. In this case, the option writer doesn't need the riskless bond to hedge his position. We treat some examples as the Margrabe option on two stocks paying continuous dividends and the best of two assets option. Thanks to variational inequalities we are able to give numerical results for the pricing and the hedging of such a kind of American options.     

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.     

Modeling of certain problems in financial mathematics: Spread option pricing

The problem of valuating exotic options, namely, the option on the spread between two forward interest rates is considered. The price of the option is derived under the assumption that the dynamics of debt instruments and the interest rates are described by the Heath-Jarrow-Morton model. The parameters of the model are estimated, and the price of the option is numerically computed based on Russian bond market data.     

企业债券的欧式期权的定价公式

本文研究了带有信用风险的企业债券的欧式衍生资产的定价方法,建立风险债券与无风险债券期权价格的相互关系。     

美式债券期权定价熵模型

基于熵定价理论,结合美式期权解析近似求解的G eske-Johnson方法,构建了美式债券期权定价熵模型,给出了标的资产为零息票债券和息票债券的美式期权估值的解析近似计算公式,并展示了具体的算法步骤.