Pricing and Hedging Discount Bond Options in the Presence of Model Risk

This paper focuses on pricing and hedging options on a zero-couponbond in a Heath—Jarrow—Morton (1992) framework whenthe value and/or functional form of forward interest rates volatilityis unknown, but is assumed to lie between two fixed values.Due to the link existing between the drift and the diffusioncoefficients of the forward rates in the Heath, Jarrow and Mortonframework, this is equivalent to hedging and pricing the optionwhen the underlying interest rate model is unknown. We showthat a continuous range of option prices consistent with noarbitrage exist. This range is bounded by the smallest upper-hedgingstrategy and the largest lower-hedging strategy prices, whichare characterized as the solutions of two non—linear partialdifferential equations. We also discuss several pricing andhedging illustrations.     

Pricing and Hedging Discount Bond Options in the Presence of Model Risk

This paper focuses on pricing and hedging options on a zero-coupon bond in a Heath–Jarrow–Morton (1992) framework when the value and/or functional form of forward interest rates volatility is unknown, but is assumed to lie between two fixed values. Due to the link existing between the drift and the diffusion coefficients of the forward rates in the Heath, Jarrow and Morton framework, this is equivalent to hedging and pricing the option when the underlying interest rate model is unknown. We show that a continuous rangeof option prices consistent with no arbitrage exist. This range is bounded by the smallest upper-hedging strategy and the largest lower-hedging strategy prices, which are characterized as the solutions of two non-linear partial differential equations. We also discuss several pricing and hedging illustrations.     

随机参数二叉树期权定价方法及其模拟研究

本文将股票波动性随机变化的因素考虑到二叉树期权定价模型中,得到了可以用数值计算方法实现的一个期权定价方法,该公式比传统二叉树模型更能反映股票波动的异方差性。以五粮液认购权证与五粮液认沽权证为样本,运用马尔科夫链蒙特卡罗方法对其进行了模拟分析,并与B-S模型进行了比较。     

Pricing Bonds and Bond Options with Default Risk

The pricing of bonds and bond options with default risk is analysed in the general equilibrium model of Cox, Ingersoll, and Ross (1985). This model is extended by means of an additional parameter in order to deal with financial and credit risk simultaneously. The estimation of such a parameter, which can be considered as the market equivalent of an agencies' bond rating, allows to extract from current quotes the market perceptions of firm's credit risk. The general pricing model for defaultable zero-coupon bond is first derived in a simple discrete-time setting and then in continuous-time. The availability of an integrated model allows for the pricing of default-free options written on defaultable bonds and of vulnerable options written either on default-free bonds or defaultable bonds. A comparison between our results and those given by Jarrow and Turnbull (1995) is also presented.     

含期权债券利率风险的衡量

久期(Duration)和凸度(Convexity)是度量普通债券利率风险的常用指标。含权债券中内嵌的期权会改变债券价格变动和利率变动的关系,使债券面临更大的利率风险,但常用的久期和凸度无法体现这一影响。实际久期和实际凸度可以弥补这一缺陷,是衡量含权债券利率风险的有效指标。对国家开发银行发行的可赎回债券和可回售债券的模拟和实证分析表明,由于内嵌了期权,在有些情况下实际凸度解释了大部分的利率风险,因此建议在投资中使用实际久期和实际凸度来衡量含权债券的利率风险,而且在利率比较高或比较低时不可忽略实际凸度对利率风险的解释作用。     

Heterogeneity and Option Pricing

An economy with agents having constant yetheterogeneous degrees of relative risk aversion prices assetsas though there were a single decreasing relative risk aversion``pricing representative' agent. The pricing kernel has fattails, and option prices do not conform to the Black-Scholesformula. Implied volatility exhibits a ``smile.' Heterogeneityas the source of non-stationary pricing fits Rubenstein's (1994)interpretation of the ``over-pricing' as an indication of ``crash-o-phobia'.Rubinstein's term suggests that those who hold out-of-the moneyput options have relatively high risk aversion (or relativelyhigh subjective probability assessments of low market outcomes).The essence of this explanation is investor heterogeneity.     

A Non-Parametric Option Pricing Model: Theory and Empirical Evidence

In this paper, we propose an empirically-based, non-parametric option pricing model to evaluate S&P 500 index options. Given the fact that the model is derived under the real measure, an equilibrium asset pricing model, instead of no-arbitrage, must be assumed. Using the histogram of past S&P 500 index returns, we find that most of the volatility smile documented in the literature disappears.     

Option Pricing Bounds and the Elasticity of the Pricing Kernel

In this paper we use power functions as pricing kernels to derive option-pricing bounds. We derive option pricing bounds given the bounds of the elasticity of the true pricing kernel. The bounds of the elasticity of the true pricing kernel are closely related to the bounds of the representative investor's coefficient of relative risk aversion. This methodology produces a tighter upper call option bound than traditional approaches. As a special case we show how to use the Black–Scholes formula to obtain option pricing bounds under the assumption of lognormality.     

基于B-S期权定价模型的可转换债券定价实证分析

可转换债券是一种混合金融衍生工具,它把相应的股票看涨期权内嵌在传统的公司债券之中,具有债券和股票的双重性质,因而可转债的定价问题逐渐为企业和投资者所关注。本文借助Black—Scholes定价模型研究定价理论,对Black-Scholes定价模型进行修正,体现了红利发放对可转换债券定价的影响。     

Analysis of the Nonlinear Option Pricing Model Under Variable Transaction Costs

In this paper we analyze a nonlinear Black–Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price V is assumed to be a function of the underlying asset price and the Gamma of the option. We show that the generalizations of the classical Black–Scholes model can be analyzed by means of transformation of the fully nonlinear parabolic equation into a quasilinear parabolic equation for the second derivative of the option price. We show existence of a classical smooth solution and prove useful bounds on the option prices. Furthermore, we construct an effective numerical scheme for approximation of the solution. The solutions are obtained by means of the efficient numerical discretization scheme of the Gamma equation. Several computational examples are presented.     

LSM可转债定价模型及其应用研究

可转债定价一直是可转债发行与投资分析的关键,通过引入最小二乘蒙特卡罗模拟法(LSM)对可转债进行定价研究,利用GARCH模型对股价波动率、无风险利率等参数进行估计,并利用平赌过程适配法提高LSM的执行效率.实证结果表明,最小二乘蒙特卡罗模拟法具有较好的预测效果,为可转债定价提供了一条有效途径.     

Original-Issue Systematic and Default Risk Pricing Efficiency of Speculative-Grade Bonds

We investigate whether primary market, original‐issue risk premiums on speculative‐grade debt are justified solely by expected defaults or whether these risk premiums also include other orthogonal risk components. Studies of secondary‐market holding period risk and return have hypothesized that risk premiums on speculative‐grade debt may be explained by bond‐ and equity‐related systematic risk and possibly other types of risk. Using an actuarial approach that considers contemporaneous correlation between default frequency and severity and first‐order serial correlation, we cannot reject the hypothesis that the entire original‐issue risk premium can be explained by expected default losses. This suggests that speculative‐grade bond primary markets efficiently price default risk and that other types of risk are priced as coincident as opposed to orthogonal risks.     

An Event Option Pricing Model with Scheduled and Unscheduled Announcement Effects

There is considerable evidence supporting the time-varying distribution of asset returns. There is also ample evidence that scheduled announcement events such as money supply announcements (in the case of foreign exchange), earnings announcements (in the case of stocks), and crop reports (in the case of commodities), as well as random unscheduled events, can affect the level and volatility of asset returns. This study provides an Event Model for European call options which explicitly addresses effects of these two classes of events. This specification requires estimation of more parameters, but it could provide a more accurate basis for pricing options than previous Poisson jump-diffusion models. Parametric analysis shows that the standard models under price the options relative to the Event Model. The Event Model may be particularly useful in pricing short-term deep out-of-the-money options when scheduled events are present in the market.     

VIX期权定价与校正

VIX期权作为波动率衍生品能为金融机构提供有效的市场风险对冲工具。文献中对VIX期权定价的实证分析误差都很大,原因在于模型的选取误差以及校正方法和样本选取不妥。通过在VIX模型中加入均值回复因素和跳因素,可以使VIX过程更加合理,也可以使VIX期权定价精度更高。通过对VIX期权市场中间报价进行校正,得到了4个文献模型的参数估计,并比较4个模型的定价精度和正向隐含波动率偏斜拟合效果。     

Jackknifing Bond Option Prices

Prices of interest rate derivative securities depend cruciallyon the mean reversion parameters of the underlying diffusions.These parameters are subject to estimation bias when standardmethods are used. The estimation bias can be substantial evenin very large samples and much more serious than the discretizationbias, and it translates into a bias in pricing bond optionsand other derivative securities that is important in practicalwork. This article proposes a very general and computationallyinexpensive method of bias reduction that is based on Quenouille's(1956; Biometrika, 43, 353–360) jackknife. We show howthe method can be applied directly to the options price itselfas well as the coefficients in the models. We investigate itsperformance in a Monte Carlo study. Empirical applications toU.S. dollar swap rates highlight the differences between bondand option prices implied by the jackknife procedure and thoseimplied by the standard approach. These differences are largeand suggest that bias reduction in pricing options is importantin practical applications.