基于随机波动率假设的权证定价理论评述

随机波动率(SV)模型在衍生品定价和风险管理中的应用开始发挥越来越重要的作用,但是,由于很难得到似然函数的闭型表达式,SV模型的参数估计问题严重限制了它在金融实践领域的普及应用。不过,近年来,学者们提出了许多旨在解决SV模型参数估计问题的有效且可行的新方法,大大推进了SV模型的应用化进程。本文将在权证定价分析的框架内,重点评述SV模型的参数估计方法,并从理论和实证的角度对它们的优点和不足进行简要评介和比较。     

低波动率溢价条件下的备兑权证定价

作为对传统期权定价模型的改良，本文将不同的波动率模型导入BlackSchole（1973）模型以及Hull＆White（1987）模型，研究了在低波动率溢价条件下各种波动率模型与定价模型结合而形成的新定价模型对中资股背景的备兑权证定价的能力。根据样本所计算的结果显示，Hull＆White模型与GARCH$波动率模型的结合能够较为精准地对备兑权证进行定价。此外，面对我国证券市场可能迎来的备兑权证即将发行的格局，本文还提出了加强发行商资格审批、发行后风险控制监管相对灵活等建议。     

基于历史和隐含波动率的权证定价效率研究

该文选取了2008年12月在沪深股票交易所交易的所有处于实值状态的权证和2只处于虚值状态的权证、2只过期权证,分别运用历史波动率和隐含波动率,计算了基于B-S定价方法的理论价格,结果发现基于历史波动率的B-S理论价格倾向于低估市场价格,对于处于深度虚值状态的权证,其已失去对价格的解释和预测能力;而基于隐含波动率的B-S理论价格对市场价格的短期解释和预测能力较好,在本文测试的样本内偏误均在1%以内;通过对两只过期权证的测算,结果表明基于历史波动率的B-S理论价格对权证在整个存续区间的运行趋势起到了决定性的作用,但市场价格的运行要高于理论价格且背离理论价格的运行具有一定的规律性,我国权证市场存在较大的投机成分.     

基于B-S期权定价公式对权证定价的研究

权证作为一个为规避风险的衍生金融工具.曾经在中国有过一段短暂的权证发展时期.但由于种种原因最终导致权证这种金融衍生工具逐渐淡出市场长达10年之久.2005年8月22日宝钢权证上市,标志着中国证券市场再次推出权证.经过5年多的发展,我国权证市场逐渐向规范和成熟方向努力.本文以长虹CWB1权证为例通过Black-Scholes公式进行定价,并对目前该权证的实际价格情况进行检验,分析其中的原因.     

权证产品理论定价与市场定价偏离度分析

通过选取宝钢权证对我国的权证市场进行偏离度静态统计及动态分析,发现市场定价不仅在多个时点大大高于理论定价,而且长期来看其变化趋势也独立于理论定价,理论定价对预测市场定价是没有帮助的,两者的偏离是不稳定的、随机的。市场投机因素是导致这一结果的主要原因。     

关于权证定价修正模型的比较研究——基于交易成本和股息分红因素的分析框架

在我国股权分置改革中，权证推动了证券市场的金融创新。鉴于权证定价可以借鉴期权理论，国外B—S模型对我国权证市场的创新和风险管理具有一定的参考意义。本文采用B—S定价模型定价宝钢认购权证和长电认购权证，分别从交易成本和股息分红的角度进行了相应的模型调整，以改进、完善适应我国权证市场的定价方法。     

权证影响正股的定价效率吗

本文回答了权证在上市后是否能提高正股定价效率这一问题，以正股的收益率为研究对象，本文用EGARCH模型分析了日收益率的大小及其方差的变动情况在双证上市前后是否有显著差异，实证结果表明，从整体看双证尽管不会显著降低正股的定价效率，但是作为一种金融衍生品，权证并没有对正股定价效率的提高发挥显著作用。本文认为原因可能来自我国权证制度本身，包括卖方资格的限制以及创设保证金的要求所导致的套期保值和套利成本过高。因此，保证金融衍生品套期保证值和套利功能的实现，是提高标的资产定价效率的必要条件。     

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.     

Black-Scholes期权定价、二叉树定价及其在我国权证市场适用性分析

运用B-S期权定价和二叉树定价对我国沪市发行4只认购权证和1只认沽权证的理论价值进行测度,并采用偏离度和T统计量分析两种期权定价方法的定价效率。研究结果表明,与二叉树定价相比,B-S期权定价得到的权证理论价格更加贴近于市场实际价格,其偏离度小于二叉树定价结果的偏离度。由此可见,B-S定价模型更适用于我国权证市场的定价,其定价效率较高。但是,分析的结果也表明,两种定价方法测度的理论价值与实际价格仍存在较大的差异,制度因素可能是导致定价偏差的一个重要原因,因此,如何考虑我国权证市场的实际情况,从而对理论模型进行修正是后续研究的一个重要方向。     

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 Discrete Barrier Options Under Stochastic Volatility

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in pricing barrier options with discrete monitoring. To the best of our knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Furthermore, it provides numerical examples for pricing double barrier call options with discrete monitoring under Heston and λ-SABR models.     

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

This paper specifies a multivariate stochasticvolatility (SV) model for the S & P500 index and spot interest rateprocesses. We first estimate the multivariate SV model via theefficient method of moments (EMM) technique based on observations ofunderlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S & P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premiumof stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or leverage effect does help to explain the skewness of the volatility smile, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficientin modeling short-term kurtosis of asset returns, an SV model withfatter-tailed noise or jump component may have better explanatory power.     

Pricing Options under Generalized GARCH and Stochastic Volatility Processes

In this paper, we develop an efficient lattice algorithm to price European and American options under discrete time GARCH processes. We show that this algorithm is easily extended to price options under generalized GARCH processes, with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases. We establish one unifying algorithm that can price options under almost all existing GARCH specifications as well as under a large family of bivariate diffusions in which volatility follows its own, perhaps correlated, process.     

基于非对称随机波动模型的人民币汇率波动特征研究

本文使用非对称随机波动模型,对2005年7月22日至2012年9月5日期间美元兑人民币汇率的波动特征进行了实证分析。模型拟合检验结论显示,非对称随机波动模型能够很好地拟合美元兑人民币汇率波动过程中存在的时变性、持续性和非对称性特征。来自MCMC估计结果进一步表明:美元兑人民币汇率波动过程存在的非对称特征不同于在股票市场普遍发现的"放大利空,缩小利好"型的"杠杆效应",而是突出表现为"放大利好,缩小利空"。但波动的非对称效应和强度较弱,这意味着央行在采取措施干预和管理汇率波动时,在时机选择和力度把握上不仅要充分考虑到人民币汇率波动的时变性和持续性特征,而且更应注意汇率波动的非对称性及非对称类型。     

期权定价理论的发展和倒向随机微分方程

本文总结了期权定价理论的发展历程及其主要的数学模型,而期权定价理论在发展的过程中促进了一类新的方程———倒向随机微分方程的发展,并且倒向随机微分方程在期权定价中也有重要应用。     

Capital Asset Pricing Model and Stochastic Volatility: A Case Study of India

The existing literature demonstrates that under a general equilibrium model, the performance of the Capital Asset Pricing Model (CAPM) can be improved significantly by using conditional consumption and market return volatilities as factors. This article tests the validity of these factors explaining stock return differences using a less developed country (India) as a case study. While the earlier studies used panel data to test CAPM, we use portfolios sorted by size and book-to-market equity (BE/ME) ratio. We found that conditional volatility has a limited effect on firms with large capitalization but a significant impact on small-growth and small-value firms.     

A Remark on a Singular Perturbation Method for Option Pricing Under a Stochastic Volatility Model

This paper studies the approximation accuracy of a singular perturbation method for option pricing up to the second order under a stochastic volatility model. First, numerical experiments confirm that the first order approximation provides sufficiently accurate option prices in a fast mean-reversion volatility case. On the other hand, it creates relatively large errors in a non-fast mean-reversion volatility environment. Then, the second order approximation formula is derived and the improvement of the approximation is investigated.     

Testing for Volatility Jumps in the Stochastic Volatility Process

This paper considers the stochastic volatility process with contemporaneous and correlated jumps in returns and volatility, which was proposed by Eraker, B., Johannes, M. and Poison, N. G. (Journal of Finance 53, 2003, 1269--1300) and proposes the Lagrange multiplier test for the presence of jumps in volatility. The test statistic is derived by regarding the degenerate density of volatility jumps with zero variance under the null as Dirac's delta function. The correlation parameter between jumps, which is a nuisance parameter unidentified under the null, is cancelled out in this test statistic and hence the test is free from the Davies problem (Davies, R. B., Biometrika 64, 1977, 247–254).