The double exponential jump diffusion model for pricing European options under fuzzy environments

The interest rate and volatility may have different values in the different commercial banks and financial institutions. Moreover, the fluctuations of the underlying assets are rare events, and there are not enough historical data to estimate the jump intensity in a precise sense. This paper considers European option pricing problems with the fuzzy interest rate, fuzzy drift, fuzzy volatility and fuzzy jump intensity. We present the fuzzy pricing formula of European options based on the Kou's double exponential jump diffusion model. We also obtain the crisp possibilistic mean option pricing formula in fuzzy double exponential jump diffusion model by using the crisp possibilistic mean values of the fuzzy numbers. Comparing with B-S formula, numerical analysis and empirical results show that the fuzzy double exponential jump diffusion formula and the crisp possibilistic mean option pricing formula are reasonable and can be taken as reference pricing tools for the financial investors.     

含权债券定价的统一框架及其数值分析

本文从理论上推导了一般债券定价的偏微分方程，详细分析了包含欧式和美式看涨和看跌期权的4类债券，并给出了4类含权债券定价的边界条件。利用隐性差分法数值求解了偏微分方程，针对4类期权对不同利率参数的敏感性进行了分析。     

Warrant pricing under GARCH diffusion model

The GARCH diffusion model has attracted a great deal of attention in recent years, as it is able to describe financial time series better, when comparing to many other models. This paper considers the problem of warrant pricing when the underlying asset follows the GARCH diffusion model. An analytical approximate solution for European option prices is derived by means of Fourier transform. The approximate solution can be quickly computed by the fast Fourier transform (FFT) algorithm. Monte Carlo simulations show that this approximate solution is correct and the FFT is accurate and efficient, and hence it enables us to investigate the volatility smile implied by the GARCH diffusion model. Then a method is developed to provide the maximum likelihood (ML) estimation of the GARCH diffusion model based on the efficient importance sampling (EIS) procedure. Furthermore, the empirical performance of the GARCH diffusion model applied to the valuation of Hang Seng Index (HSI) warrants traded on the Hong Kong Stock Exchange (HKEx) is investigated. Empirical results show that the GARCH diffusion model outperforms the Black–Scholes (B–S) model in terms of the pricing accuracy, indicating that the pricing model incorporated with stochastic volatility can improve the pricing of warrants.     

Pricing currency options in a fractional Brownian motion with jumps

A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a fractional Brownian motion with jumps. An analytic formula for pricing European foreign currency options is proposed using the equivalent martingale measure and the estimation method of parameters in the pricing model is given, enabling option prices to be computed efficiently and accurately. For the purpose of understanding the pricing model, some properties of this pricing model are discussed in the latter part of this paper. Finally, the numerical simulations illustrate that our model is flexible and easy to implement.     

结合新产品扩散特征的实物期权定价模型研究

现有实物期权定价模型未能考虑新产品销售量所呈现的扩散特征,模型的分析结果与实际情况有较大差距。文章假设新产品价格服从几何布朗运动,并以Bass模型预测新产品的销售过程,运用二叉树方法,构建了离散时间状态下结合新产品扩散特征的实物期权定价模型,并得到新技术采用的最优时机。     

基于Poisson跳跃的信用价差期权定价

信用价差是用以向投资者补偿参照资产违约风险的、高于无风险利率的利差。信用价差期权作为风险控制的重要手段之一,其定价也日益得到人们的关注。现有文献几乎是单纯地利用几何布朗运动来刻画资产的价格变化过程从而对信用价差期权进行定价。而在实际中会出现某些不寻常的事件导致资产价格出现不间断的跳跃现象,普通的定价方法对这种现象的解释力度不够。因此本文引入Poisson跳跃来描述信用价差变化过程中的异常情况,更好地解释当遇到金融危机等情况时资产价值的跳跃现象。由于Longstaff和Schwartz的模型引入了随机利率,可以给出定价公式的封闭解析解的优点,本文在此模型上进行进行研究,将刻画信用价差动态过程的O-U过程与Poisson跳跃结合,利用伊藤公式进行推导并引入了利率的平方根过程,得到了欧式信用价差期权的定价公式,更好地考虑了资产价格的跳跃情况。     

Viewpoint: Option prices, preferences, and state variables

Abstract.  This paper surveys recent developments in the theory of option pricing. The emphasis is on the interplay between option prices and investors' impatience and their aversion to risk. The traditional view, steeped in the risk‐neutral approach to derivative pricing, has been that these preferences play no role in the determination of option prices. However, the usual lognormality assumption required to obtain preference‐free option pricing formulas is at odds with the empirical properties of financial assets. The lognormality assumption is easily reconcilable with those properties by the introduction of a latent state variable whose values can be interpreted as the states of the economy. The presence of a covariance risk with the state variable makes option prices depend explicitly on preferences. Generalized option pricing formulas, in which preferences matter, can explain several well‐known empirical biases associated with preference‐free models such as that of Black and Scholes (1973) and the stochastic volatility extensions of Hull and White (1987) and Heston (1993) .     

A semiparametric estimation of liquidity effects on option pricing

Abstract. This paper proposes a semiparametric option pricing model with liquidity, as proxied by the relative bid-ask spread. A nonparametric volatility function with liquidity costs as an explanatory variable is estimated using the Symmetrized Nearest Neighbors (SNN) estimator rather than the traditional kernel estimator. The SNN estimator is particularly suitable for the characteristics of option data in financial markets. Moreover, we propose a natural extension of the univariate bandwidth parameter optimal estimation to the multivariate case. A statistical design to test competing option pricing models which takes into account the lack of independence between them is also presented. The in-sample performance of the model turns out to be statistically favorable relative to the competing model without liquidity. Also, an additional experiment is performed within sample, but with just a subsample of options not employed in the nonparametric estimation of the implied volatility function being priced. The results are also favorable to our semiparametic theoretical option pricing model with liquidity. However, the out-of-sample performance is quite disappointing regardless of what option pricing model is employed in the estimation. Eva Ferreira and Gonzalo Rubio acknowledge the financial support provided by Dirección Interministerial Científica y Técnica (DGICYT) grants PB98-0149 and PB97-0621 respectively. All three authors aknowledge the financial support provided by Universidad del País Vasco (UPV/EHU) grant UPV 038.321-HA129/99, and the BSI Gamma Foundation. We appreciate the helpful comments of two anonymous referees, ángel León, José M. Campa, Fernando Tusell and Javier Fernández Navas, seminar participants at the Bank of Spain and the European Financial Management Association (Athens), and the computational assistance of Gregorio Serna. We thank Juan Ayuso and MEFF for providing the data used in this article. The contents of this paper are the sole responsability of the authors.     

A comparison of pricing and hedging performances of equity derivatives models

This article investigates the pricing/hedging conundrum, i.e. the observation of a mismatch between derivatives models’ pricing and hedging performances, that has so far been under-emphasized as the literature tends to focus on increasingly complicated option pricing models, without adequately addressing hedging performance. Hence, we analyse the ability of the Black–Scholes, Practitioner Black–Scholes, Heston–Nandi and Heston models to Delta-hedge a set of call options on the S&P500 index and Apple stock. We extend earlier studies in that we consider the impact of asset dynamics, apply a stringent payoff replication strategy, look at the impact of moneyness at maturity and test for the robustness to the parameters’ calibration frequency and Delta-Vega hedging. The study shows that adding risk factors to a model, as stochastic volatility, should only be considered in light of the data dynamics. Even then, however, more complicated models generally fare poorly for hedging purposes. Hence, a better fit of a model to option prices is not a good indicator of its hedging performance, and so of its ability to describe the underlying dynamics. This can be understood for reasons of over-fitting. Those findings hint to a potentially appealing hedging-based calibration of models’ parameters, rather than the standard pricing-based one.     

A nonparametric kernel regression approach for pricing options on stock market index

Previous options studies typically assume that the dynamics of the underlying asset price follow a geometric Brownian motion (GBM) when pricing options on stocks, stock indices, currencies or futures. However, there is mounting empirical evidence that the volatility of asset price or return is far from constant. This article, in contrast to studies that use parametric approach for option pricing, employs nonparametric kernel regression to deal with changing volatility and, accordingly, prices options on stock index. Specifically, we first estimate nonparametrically the volatility of asset return in the GBM based on the Nadaraya–Watson (N–W) kernel estimator. Then, based on the N–W estimates for the volatility, we use Monte Carlo simulation to compute option prices under different settings. Finally, we compare the index option prices under our nonparametric model with those under the Black–Scholes model and the Stein–Stein model.     

违约风险与贷款定价:一个基于期权方法和软预算约束的新模型

由于忽视了软预算约束导致的"优先原则"不成立以及由此产生的还贷道德风险等现实问题,贷款定价传统期权方法在中国的适用性受到了影响。通过引入信贷合同效率,本文构造了二维违约风险,并据此建立了贷款定价的新模型。新模型解决了上述问题,得到以下结论:第一类与第二类违约风险的联动对贷款定价的影响是不确定的,第一类与第二类违约风险相关度越高则贷款定价越低,贷款期限与贷款定价之间的关系受违约风险构成的影响等。     

Pricing bond options under a Markovian regime-switching Hull–White model

In this paper, we investigate the valuation of bond options under a Markovian regime-switching Hull–White model, where both the mean-reverting level and the volatility of the interest rate are modulated by a continuous-time, finite-state Markov chain. Using techniques of measure changes and the inverse Fourier transform, we obtain an integral representation for the pricing formula of a standard European option on a zero-coupon bond. Numerical results for the prices and implied volatilities of bond options arising in our model are given in a two-regime case.     

OPTIONAL REAL-TIME PRICING OF ELECTRICITY FOR INDUSTRIAL FIRMS

Abstract. This paper proposes a pricing mechanism, optional real-time pricing (RTP), with day-ahead hourly prices, that exploits the potential offered by a competitive wholesale power market. When an electric utility offers the option to its industrial customers, the retail prices are based on an existing Hopkinson tariff and expectations as to the wholesale market's next-day hourly spot prices. The proposed RTP mechanism is Pareto-superior to the tariff in that it assures both the utility and the customer of profits that will be at least as great as under the tariff.     

Between a Rock and a Hard Place: A Trade-Theory Analysis of Leakage Under Production- and Consumption-Based Policies

Without a comprehensive global climate agreement, carbon leakage remains a contentious issue. Consumption-based pricing of emissions—which could in practice be implemented with a full border tax adjustment (BTA)—has been forwarded as an option to increase the effectiveness of unilateral climate policy. This paper questions the economic rationale behind this approach, using a theoretical $2 \times 2$ trade model in which leakage occurs through terms-of-trade effects. We show analytically, first, that consumption-based pricing of emissions does not necessarily result in less leakage than production-based policies. Second, the sign of the optimal unilateral carbon tariff depends on the carbon-intensity differential between the foreign country’s exporting and non-exporting sectors, and not on the differential between home’s and foreign’s exporting sectors, as implied by the full BTA approach. Third, based on empirical data for the year 2004, our model implies that full BTA applied by the European Union on e.g. imports from and exports to China would—by shifting China’s production from the export sector with a relatively low carbon-intensity towards the more carbon-intensive non-export sector—actually increase leakage.     

基于正态云的基础设施建设实物期权定价方法

基础设施建设以及开发环境涉及的不确定性是政府或投资者关注的核心问题之一。实物期权方法是解决不确定性问题的一个有效途径,云理论对于不确定性有更准确的描述。首先,结合实物期权理论及云理论,建立了基于正态云的基础设施建设实物期权定价模型,可以更准确地描述项目的期望与风险程度;其次,结合基础设施建设项目特征,用正态云模型的期望、熵和超熵表示期望现金流现值和投资成本,得到实物期权价值计算方法;最后,通过实际案例分析,验证了方法的有效性,并提出了未来研究的方向与建议。     

Investor Attention Strategy

This article documents the motivation, the construction, and the profitability of an investment strategy based on investor attention in the options market. Using the option volume after a 1-week dormant period as a proxy for investor attention, the author shows that heightened investor attention after the dormant period has rich investment implications. A portfolio constructed on the basis of volume spike events immediately after the dormant period generates an abnormal return of 68 basis points on a monthly basis (8.16% on an annualized basis). This abnormal return is robust to risk adjustment using standard asset pricing models. The author's findings constitute strong evidence that it is profitable for outside investors to mimic attentive investors in the options market and reap economically and statistically significant profits.     

二元结构环境下的IPO定价模型研究

本文传承我国国情和股票发行定价制度的历史、现状,基于相对估价法的基本原理,采用"变异系数法"分析企业特质,辅之以相关性的技术处理,构建了一个企业特质评价指标体系,采用"标准化加权评价法"加以评价后,创造性地通过"标准差倍数法"的技术处理将之纳入定价模型.然后分别立足于一级市场和二级市场,构建一步静态模型和两步静态模型,为检验模型的应用效果,本文提出了IPO定价的四个检验标准,并做了实证检验评估.最后结合新股循价制度改革和实践,对IPO定价问题做进一步的检验探讨.     

基于实物期权的创业板企业价值评估

本文针对创业板企业的特点,探讨了传统估值方法对创业板企业的不适应性;借鉴实物期权理论中二叉树期权定价模型,构建了适合创业板企业价值评估的模型。最后,通过实例论述了如何应用该模型评估企业价值。     

Analytical American Option Pricing: The Flat‐barrier Lower Bound*

In a Black and Scholes (1973) world, this paper studies the pricing performance of a closed‐form lower bound to American option values based on an exercise strategy corresponding to a flat‐exercise boundary. The lower bound has a simple two‐step implementation akin to Barone‐Adesi and Whaley (1987) formula and shows superior pricing performance in the out‐of‐the‐money region and for long maturities.     

基于复合期权的创业板上市公司IPO定价研究

指出传统IPO定价方法用于具有高风险、高成长性等特征的高新技术企业IPO定价的缺陷,将实物期权概念引入IPO定价研究中。根据高新技术企业项目投资的特征,引入复合期权建立相应的数学模型,采用复合期权方法建立高新技术企业的IPO定价模型。最后,通过算例分析说明该模型在实践运用中具有一定的借鉴意义。