用模拟退火算法寻找Heston期权定价模型参数

随机波动率模型由于放松了Black-Sholes模型的假定而更符合市场情况,因此成为研究金融衍生品定价的热点。Heston随机波动率不同于其他随机波动率模型之处在于其存在闭形式解。Heston期权定价模型在应用中需要确定五个待估参数,此问题通常比较困难。本文采用模拟退火算法并利用最小化残差平方和来估算,该算法以一定概率跳出局部极小值,从而以概率1收敛到全局极小值,最终得到Heston模型的待估参数。在实证研究中,本文利用香港恒生股票指数期权在2010年10月15日交易的数据,得到待估参数,并用该参数对2010年10月18日期权进行了模拟定价。     

基于量子三叉树的量子Black-Scholes期权定价

将量子概率引入到期权定价是最近几年一个新的研究趋势,也称为量子金融.为了期权定价更方便,文章建立了量子三叉树模型,同时利用量子概率建立了连续量子Black-Scholes(B-S)模型。实例应用和Matlab期权敏感性分析都验证了量子B-S优于经典B-S,从而为连续期权定价提供量子决策的途径。     

基于Lévy过程带模糊参数的欧式期权定价

在实际经济行为中，标的资产的价格会受到突发事件（如自然灾害、疾病等）的影响而产生跳跃，为了描述这个跳跃，文章以标的资产价格服从几何Lévy过程为基本模型研究欧式期权的定价问题。给出了欧式期权在0时刻和t (0 t T<≤时刻的定价公式。由于实际中我们不能精确地确定模型参数，需要将模型参数做模糊化处理，进而)可以得到参数是模糊数情形下的欧式期权定价公式。     

期权定价的“有限理性”视角：基于投资者情绪的研究

2013年的种种迹象表明我国金融市场将进入期权时代。期权价值的确定是期权功能发挥的前提和基础。本文从行为金融学的角度出发,在传统二叉树期权定价模型的基础上,通过引入投资者情绪变量构建基于投资者情绪的欧式看涨期权定价模型。模型表明,投资者情绪不仅通过行为随机折现因子直接影响期权价值,而且通过影响标的证券的价值运行概率间接影响期权的最终价值;投资者情绪与期权价格之间呈现正相关关系。最后,基于长虹CWB1的实证研究也表明了传统期权定价模型存在的缺陷,通过求解权证实际交易价格与理论价格之间的偏差,可以反算出投资者情绪,进而预测权证的行为价值。     

基于双指数跳扩散过程的亚式期权的解析定价

研究了双指数跳-扩散模型下亚式期权的定价,得到了这些期权定价得解析公式。在风险中性下,亚式期权的值在恰当的边际条件和终值条件下满足广义Black-Scholes方程;我们提出一种在跳扩散模型下亚式期权定价的新方法。该方法在于为亚式期权所满足的偏积分——微分方程指定恰当的边际条件和终值条件;然后,利用拉普拉斯变换求解该方程,得到了亚式期权的解析定价公式。     

美式期权的二叉树定价模型

美式期权不同于欧式期权,可以在到期日以前任意时间操作.一般而言,美式期权定价的解析解是很上得到的,二叉树模型是目前金融界最基本的期权定价方法之一,是比较好的数值计算方法,收敛于Black2Schoes期权定价公式的价格本文对二叉树模型进行介绍,并用其来研究美式期权的定价问题.     

BDT模型的扩展及应用研究

本文通过引入转移概率参数，证明了短期利率满足的一般动态变化方程，建立了离散形式的利率期限结构模型，讨论求解方法，从而拓展了BDT模型。同时，探讨了模型的理论应用，给出了息票国债与基于息票国债的欧式期权定价公式。最后，对BDT数例进行了校正，并针对息票国债，提出了一种新的定价方法，且进行了实证研究。     

随机波动率下的障碍期权定价

针对障碍期权的定价问题,建立具有随机波动率和有交易费用的障碍期权的定价模型。在无套利定价原则和风险中性定价原则下推导出期权价格方程。采用有限差分法求解该方程,获得了期权价格的数值解。并通过数值试验的方法分析和讨论了模型中部分参数对期权价格的影响。     

支付时间不确定的指数化股票期权的定价

大多数股票期权的研究忽视了收益获取时间的不确定对期权价值的影响。本文探讨了支付时间不确定的指数化股票期权的定价问题，改进了原来的模型，并进行了实例验证。     

住房逆抵押贷款定价分析

本文从住房逆抵押贷款具有期权产品特性出发,将布莱克一斯科尔斯期权定价模型运用于住房逆抵押贷款利率定价,将逆抵押贷款定价问题转换为隐含期权的定价问题,提供了独特的定价思路和方法,最终推导出住房逆抵押贷款的定价模型,并说明了该模型的使用方法.     

The valuation of barrier options under a threshold rough Heston model

In this paper, we propose a novel model for pricing double barrier options, where the asset price is modeled as a threshold geometric Brownian motion time changed by an integrated activity rate process, which is driven by the convolution of a fractional kernel with the CIR process. The new model both captures the leverage effect and produces rough paths for the volatility process. The model also nests the threshold diffusion, Heston and rough Heston models. We can derive analytical formulas for the double barrier option prices based on the eigenfunction expansion method. We also implement the model and numerically investigate the sensitivities of option prices with respect to the parameters of the model.     

存货购销中最优期权合约交易量研究

在分析利用期权合约规避价格波动风险的原理的基础上,分别给出存货购销两个环节中可以运用的期权策略,然后利用均值方差模型计算使投资组合达到效用最大化时所对应的最优期权合约交易量及其对经营利润的影响,研究发现：在存货采购环节,企业可以通过购入看涨期权、购入看涨期权同时售出看跌期权两种策略控制采购价格波动的风险,在存货销售环节,企业可以通过购入看跌期权、同时购入看跌期权并售出看涨期权两种策略来稳定销售利润;从最优期权合约交易量及其对企业经营利润的影响来看,期权工具在控制存货采购价格、稳定销售利润中可以发挥良好作用。     

Exponential stock models driven by tempered stable processes

We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. This includes the existence of Esscher martingale measures and martingale measures having minimal distance to the physical probability measure. Moreover, we provide pricing formulae for European call options and perform a case study.     

Filtering and identification of Heston's stochastic volatility model and its market risk

We study the filtering problem for the stochastic volatility model of Heston by using the nonlinear estimation theory. To solve the estimation problem for the stochastic volatility process, we use the random time change method. The derived basic equation for the filtering is the so-called Zakai equation and its numerically realized algorithm is proposed with the aid of the splitting-up method. Regarding the European call option problem, the identification of the market price of the volatility risk is also studied. Some numerical simulation studies are demonstrated to show the advantage of the proposed method.     

An analytical approximation formula for European option pricing under a new stochastic volatility model with regime-switching

In this paper, an analytical approximation formula for pricing European options is obtained under a newly proposed hybrid model with the volatility of volatility in the Heston model following a Markov chain, the adoption of which is motivated by the empirical evidence of the existence of regime-switching in real markets. We first derive the coupled PDE (partial differential equation) system that governs the European option price, which is solved with the perturbation method. It should be noted that the newly derived formula is fast and easy to implement with only normal distribution function involved, and numerical experiments confirm that our formula could provide quite accurate option prices, especially for relatively short-tenor ones. Finally, empirical studies are carried out to show the superiority of our model based on S&P 500 returns and options with the time to expiry less than one month.     

Jump dynamics,spillover effect and option valuation

In this paper, we propose an affine discrete-time model that incorporates the jump process and spillover effect for valuing the 50 ETF options in China. Based on the proposed model, a closed-form solution is also derived for the new dynamics of underlying asset, which facilitates option pricing. The empirical results show that the proposed model offers greater economic benefit with reduced pricing errors than the traditional benchmark models, including the popular HNGARCH model of Heston and Nandi (2000), GARV model of Christoffersen et al. (2014), and BPJVM model of Christoffersen et al. (2015). Our finding is important for financial risk management and investment in Chinese derivatives market.     

A comparative goodness-of-fit analysis of distributions of some Lévy processes and Heston model to stock index returns

In this paper, we investigate the goodness-of-fit of three Lévy processes, namely Variance-Gamma (VG), Normal-Inverse Gaussian (NIG) and Generalized Hyperbolic (GH) distributions, and probability distribution of the Heston model to index returns of twenty developed and emerging stock markets. Furthermore, we extend our analysis by applying a Markov regime switching model to identify normal and turbulent periods. Our findings indicate that the probability distribution of the Heston model performs well for emerging markets under full sample estimation and retains goodness of fit for high volatility periods, as it explicitly accounts for the volatility process. On the other hand, the distributions of the Lévy processes, especially the VG and NIG distributions, generally improves upon the fit of the Heston model, particularly for developed markets and low volatility periods. Furthermore, some distributions yield to significantly large test statistics for some countries, even though they fit well to other markets, which suggest that properties of the stock markets are crucial in identifying the best distribution representing empirical returns.     

Quadratic hedging schemes for non-Gaussian GARCH models

We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan׳s (1995) delta hedge. Since the minimal martingale measure fails to produce a probability measure in this setting, we construct local risk minimization hedging strategies with respect to a pricing kernel. These approaches are investigated in the context of non-Gaussian driven models. Furthermore, we analyze these methods for non-Gaussian GARCH diffusion limit processes and link them to the corresponding discrete time counterparts. A detailed numerical analysis based on S&P 500 European call options is provided to assess the empirical performance of the proposed schemes. We also test the sensitivity of the hedging strategies with respect to the risk neutral measure used by recomputing some of our results with an exponential affine pricing kernel.     

Exchange options for catastrophe risk management

In this paper, we investigate the pricing issue and catastrophe risk management of exchange options. Exchange options allow the holder to exchange its stocks for another at maturity and can be seen as an extended version of catastrophe equity put options with another traded asset price as strike prices. Since option holders have to issue new shares to exercise the option, we illustrate the differences between option prices calculated using pre-exercise and post-exercise share prices. The effects of default risk on option prices and risk management are also considered. Finally, risk management analysis shows that exchange options can effectively hedge catastrophe risk.