PRICING CATASTROPHE OPTIONS WITH COUNTERPARTY CREDIT RISK IN A REDUCED FORM MODEL

In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.

Pricing Stochastic Barrier Options under Hull-White Interest Rate Model

A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.

Pricing VIX options in a 3/2 plus jumps model

This paper proposes and makes a study of a new model(called the 3/2 plus jumps model) for VIX option pricing. The model allows the mean-reversion speed and volatility of volatility to be highly sensitive to the actual level of VIX. In particular, the positive volatility skew is addressed by the 3/2 plus jumps model. Daily calibration is used to prove that the proposed model preserves its validity and reliability for both in-sample and out-of-sample tests.The results show that the models are capable of fitting the market price while generating positive volatility skew.

Early exercise premium method for pricing American options under the J-model

Background:This study develops a new model called J-am for pricing American options and for determining the related early exercise boundary(EEB).This model is based on a closed-form solution J-formula for pricing European options,defined in the study by Jerbi(Quantitative Finance,15:2041-2052,2015).The J-am pricing formula is a solution of the Black&Scholes(BS)PDE with an additional function called f as a second member and with limit conditions adapted to the American option context.The aforesaid function f represents the cash flows resulting from an early exercise of the option.Methods:This study develops the theoretical formulas of the early exercise premium value related to three American option pricing models called J-am,BS-am,and Heston-am models.These three models are based on the J-formula by Jerbi(Quantitative Finance,15:2041-2052,2015),BS model,and Heston(Rev Financ Stud,6:327-343,1993)model,respectively.This study performs a general algorithm leading to the EEB and to the American option price for the three models.Results:After implementing the algorithms,we compare the three aforesaid models in terms of pricing and the EEB curve.In particular,we examine the equivalence between J-am and Heston-am as an extension of the equivalence studied by Jerbi(Quantitative Finance,15:2041-2052,2015).This equivalence is interesting since it can reduce a bi-dimensional model to an equivalent uni-dimensional model.Conclusions:We deduce that our model J-am exactly fits the Heston-am one for certain parameters values to be optimized and that all the theoretical results conform with the empirical studies.The required CPU time to compute the solution is significantly less in the case of the J-am model compared with to the Heston-am model.

Investment in deepwater oil and gas exploration projects:a multi-factor analysis with a real options model

Deepwater oil and gas projects embody high risks from geology and engineering aspects, which exert substantial influence on project valuation. But the uncer- tainties may be converted to additional value to the projects in the case of flexible management. Given the flexibility of project management, this paper extends the classical real options model to a multi-factor model which contains oil price, geology, and engineering uncertainties. It then gives an application example of the new model to evaluate deepwater oil and gas projects with a numerical analytical method. Compared with other methods and models, this multi-factor real options model contains more project information. It reflects the potential value deriving not only from oil price variation but also from geology and engi- neering uncertainties, which provides more accurate and reliable valuation information for decision makers.

NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH

Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black_Scholes model is generalized to the case where the risk_less asset (bond or bank account) earns a time_dependent interest rate and risk asset (stock) has time_dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put_call parity of European option are obtained. The general approach of option pricing is given for the general Black_Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put_call parity of European option on a stock whose price process is driven by general Ornstein_Uhlenback (O_U) process are given by actuarial approach.

Research on the Protection of Vulnerable Groups in Water Pollution Conflicts Based on Binomial Tree Pricing Model

The interests of vulnerable groups can’t be guaranteed due to their weaker capacity and the limited interests demand channels during the water pollution conflicts. The interest protection for the vulnerable people in the water pollution conflicts has attracted attentions of the international scholars. The paper tries to construct the market mechanism which can make the vulnerable people to involve in the emission trading. The vulnerable people can buy American put option in the emission trading market. When the price of the emission runs below the contract price, the vulnerable people can get the benefit through executing the option. When the price of the emission runs above the contract price, the vulnerable people can give up the right. The binomial tree option pricing model can help the vulnerable people to make a decision through the analysis of the worth of the American put option.

Option Pricing and Hedging under a Markov Switching Lévy Process Model

In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging. In this model, the market interest rate, the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process. We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure. The option price using this model is obtained by the Fourier transform method. We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.

An ETD Method for American Options under the Heston Model

A numerical method for American options pricing on assets under the Heston stochastic volatility model is developed.A preliminary transformation is applied to remove the mixed derivative term avoiding known numerical drawbacks and reducing computational costs.Free boundary is treated by the penalty method.Transformed nonlinear partial differential equation is solved numerically by using the method of lines.For full discretization the exponential time differencing method is used.Numerical analysis establishes the stability and positivity of the proposed method.The numerical convergence behaviour and effectiveness are investigated in extensive numerical experiments.

Trinomial tree model of the real options approach used in mining investment price forecast and analysis

In order to effectively avoid the defects of a traditional discounted cash flow method, a trinomial tree pricing model of the real option is improved and used to forecast the investment price of mining. Taking Molybdenum ore as an example, a theoretical model for the hurdle price under the optimal investment timing is constructed. Based on the example data, the op- tion price model is simulated. By the model, mine investment price can be computed and forecast effectively. According to the characteristics of mine investment, cut-off grade, reserve estimation and mine life in different price also can be quantified. The result shows that it is reliable and practical to enhance the accuracy for mining investment decision.

Indifference Pricing in the Single Period Binomial with Complete Market Model

Binomial no-arbitrage price have a method is the traditional approach for derivative pricing,which is,the complete model,which makes possible the perfect replication in the market.Risk neutral pricing is an appropriate method of asset pricing in a complete market.We have discussed an incomplete market,a non-transaction asset that produces incompleteness of the market.An effective method of asset pricing in incomplete markets is the undifferentiated pricing method.This technique was firstly introduced by Bernoulli in(1738)the sense of gambling,lottery and their expected return.It is used to command investors'preferences and better returns the results they expect.In addition,we also discuss the utility function,which is the core element of the undifferentiated pricing.We also studied some important behavior preferences of agents,and injected exponential effect of risk aversion in the model,so that the model was nonlinear in the process of claim settlement.

Application of Binomial Option Pricing Model to the Appraisal of Knowledge Management Investment

This paper views knowledge management （KM） investment from the angle of real options, and demonstrates the utility of the real options approach to KM investment analysis. First, KM project has characteristics of uncertainty, irreversibility and choice of timing, which suggests that we can appraise KM investment by real options theory. Second, the paper analyses corresponding states of real options in KM and finance options. Then, this paper sheds light on the way to the application of binomial pricing method to KM investment model, which includes modeling and conducting KM options. Finally, different results are shown of using DCF method and binomial model of option evaluation via a case.

可变风险溢价结构下跳扩散模型的期权定价

风险溢价结构是真实测度与风险中性测度间的纽带,能够帮助提取投资者的风险偏好特征。本文针对跳扩散模型构建了灵活的风险溢价形式,允许期权市场隐含信息参与校准跳跃风险的市场价格,进而研究存在跳跃情形下的期权定价,并探索市场风险溢价结构。数值分析和实证研究表明,可变风险溢价结构有助于准确刻画市场定价核曲线,且市场风险溢价结构具有明显的时变特征,跳跃风险溢价能够较好解释隐含波动率曲面。此外,跳扩散模型的可变风险溢价结构在样本内外都具有明显的期权定价优势。考虑了不同样本长度、定价方法、定价区间以及期权产品后,以上结论均是稳健的。本研究有助于系统了解不同市场风险溢价结构与定价规律,有利于深入探索跳跃风险溢价补偿机制。

基于前景理论框架和Heston模型的行为期权定价

行为期权定价是当前国际金融领域的热门研究主题之一。虽然随机波动率模型已成为国际衍生品定价领域的标准模型,但该模型对短到期期权(尤其是虚值期权)的定价仍不准确,其原因之一是传统的期权定价方法忽略了现实市场中的非理性心理和行为因素。针对上述问题,本文运用前景理论期权定价框架,引入价值函数来刻画投资者面对收益与损失的前景价值判断,引入决策权重函数来修正Heston随机波动率模型刻画的资产价格路径的概率密度函数,将期权合约签订与交割的现金流视为分散的心理账户情形,在市场均衡条件下推导出Heston模型下欧氏行为期权的定价公式。上证50ETF期权的实证结果表明:考虑了前景理论的Heston随机波动率模型,能显著地提升短到期虚值期权的定价准确度;参数校正结果发现,定价性能的提升要归因于Heston模型中纳入的表征非理性心理与情绪的行为参数;相对而言,投资者对实值期权的风险态度偏中性,因此行为参数对其定价精度的提升有限。

基于“分解-重组-预测-集成”模式的Heston期权定价模型

精准合理地期权定价对于改善市场流动性、优化投资者结构、稳定金融市场拥有重要意义。本文提出了一种结合“分解-重组-预测-集成”思想的Heston期权定价模型,该模型利用Heston模型进行初始定价,通过自适应噪声完全集合经验模态分解(CEEMDAN)对定价误差进行分解与重构,获得高频项、低频项及趋势项,然后使用门控循环单元(GRU)估计高频项及低频项,使用差分整合移动平均自回归(ARIMA)估计趋势项,所有估计值集成汇总得到定价误差估计值,最后使用定价误差估计值对Heston模型的初始定价结果进行修正后获得最终定价结果。使用华夏上证50ETF、华泰柏瑞沪深300ETF和嘉实沪深300ETF期权数据验证模型,实证结果显示,在模型结构更加简单的基础上,本文提出模型的精度普遍优于基准模型。

福建省林业碳汇项目价值评估及金融产品定价——基于实物期权理论

文章结合林业碳汇投资规模大、回收周期长、碳汇产品定价难等特征,基于实物期权定价理论,利用Black-Scholes模型,对福建省碳汇造林项目价值和碳汇交易价格进行实证研究。结果表明,采用常规的净现值法计算出的项目价值与引入实物期权评价模型计算出的项目价值运用灰色预测模型与2022年福建省林业碳汇成交均价相比较,林业碳汇造林项目价值及碳汇产品交易价格均被严重低估,基于实物期权理论的评估方法对林业碳汇产品进行定价更加科学合理。为进一步丰富林业碳汇金属产品交易体系,提高碳汇市场活跃度,文章提出对策建议:①深化林权制度改革,激励林农营林造林;②科学核算投资回报,提高经营者积极性;③创新碳金融产品,规避价格波动风险;④引入多元交易主体,促进碳汇流通交易。

基于DCF-BS模型的可衍生电影版权投资价值评估——以英皇影业投资《古董局中局》为例

针对可衍生电影版权投资收益的不确定性,本文运用期权定价方法给出衍生品追加投资选择权价值评估的BS模型,进而给出可衍生电影版权投资价值评估的DCF-BS模型。将模型应用于英皇影业对《古董局中局》的投资价值评估案例,以检验模型有效性。结果表明:DCF-BS模型相对单纯的DCF模型不仅适用于可衍生电影版权价值评估,而且估值结果并不是传统的DCF模型估值与BS模型估值的简单相加,而是两种模型相互融合的结果,即估值结果对票房收益的高度不确定性表现出较低的敏感性,对促进可衍生电影的市场化投资具有重要意义。

碳排放期权定价及实证研究——以湖北碳排放交易中心为例

碳期权作为碳金融市场上重要的交易产品,合理定价有利于投资者做出理性的碳期权套期保值决策,降低碳交易市场风险。因此,本文基于湖北碳排放交易中心碳配额数据构建定价模型,以此对我国八大碳交易市场价格提供一定的借鉴。本文将GARCH模型和期权定价模型B-S引入碳排放交易期权的定价研究中。通过碳排放交易中心配额期货收盘价的数据检验,发现价格波动情况具有非正态性和尖峰厚尾的特征,并采用GARCH模型拟合预测碳价收益率波动率,将预测的数据求取标准差后得到最终日波动率,从而带入B-S定价模型中进行价值估值。结果表明,GARCH模型具有良好的拟合性,有利于提高定价的精准度。

基于4/2-CIR模型的欧式期权定价及实证研究

在假设波动率服从均值回复过程的条件下,探讨了具有随机利率的4/2随机波动率模型下的期权定价问题。首先,基于4/2随机波动率模型提出4/2-CIR随机混合模型,并利用快速傅里叶变换方法推出4/2-CIR随机混合模型下的欧式期权定价公式。其次,通过数值分析的方法,对比4/2随机波动率模型与4/2-CIR随机混合模型的定价结果,分析新模型的定价性能,并运用交叉验证法,对模型中参数进行敏感性分析。最后,选取上证50ETF期权数据进行实证分析。研究发现:随机利率对模型定价结果具有显著影响;期权价格对利率的波动率参数不敏感,而对其它参数都较敏感;与经典B-S模型及4/2随机波动率模型相比,4/2-CIR随机混合模型的定价误差更小,定价结果更接近真实值。

On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options under Regime-Switching Kou’s Jump-Diffusion Models

In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.