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.

Valuation of European and American Options under Variance Gamma Process

Geometric Brownian Motion (GBM) is widely used to model the asset price dynamics. Option price models such as the Black-Sholes and the binomial tree models rely on the assumption that the underlying asset price dynamics follow the GBM. Modeling the asset price dynamics by using the GBM implies that the log return of assets at particular time is normally distributed. Many studies on real data in the markets showed that the GBM fails to capture the characteristic features of asset price dynamics that exhibit heavy tails and excess kurtosis. In our study, a class of Levy process, which is called a variance gamma (VG) process, performs much better than GBM model for modeling the dynamics of those stock indices. However, valuation of financial instruments, e.g. options, under the VG process has not been well developed. Here, we propose a new approach to the valuation of European option. It is based on the conditional distribution of the VG process. We also apply the path simulation model to value American options by assuming the underlying asset log return follow the VG process. Such a model is similar with that proposed by Tiley [1]. Simulation study shows that the proposed method performs well in term of the option price.

OPTIONAL AND PREDICTABLE PROJECTIONS OF SET-VALUED MEASURABLE PROCESSES

In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.

Attitude Analysis in Process Conflict for C919 Aircraft Manufacturing

Based on the option prioritization in graph model for conflict resolution of two decision makers(DMs),new logical and matrix representations of four stability concepts for DMs′attitude are proposed.The logical representation of attitude is defined,and converted to the matrix form in order to develop a decision support system(DSS)efficiently.Compared with existing definitions of DMs′attitude based on states,the proposed definitions of attitude based on options are convenient and more effective to generate preferences since that of states can be significantly larger than that of options in a large conflict.In addition,it is easier to obtain the information of the prioritization of option statements than to obtain preference of states for users.The proposed representations are applied to the process conflict during aircraft manufacturing to demonstrate the efficiency of the new approach.

The mean correcting martingale measures for exponential additive processes

The mean correcting martingale measure for the stochastic process defined as the exponential of an additive process is constructed. Necessary and sufficient conditions for the existence of mean correcting martingale are also obtained. The investigation of this paper will establish a unified way that is applicable both to the case of Ldvy processes and that of the sums of independent random variables. As an application, we present the necessary and sufficient conditions that the discounted stock price process is a martingale.

HETEROGENEOUS INFORMATION ARRIVAL AND R&D OPTION PRICING

The paper models the arrival of heterogeneous information during R&D stages as a doubly stochastic Poisson process(DSPP). The new product market introduction is considered as a timing option(an American perpetual option). Investment in R&D can be thought of as option on an option(a compound option). This paper derives an analytic approximation valuation formula for the R&D option, and demonstrates that the accounts for heterogeneous information arrival may reduce the pricing biases. This way, the gap between real option theory and the practice of decision making with respect to investment in R&D is diminished.

A New Binomial Tree Method for European Options under the Jump Diffusion Model

In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design the pricing formula for European option. Compared with the continuous situation, the proposed value equation of option under the new binomial tree model converges to Merton’s accurate analytical solution, and the established binomial tree method can be proved to work better than the traditional binomial tree. Finally, a numerical example is presented to illustrate the effectiveness of the proposed pricing methods.

Pricing Study on Two Kinds of Power Options in Jump-Diffusion Models with Fractional Brownian Motion and Stochastic Rate

In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.

Valuation of Asian American Option Using a Modified Path Simulation Method

In this paper, we use a modified path simulation method for valuation of Asian American Options. This method is a modification of the path simulation model proposed by Tiley. We assume that the behavior of the log return of the underlying assets follows the Variance Gamma (VG) process, since its distribution is heavy tail and leptokurtic. We provide sensitivity analysis of this method and compare the obtained prices to Asian European option prices.

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.

Option Pricing with Markov Switching in Uncertainty Markets

In this paper, we present a stock model with Markov switching in the uncertainty markets, where the parameters of drift and volatility change according to the states of a Markov process. To price the option, we firstly establish a risk-neutral probability based on the uncertain measure given by Liu. Then a closed form of the European option pricing formula is obtained by applying the Laplace transforms and the inverse Laplace transforms.

刘庄选煤厂原煤系统工艺改造方案

由于刘庄矿井开采能力提升,选煤厂设计生产能力无法满足生产需要,提出对小于50 mm粒级原煤进行分级入洗的3个生产工艺改造方案。对比后拟采用13 mm分级方案,小于13 mm粒级原煤直接作为产品,仅入洗50~13 mm粒级原煤。现有生产系统设计最大处理能力5.24 Mt/a,全部用来处理50~13 mm粒级块原煤,根据现有煤质资料推测出选煤厂理论处理原煤能力可提高到17.73 Mt/a,比设计能力提高了2.38倍,明显改善当前生产能力不足的状况,同时可降低吨煤生产成本、煤泥产率、介质损耗和药耗,提高经济效益。

次扩散过程驱动下的两值期权定价

期权定价是金融数学的重要问题之一,而两值期权是一种具有不连续收益的新型期权,其作为一种重要的新型期权使得资产收益更贴合投资者需求,为研究复杂期权提供了一种重要工具。在已有期权定价模型中,标的资产价格变化的随机驱动源通常为布朗运动和分数布朗运动,但它们无法刻画标的资产常值周期性的特征。为了解决这一问题,本文基于次扩散过程,对两值期权产品的定价展开研究,建立了次扩散机制下两值期权定价模型。运用Δ对冲技巧和Ito公式得到了两值期权在次扩散机制下所满足的偏微分方程,并给出了资产或无值看涨期权和现金或无值看涨期权的定价公式。

基于混合次分数跳过程的亚式期权模糊定价

考虑到金融资产价格的长记忆性及跳跃现象,基于混合次分数布朗运动和泊松过程,建立了几何亚式期权定价模型;进一步考虑金融市场模糊性,引入模糊理论得到模糊定价模型.首先,得到混合次分数跳过程Ito∧公式及其股价所满足随机微分方程的解析解;其次,运用风险中性原理给出几何亚式期权的定价公式;然后,运用模糊理论构建了几何亚式模糊期权定价模型;最后,数值模拟分析了置信度和Hurst指数对模糊价格的影响,并将本文所建立模型与经典BS模型进行对比.结果表明,在相应的置信度下模糊定价模型能够给出较为合理的价格区间,有助于金融投资者的决策,从而验证了模型的合理性和实用性.

股票价格服从跳-扩散过程的期权定价模型

研究了股票价格的行为模型问题.假定股票价格的跳过程为一类特殊的更新过程,建立了股票价格服从跳 扩散过程的行为模型.在风险中性的假设下,推导出了基于股票的欧式期权定价公式.

股票价格遵循指数O-U过程的最大值期权定价

讨论了股票价格过程遵循指数O-U过程的变异期权定价问题。利用Girsanov定理获得了指数O-U过程模型的唯一等价鞅测度。利用期权定价的鞅方法,得到了离散时间最大值期权和虹式期权的定价公式。

含有期权的最优投资与比例再保险策略

在Black-Scholes模型假设的市场条件下,研究了保险公司投资对象含有欧式看涨期权的情形下,进行投资和比例再保险的策略问题.以保险公司到期财富效用最大化为目标,运用动态规划原理得到了最优值函数满足的HJB方程,得到了包含期权在内的资产最优投资策略和比例再保险策略的显式解,并证明了解的验证定理.最后分析了不同参数对模型策略的影响.

金融衍生证券定价理论进展评述

准确地为金融衍生证券定价是金融交易市场规避风险的迫切需要．在ＢｌａｃｋＳｃｈｏｌｅｓ期权定价方程的基础上，研究了衍生证券的一般定价方法，对金融衍生证券的定价理论的研究内容、方法和结果作了初步的介绍，并对这一领域中存在的问题及最新研究方向进行了简单的综合评述．

基于混合过程的衍生证券定价策略分析

本文通过对标的资产的价格行为过程进行分析，引入一种基于混合过程的新的期权模式，推导出一种新的期权定价模型。

GARCH驱动下历史滤波服从Levy过程的期权定价

为了刻画对数收益率分布的尖峰、厚尾和偏度现象,同时体现波动率集聚效应,通过历史滤波模型构建GARCH波动率驱动下的历史滤波分布,并假设服从五种纯跳跃Levy过程从而估计模型参数,进行Levy-GARCH模型的恒生指数拟合检验及期权定价的实证研究.对比无跳跃模型及历史滤波模拟,结果显示:不同模型有着不同的风险溢价;纯跳跃GARCH模型的残差估计量与市场数据有着良好的拟合效果,期权定价精确度优越于无跳跃GARCH模型.其中,TS分布对历史滤波拟合效果最佳,CGMY-GARCH模型的定价精度最为准确.