跳扩散模型中的测度变换与期权定价

本文研究在跳扩散模型中概率测度的变换对于期权定价的影响．通过选取不同的记价单位以及相应的概率测度，简化了期权定价中一些复杂的理论，得到了在具有随机利率的跳扩散模型中欧式期权的定价公式以及关于跳扩散模型中交换期权、亚式期权等新型期权的定性、定解性质．     

鞅分析在具有红利支付的n次幂型欧式期权定价中的应用

本文探讨了鞅分析在具有红利支付的n次幂型欧式期权定价中的应用,即用鞅分析的技巧与方法研究了在标的资产服从分数布朗运动的条件下具有红利支付的n次幂型欧式期权定价问题,并获得了其公式。丰富了已有期权定价结果,使期权定价公式更有利于实际的应用。     

广义交换期权定价

基于风险中性(等价鞅测度)定价理论和经典的Black-Scholes市场环境,我们给出了更一般情形下的欧式交换期权(ExchangeOption)封闭形式的解析定价公式,进而得出了欧式交换期权的价格公式、Black-Scholes期权定价公式.     

指数Levy跳扩散模型下一类新型期权的定价研究

在指数levy跳扩散模型下,通过在确定的两个时间点之间设置一个特定的常数障碍水平,构造出一类两时间点两资产最大或最小值障碍期权.这种新型期权具有两时间点彩虹期权与障碍期权的双重性质,使得该新型期权在未定权益定价方面的应用更为广泛.最后利用鞅方法,给出了该类期权的定价公式.     

含信用风险的上限型权证期权定价

本文通过公司价值模型研究一类含信用风险的上限型权证期权的定价.一方面利用鞅的方法推导出公司负债和无风险利率为常数情况下上限型权证期权的定价;另一方面通过概率的方法推导出含信用风险的上限型权证期权定价公式,该公式推广了Black-Scholes的欧式期权定价.     

随机利率情形下跳-扩散模型的未定权益定价

讨论Vasicek短期利率模型下,风险资产的价格过程服从跳-扩散过程的欧式未定权益定价问题,利用鞅方法得到了欧式看涨期权和看跌期权定价公式及平价关系,最后给出了基于风险资产支付连续红利收益的欧式期权定价公式.     

障碍期权的定价问题

障碍期权是与路径相关的期权 ,因而它的定价计算是非常复杂的 .本文利用反射原理对障碍期权的定价问题进行了简化 ,从而最终给出障碍期权的定价公式 .而文中多次运用 Girsanov定理构造等价鞅测度是解决问题的关键 ,它为反射原理的使用创造了基本条件 .     

Erlang(2)过程的风险分析与美式看跌期权

在经典的风险理论中涉及到的索赔风险是服从复合Poission过程的, 与之不同, 我们考虑Erlang(2)风险过程\bd Erlang(2)分布往往见诸于控制理论中, 这里它作为索赔发生间隔时间的分布被引入了\bd 本文中, 我们介绍一个与破产时刻、破产前时刻的盈余以及破产时刻赤字有关的辅助函数$\phi(\cdot)$, 函数中涉及的这三个变量对风险模型的研究都是最基本也是最重要的\bdWillmot and Lin (1999)曾在古典连续时间风险模型之中研讨过这一函数\bd受Gerber and Shi(1997)及Willmot and Lin (2000)在古典模型下的研究过程的启发, 本文的一个重要结果就是找到破产前时刻的盈余以及破产时刻赤字的联合分布密度函数\bd 更得益于Gerber and Landry (1998)及Gerber and Shiu (1999)的思想, 我们应用以上的结果去寻求基础资产服从一定风险资产价格过程的美式看跌期权最优交易策略.     

几何平均下的水平重置期权定价

针对重置期权的风险对冲△跳现象,研究了一种亚式特征的水平重置期权的定价问题.首先在BS模型下用股票的几何平均价格作为水平重置期权执行价格重置与否的统计量,然后运用测度变换和鞅定价方法得到了风险中性定价公式,最后利用风险中性定价公式得出风险对冲△值的显示解,改进了水平重置期权的部分已有结果.     

随机利率下奇异期权的定价公式

在随机利率条件下,借助于测度变换获得了复合看涨期权的一般的定价公式,同时利用鞅理论和Girsanov定理,在利率服从于扩展的Vasicek利率模型时,得到了复合看涨期权精确的定价公式.用同样的方法,考虑了预设日期的重置看涨期权的定价问题,在利率服从同样的利率模型时,获得了重置看涨期权的定价公式.数值化的结果进一步说明了当利率遵循扩展的Vasicek利率模型时,B-S看涨期权的价格关于标的资产的价格是严格单调递增的,复合看涨期权的Geske公式是可以推广到随机利率的情况.     

Catastrophe risk management with counterparty risk using alternative instruments

Since weather-related disasters have an upward trend-cycle movement and the global financial crisis has revealed the severity of counterparty risk, this study reinvestigates and incorporates the catastrophe characteristics and counterparty risk into the valuation of catastrophe products. First, the excess of loss reinsurance is traditionally used to reduce catastrophe risk. Its premium is estimated under these catastrophe characteristics. Second, this paper looks into the price of catastrophe futures and spread option contracts that are based on a catastrophe index. The (re)insurer can apply these exchange-traded derivatives to reduce catastrophe risk without counterparty risk. Third, this paper takes counterparty risk into account to value catastrophe bonds and catastrophe equity puts. Thus, the fair valuations of these two instruments are revealed to the buyer.     

双跳-扩散过程下的脆弱期权定价

本文考虑含有交易对手违约风险的衍生产品的定价,以公司价值信用风险模型为基础,在标的资产价格和公司价值均服从跳-扩散过程的情况下,运用结构化的方法对脆弱期权定价进行建模,建立了双跳-扩散过程下的脆弱期权定价模型,分别在公司负债固定和随机的情况下推导出了脆弱期权的定价公式.     

Լ��ģ���к��н��׶������÷��յĿ�ת��ծȯ�Ķ���

??This paper studies the price of convertible bonds with counterparty credit risk in a reduced-form model. We suppose that the default intensity process and the interest rate process follow the Vasicek model, and derive the price expression of convertible bonds using the method of measure changes. Moreover, we make some numerical analysis on the explicit formulae to demonstrate the sensitivity of a convertible bond price to changes in the parameters of the model.     

A tractable LIBOR model with default risk

We develop a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework. Utilizing the class of affine processes, this model produces positive LIBOR rates and spreads, while the dynamics are analytically tractable under defaultable forward measures. This leads to explicit formulas for CDS spreads, while semi-analytical formulas are derived for other credit derivatives. Finally, we give an application to counterparty risk.     

Bilateral Counterparty Risk Valuation on a CDS with a Common Shock Model

In this paper, we study the counterparty risk on a CDS in a common shock model. We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk. Especially, we consider the pricing problem of credit default swap with counterparty risk under a common shock model with regime switching. The arrivals of the shock events are modeled by conditionally independent Cox processes whose stochastic intensities depend on the state of the economy described by a Markov chain. We give the explicit formula for the credit valuation adjustment (CVA) and examine the impact of the change of economic state on the CVA.     

利用传染模型对含有对手风险的信用证券定价(英文)

本文利用传染模型研究了可违约债券和含有对手风险的信用违约互换的定价。我们在约化模型中引入具有违约相关性的传染模型,该模型假设违约过程的强度依赖于由随机微分方程驱动的随机利率过程和交易对手的违约过程.本文模型可视为Jarrow和Yu(2001)及Hao和Ye(2011)中模型的推广.进一步地,我们利用随机指数的性质导出了可违约债券和含有对手风险的信用违约互换的定价公式并进行了数值分析.     

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.     

约化模型中含有对手风险的信用违约互换定价

在约化模型中研究了含有对手风险的信用违约互换的定价问题.通过构建信用违约互换买方、卖方和参考资产之间的衰减传染结构,借助于测度变换的方法分别导出了含有单边和双边对手风险的信用违约的定价表达式.     

American options under uncertain volatility

The uncertain volatility approach to financial derivatives is extended to American options (which allow early exercise before expiry). The requirement to model at the portfolio level made necessary by the non-linearity of the approach is found to lead to a recursive structure to the exercise possibilities across options. Other novel features include: the optimality sometimes of partial exercise; an interesting resolution to the issues surrounding short options whose exercise is controlled by a buyer counterparty; and the occurrence of a simple game structure for portfolios containing both long and short options. It is demonstrated that the exercise strategies resulting can significantly alter measured uncertain volatility risk. Contrary to the set of attributes for sensible risk measures put forward by Artzner, Delbaen, Eber and Heath, this risk need not be homogenous in portfolio size- forming a convincing argument for weakening this particular requirement.     

Counterparty risk valuation on credit-linked notes under a Markov Chain framework

A credit-linked note(CLN) is a note paying an enhanced coupon to investors for bearing the credit risk of a reference entity. In this paper, we study the counterparty risk on CLNs under a Markov chain framework, and introduce a Markov copula model to describe joint defaults between the reference entity underlying the CLN and CLN issuer. Assuming that the respective default intensities are directly and inversely proportional to the interest rate, which follows a CIR process, we obtain the explicit formulae for CLN values through a PDE approach.Finally, credit valuation adjustment(CVA) formula is derived to price counterparty credit risk.