【作者】 王秀玲；

【导师】 李翠香；

【作者基本信息】 河北师范大学 ， 概率论与数理统计， 2013， 硕士

【摘要】 期权是一种复杂的金融衍生产品,在套利保值与风险投资中得到广泛应用.近几十年来,很多学者对期权定价作了大量研究.随着场外衍生产品市场的发展,交易对手发生违约的可能性即信用风险受到人们越来越多的关注.因此,研究具有违约风险的期权的定价问题具有实际意义.本文主要讨论了具有违约性质的看涨期权与看涨-看涨期权的定价问题.目前国际上比较流行的描述违约风险的模型主要有两类：结构化模型与简化模型.本文假设违约风险是由结构化模型来描述的.具体而言,假定期权的承约方A公司的资产价格Vt服从几何布朗运动在期权期限内,若Vt低于一个事先设定好的常数L(称为违约水平)时,A公司将会违约.首先,我们假定期权的标的资产为股票,其价格过程St服从几何布朗运动其中ρ为Vt与St的瞬时相关系数,0≤ρ≤1.利用测度变换和鞅方法分别给出当ρ=0,0<ρ<1,ρ=1时的含违约风险的看涨期权的解析公式.然后,我们进一步假定期权的标的资产为B公司的股票St,而St可以看成B公司资产Vt2上的看涨期权.这时的期权实际上为看涨上的看涨期权即复合期权.我们假设Vt2服从几何布朗运动利用测度变换和鞅方法分别得到了当ρ=0,0<ρ<1,ρ=1时的含违约风险的看涨-看涨期权的解析公式.更多还原

【Abstract】 Options are complex derivatives, which are widely used in the arbitrage and risk in-vestment. In recent decades, many scholars have done a lot of research in option’s pricing.With the exciting developments of the over-the-counter derivatives markets, people paymore and more attention to the possibility that counterparties in derivatives transactionsmay default, which is also known as credit risk. Therefore, it is very interesting to pricethe options with default risk. The aim of this paper is to study the pricing issues ofoptions with default risk.Two types of default risk models which are prevalent internationally are referred toas structural model and reduced form. We assume the default risk is described by thestructural model in this paper. That is, suppose the asset value Vtof company A whichis the underwriter of an option follows the geometric Brownian motionand default would occur if Vtwas under a pre-specifed level during the life of the option.Firstly, we presume the undering asset of the option is a stock, whose value followsthe geometric Brownian motionhere ρ is the instantaneous correlation coefcient of Stand Vtand0≤ρ≤1. In threecases of ρ=0,0<ρ <1, ρ=1, we respectively get the analytic pricing formulas ofthe European call option with default risk through the measure transformation and themartingale method.Secondly, we suppose the undering asset Stof the option is the stock of company B.Since Stis viewed as a call option on the asset value Vt2of company B. In this case, theoption actually is a call-on-a-call compound option. We assume Vt2follows the geometricBrownian motion In three cases of ρ=0,0<ρ <1, ρ=1, the analytic pricing formulas of the Euro-pean call-on-a-call option with default risk are respectively found through the measuretransformation and the martingale method.更多还原