带有违约风险的期权定价

发布时间：2018-06-21 20:24

  本文选题：看涨期权 + 复合期权　； 参考：《河北师范大学》2013年硕士论文

【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=0,0ρ1,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=0,0ρ1,ρ=1时的含违约风险的看涨-看涨期权的解析公式.
[Abstract]:Option is a complex financial derivative, which is widely used in arbitrage and venture capital. In recent decades, many scholars have done a lot of research on option pricing. With the development of OTC derivatives market, people pay more and more attention to the possibility of counterparty default, namely credit risk. Therefore, it is of practical significance to study the pricing of options with default risk. This paper mainly discusses the pricing of call options and call-call options with default. There are two kinds of models to describe default risk: structured model and simplified model. This paper assumes that default risk is described by a structured model. In particular, assuming that the asset price of option contractor A Company A follows the geometric Brownian motion during the term of the option, if Vt is below a predetermined constant L (called default level), company A will default. First of all, we assume that the underlying asset of the option is a stock, and its price process is from geometric Brownian motion where 蟻 is the instantaneous correlation coefficient of V t and St 0 鈮，

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