基于Poisson跳跃的信用价差期权定价

Credit Spread Option Pricing based on Poisson Jump

信用价差是用以向投资者补偿参照资产违约风险的、高于无风险利率的利差。信用价差期权作为风险控制的重要手段之一,其定价也日益得到人们的关注。现有文献几乎是单纯地利用几何布朗运动来刻画资产的价格变化过程从而对信用价差期权进行定价。而在实际中会出现某些不寻常的事件导致资产价格出现不间断的跳跃现象,普通的定价方法对这种现象的解释力度不够。因此本文引入Poisson跳跃来描述信用价差变化过程中的异常情况,更好地解释当遇到金融危机等情况时资产价值的跳跃现象。由于Longstaff和Schwartz的模型引入了随机利率,可以给出定价公式的封闭解析解的优点,本文在此模型上进行进行研究,将刻画信用价差动态过程的O-U过程与Poisson跳跃结合,利用伊藤公式进行推导并引入了利率的平方根过程,得到了欧式信用价差期权的定价公式,更好地考虑了资产价格的跳跃情况。

Credit spread is used to compensate for investor on the basis of underlying asset＇s default risk which is the interest margin higher than the risk-free interest rate.Credit spread option plays a role in hedging the risk of credit spread.As an important means of risk control,credit spread option＇s pricing is also the focus of attention problems.At present,almost studies simply use the geometric Brownian motion to describe the process of asset price changes to price credit spread option.However,in practice,there are some unusual events that lead to asset prices arising uninterrupted jumping phenomenon,common pricing methods have inadequate explanation for this phenomenon.This article introduces poisson jump to describe the unusual circumstances in the process of change in the credit spread,which better explains the jump of asset value when faced with financial crisis.As Longstaff and Schwartz＇s model introduces stochastic interest rate and can give a closed analytical solution of the pricing formulas,this article is based on the model and combines poisson jump with Ornstein-Uhlehbeck Model which characterizes the dynamic process of credit spreads,uses Ito for-mula,introduces the process of the square root of interest rate,obtains the pricing formula of European credit spread option and better takes into account the case of asset price jump.