The Study Of Option Pricing With Default Risk And Its Numerical Calculation

With the continuous development and innovation of financial derivative products, one major problem is: the possibility of not being able to keep the promises of trade becomes even greater as the counterparties are subject to various factors. Therefore, the study about the credit risk model of the derivative has become extremely important and meaningful.This paper is divided into two parts:For the first part, we study on the default risk of the option pricing with the tradable underlying asset. Firstly, we make a detailed analysis on the risk option pricing issue when the default intensity is a decaying function. Using the method of numerical analysis, we compare the risk option-pricing with the condition that the default intensity is Jarrow & Yu model and a decaying function respectively. And we conclude that the price of default option which default intensity is a decaying function is higher than that of the option which default intensity is the JY model. Secondly, taking notice of the deficiency of the default risk option pricing model that Vasicek stochastic interest rate may be negative, we make modifications to the model assumptions, and then study on the default risk option pricing based on CIR interest rate model. Moreover, we simulate the estimate of option pricing with the help of the Monte Carlo method, and analyze the impact of various risk factors on option pricing through numerical test.For the second part, we study on the default risk of the option pricing with the non-tradable underlying asset. When the underlying asset is non-tradable, we try to search for a "twin security" to derive the underlying asset's SDE model, and we simulate the numerical solution of option pricing by using the Monte Carlo method. Taking the non-tradable shares for example, we get the numerical solution of option pricing and analyze the impact of various risk factors on option pricing.At present, most of the studies are concentrated on the valuation of debt instruments such as corporate bonds, loans and mortgage. However, the credit risk of financial derivatives is generally neglected. Even today the great majority of participants and researchers of the derivatives market still use the pricing models without the consideration of the credit risk. The study of this paper is helpful for us to give a more reasonable credit risk option pricing model and to accurately assess the impact of the potential credit risk on derivatives pricing. This dissertation provides some theoretical backgrounds and empirical evidences for OTC market participants.