Pricing The Bond Option Of Vasicek And Cir Models
Name: Huajun Liu
Professor: Marco Pereira
Course: Math 624
Date: 2016/12/18
1. Abstract
This report is aimed to describe how we will use Python to build an application to price risky bond and the European options of the bond in stochastic hazard rate and interest rate models. We are going to simulate the path of interest rate using CIR model and simulate the path of hazard rate using Vasicek model. Then we will get the survival function from simulated hazard rate and get the bond price from it. Lastly we will price the European options of the risky bond based on the simulated bond price by using both closedform formula (Jamshidian, F. (1989)) and Monte Carlo simulation.
2. Introduction
Today, an increasing number of risky bond options have been introduced to customers, but only a few customers can understand how to price a risky bond option. The credit derivative is a new type of financial derivative which is based on the credit condition of the loan developed in the 1990s, and its function is to separate the credit risk from other risks of the primary assets and transfer it to the counterparty. Also, credit derivatives can make credit risk appear in a more fluid and tradable form, which has a great application in improving the portfolio of returns and presenting a highly structured risk portfolio. Meanwhile, credit derivatives can be used in the investment market Avoid risks, and thus mobilize the credit market activity.…

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