Option Pricing and Numerical Techniques for Pricing Interest Rate Derivatives

• Main Authors: Li-Shu Chen, 陳麗淑
• Other Authors: Yuan-Chung Sheu
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/75352731981694622130

碩士 === 國立交通大學 === 應用數學系 === 89 === In the world , the securities have become very popular , with a wide variety of istrument trading in the finance and investment market . And option market becomes more and more important . Here we concentrate on models for pricing interest rate derivatives and its numerical techniques . Although Black-Scholes formula can be used to price interest rate derivatives , different instruments make different assumptions , it leads special pricing methods . In order to value interest rate derivatives accurately and consistently we need to model the whole term structure of interest rates and the associated volatilities of these rates . To be automatically consistent with the initial (observed) market data , term structure consistent models set out to model the dynamics of the entire term structure . For most interest rate models , and for models which have some tractability but applied to pricing products which involve early exercise opportunities or complicated terminal pay-offs , we must use numerical techniques to solve them . First we construct binomial trees to represent a number of processes for short rate , and how the resulting tree can then be used to price a wide range of interest rate derivatives . Furthermore we extend it to building trinomial trees for short rate , the extra degree of freedom which this extension allows, enables us to implement short-rate models that exhibit mean reversion . A tree is constructed in such a way that approximates the stochastic differential equation for short rate and automatically returns the observed prices of pure discount bonds and possibly the volatilities of these bonds . Thus we can use these to price many interest rate derivatives .