Squared Bessel processes and their applications to the square root interest rate model
type: Item
instance of: scholarly article
title: Squared Bessel processes and their applications to the square root interest rate model
zbMATH Open document ID: 1034.60074
DOI: 10.1023/A:1024173313448
author: Hiroshi Shirakawa
published in: Asia-Pacific Financial Markets
publication date: 2004-02-03T00:00:00Z
review text: The author studies the extended Cox-Ingersoll-Ross (CIR) term structure model of the form \(dr_t=(\alpha_t-\beta_tr_t)dt+\sigma_t\sqrt{r_t}dW_t \), where \( \alpha_t, \beta_t \) and \( \sigma_t \) are time-varying deterministic functions. The object of the paper is to apply the basic properties of the squared Bessel processes with time-varying dimension for studying the extended CIR model with time-varying parameters in a purely probabilistic approach. It is established that there exists an equivalent martingale measure for the square root risk premium process. Then, the arbitrage free prices of pure discount bonds and their call options under this measure change are derived. At last, a special class of extended CIR models is studied which not only enables to fit every arbitrage free initial term structure, but also to give the extended CIR call option pricing formula.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 2036994
zbMATH Keywords: extended Cox-Ingersoll-Ross model
zbMATH Keywords: Bessel process
zbMATH Keywords: time-varying dimension
zbMATH Keywords: option pricing
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: a:1024173313448
OpenAlex ID: W102245012
description: scientific article; zbMATH DE number 2036994