9th Symposium on Finance, Banking, and Insurance
Universität Karlsruhe (TH), Germany, December 11 - 13, 2002

Abstract

Extended Market Models with Affine and Quadratic Volatility

Christian Zühlsdorff

Universität Bonn

The market model specifies simple forward rates as lognormalydistributed, i.e., their stochastic dynamics has a linear volatilty function.This model is extended to quadratic volatility functions and derive closed-formsolutions to interest rate derivatives in this setup.We discuss the problem of the absorbing/reflecting boundary in zero andgive examples for the difference in implied volatilities.We fit the model to market pricies. It turns out that every specification fits better than the lognormal market model.