A Two-Factor Model Of Danish Mortgage Loans

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A Two-Factor Model Of Danish Mortgage Loans

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Soren S. Nielsen, Rolf Poulsen (University of Copenhagen)

Abstract

This paper provides an extension of the Black-Scholes model for option pricing in which the logarithm of the volatility is assumed to be generated from an Ornstein-Uhlenbeck equation with fractional Riesz-Bessel motion (fRBm) input. The solution of the resulting stochastic differential equation will display intermittency, non-Gaussianity and long-range dependence (LRD) (and also volatility persistence). It should be noted that fractional Brownian motion (fBm) has been suggested in the literature as an input to the Black-Scholes model to capture the LRD in the asset price process. However, fBm is not a semimartingale, hence may imply the existence of arbitrage. On the other hand, fRBm is a semimartingale for a range of its parameters, hence admits the "no free lunch with vanishing risk" condition. We obtain the existence and uniqueness as well as exact solution of the model. An algorithm will also be provided to generate sample paths of fRBm, and therefore those of the asset price process through the exact solution of the equation.

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2000 with number 288.

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Date of creation: 05 Jul 2000
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Handle: RePEc:sce:scecf0:288

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