Article2007

DIFFUSION MODELS FOR EXCHANGE RATES IN A TARGET ZONE

Kristian Stegenborg Larsen · Michael Sørensen

116 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Monetary Policy and Economic Impact Financial Risk and Volatility Modeling

Abstract

We present two analytically tractable diffusion models for an exchange rate in a target zone. One model generalizes a model proposed by De Jong, Drost, and Werker (2001) to allow asymmetry between the currencies which is often an important feature of data. Estimation of the model parameters by the method of Kessler and Sørensen (1999) using eigenfunctions of the generator is investigated and shown to give well‐behaved estimators that are easy to calculate. The method is well suited to the models because the eigenfunctions are known so that explicit estimating functions are obtained, and because the state space is a finite interval, for which it is known that the method can be made arbitrarily efficient by including sufficiently many eigenfunctions. The model fits data on exchange rates in the European Monetary System well. In particular, the asymmetry parameter is significantly different from zero for three out of four currencies. An alternative diffusion model is presented with similarly nice properties, but with different dynamics that allow constant volatility near the boundaries of the target zone. No‐arbitrage pricing of derivative assets is considered, and the effect of realignments is briefly discussed.

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References

1973The Pricing of Options and Corporate Liabilities 1981Martingales and stochastic integrals in the theory of continuous trading 1991Target Zones and Exchange Rate Dynamics 1999Estimating Equations Based on Eigenfunctions for a Discretely Observed Diffusion Process 2005Diffusion-type models with given marginal distribution and autocorrelation function 2000Prediction‐based estimating functions

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