Asset price processes, Double exponential jump-diffusion, Pareto-beta jump diffusion, Leptokurtic distributions, Volatility smile-smirk, MLE, C32, C52, G12, G13,

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This paper extends the affine class of term structure models to describe the joint dynamics of exchange rates and interest rates. In particular, the issue of how to reconcile the low volatility of interest rates with the high volatility of exchange rates is addressed. The incomplete market approach of introducing exchange rate volatility that is orthogonal to both interest rates and the pricing kernels is shown to be infeasible in the affine setting. Models in which excess exchange rate volatility is orthogonal to interest rates but not orthogonal to the pricing kernels are proposed and validated via Kalman filter estimation of maximal 5-factor models for 6 country pairs.

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