Entropic Dynamics of Exchange Rates and Options

On the hedging of options on exploding exchange rates

We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of numéraire (change of currency) technique when the underlying is only a local martingale ...

Entropic Dynamics

Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints appropriate to the problem at hand. In this paper we review three examples of entropic dynamics. First we tackle the simpler case of a standard diffusion proces...

Nonlinearity In Exchange Rates and Forecasting

Exchange Options

The contract is described and market examples given. Essential theoretical developments are introduced and cited chronologically. The principles and techniques of hedging and unique pricing are illustrated for the two simplest nontrivial examples: the classical Black-Scholes/Merton/Margrabe exchange option model brought somewhat upto-date from its form three decades ago, and a lesser exponentia...

Asymmetric Adjustment and Nonlinear Dynamics in Real Exchange Rates

This paper examines whether deviations from PPP are stationary in the presence of nonlinearity, and whether the adjustment towards PPP is symmetric from above and below. Using alternative nonlinear models, our results support mean reversion and asymmetric adjustment dynamics. We find differences in magnitudes, frequencies and durations of the deviations of exchange rates from fixed and time-var...