An analytical approximation of target zone exchange rate functions: the technique of collocation

Exchange Rate Dynamics in a Target Zone - A Heterogeneous Expectations Approach

This paper analyzes credibility in the Colombian exchange rate target zone. A model of imperfect credibility, in the spirit of Bertola and Svensson (1993) is derived, and is used to explain why the exchange rate in Colombia has remained for prolonged periods near the borders of the zone. The main feature of the model is that central parity depreciation expectations are endogenous with respect to the position of the exchange rate inside the target zone. The krugman(1991) perfectly credible setup turns out to be a particular case of this general model. One of the main implications of the model is that depreciation expectations increase rather than decrease as the exchange rate approaches the upper band. Hence a model as the one presented in this paper, is useful to explain the recent dynamics of interest rates in Colombia. It is also shown, that this model shares empirical features with the basic target zone model. Hence, policy makers might be misled when trying to recognize their credibility stance. A estructural estimation of the underlying parameters of the model, using McFadden's (1989) method of simulated moments, is suggested to identify the presence of non credibility issues. Econometric evidence suggest that Colombia's exchange rate target zone is properly described by a model of this nature.

This article presents a new way of modeling the dynamics of an exchange rate target zone. In the presence of a single upper (lower) target boundary, the exchange rate is precisely represented as the sum of a free float and a short (long) position in a call (put) option with strike price at the boundary. To model a target zone (with two boundaries), a natural approach consists of describing the exchange rate dynamics as the combination of the two, namely the sum of free float together with a long position in a put written on the lower boundary and a short position in a call option written on the upper boundary, respectively. The authors show that this first order approximation leads to significant mispricing (as much as 20%) and must be iterated, leading to an infinite sequence of compounded “mirrored” option prices. They analyze basic properties of such mirrored nested options analytically, describe how to calculate them numerically, and show why it is crucial to take into account higher order corrections in realistic target zones. They argue that this analogy to option prices allows for conceptually simple generalizations that describe different target zone arrangements. They then apply their methodology to the estimation of the fundamental value of the Hong Kong dollar that is hidden by the target zone pegged to the US dollar. They also estimate the implied maturity and explain how this parameter serves as direct proxy for target zone credibility.

The paper aims to highlight the main difficulties on the monetary path towards the euro zone experienced by Emerging Europe. Emerging European Economies (EEEs), EU members, adopted either double shift or smooth transition monetary approach towards the euro zone. Double shift assumes changes from floating exchange rate regimes (ERRs) to the ERM II target zone and, finally, monetary union as a rigid ERR. The smooth transition is practiced by economies with mainly rigid ERRs before the ERM II entrance and, at the end, again rigid ERR of a monetary union. Despite chosen monetary path towards the euro zone, crucial difficulties or aggravating factors could be identified in the form of real exchange rate appreciation due to productivity growth or capital inflows. A reconciliation of inflation and exchange rate target zone is extremely complex, at the same time striving not to jeopardize the real convergence. What is stressed here is the vicious cycle between real and nominal convergence as the reason why the ERM II target should be regarded as a “waiting room“ not as a “training room“ in the pre-EMU phase.

An algorithmic approach to exchange rate stabilization

I examine authorities' interventions in goods and money markets to keep exchange rates within targeted zones, in an economy where both the exchange rate and the prices of goods are interdependent forward-looking variables. I show that, (1) in order to support target zones in both goods and money markets, there needs to be coordinated, simultaneous intervention in the two markets; (2) intervention takes place almost certainly before the exchange rate or the price level reaches its upper or lower bounds; and (3) zones for the exchange rate and for the price level cannot be separately designed as independent policy goals.

Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous risk-free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Weiner process and Poisson process). The corresponding partial differential equation (PDE) with terminal boundary condition of the model is drawn. The general solution with parameters of the above PDE is derived. The parameters are estimated by using the weight least squares approach with historical data for special cases. For the objective of risk assessment, downside risk has impacted on the practitioner's view of risk apparently. Variance is substituted by semi-variance. Moreover, one period portfolio selection is extended to multi-period. A class of multi-period semi-variance model is formulated. A hybrid genetic algorithm, which makes use of the position displacement strategy of the particle swarm optimiser as a mutation operation, is applied to solve the multi-period semi-variance model. Finally, in order to demonstrate the effectiveness of the theoretical models and numerical methods, fuel futures in the Shanghai exchange market is selected to be an example.

On the mean-reverting properties of target zone exchange rates: Some evidence from the ERM

Quantitative Modelling of the EUR/CHF Exchange Rate During the Target Zone Regime of September 2011 to January 2015: A Correction

Part 1 International policy co-ordination and exchange rate management: the European monetary system, exchange rate expectations and the reputation of authorities, P.Artus would US protectionism be a threat to economic stability?, A.J.Hughes Hallett and G.J.Huston international adjustment and the dollar - a game theoretic approach, J.C.Martinez Oliva exchange rates and policy co-ordination in an asymmetric model, P.Kennen international policy co-ordination, imperfect information and target zones, A.Bisin and P.Tedeschi target zones, currency options and the dollar, P.Weller. Part 2 Strategic aspects of international policy co-ordination: time inconsistency, discounting and the returns to co-operation, M.Miller, et al policy co-operation among benevolent governments may be undesirable - an extension, P.J.Kehoe can international policy co-ordination really be counterproductive?, C.Carraro and F.Giavazzi profit shifting motives and international trade union co-ordination, D.Laussel and A.Soubeyran. Part 3 Information and uncertainty: robust lyapunov games under bounded uncertainty, C.Diessenberg asymmetric information and policy co-ordination, M.Cripps international policy co-ordination in a world with model uncertainty, A.R.Ghosh and P.R.Masson.

economic equilibrium ; risk ; government spending policy ; exchange rate ; inflation

Jump-Diffusion International Asset Pricing with Nontraded Consumption Goods

A majority of countries neither freely float their currencies nor firmly peg. But most of the remainder in practice also don’t obey such well-defined intermediate exchange rate regimes as target zones. This paper proposes to define an intermediate regime, to be called “systematic managed floating,” as an arrangement where the central bank regularly responds to changes in total exchange market pressure by allowing some fraction to be reflected as a change in the exchange rate and the remaining fraction to be absorbed as a change in foreign exchange reserves. An operational criterion for judging systematic managed floaters is a high correlation between exchange rate changes and reserve changes. The paper rejects the view that exchange rate regimes make no difference. In regressions to test effects on real exchange rates, we find that positive external shocks tend to cause real appreciation for most systematic managed-floaters; more strongly so for pure floaters; and not at all for most firm peggers. Two measures of exogenous external shocks are used: (i) for commodity-exporters, a country-specific index of global prices of the export commodities and (ii) for other Asian emerging market economies, the VIX.

The first known experiment with an exchange rate band took place in Austria- Hungary between 1896 and 1914. The rationale for introducing this policy rested on precisely those intuitions that the modern literature has emphasized: the band was designed to secure both exchange rate stability and monetary policy autonomy. However, unlike more recent experiences, such as the ERM, this policy was not undermined by credibility problems. The episode provides an ideal testing ground for some important ideas in modern macroeconomics: specifically, can formal rules, when faithfully adhered to, provide policy makers with some advantages such as short term autonomy? First, we find that a credible band has a "microeconomic" influence on exchange rate stability. By reducing uncertainty, a credible fluctuation band improves the quality of expectations, a channel that has been neglected in the modern literature. Second, we show that the standard test of the basic target zone model is flawed and develop an alternative methodology. We believe that these findings shed a new light on the economics of exchange rate bands.

Exchange rate behavior is analyzed in the context of a stochastic rational expectations model in which there are random shocks to the price setting mechanism and in which the authorities choose to impose either nominal or real exchange rate bands. Results are compared to those which emerge from a simple monetary model subject to velocity shocks. The effects of a realignment of the Band, and of fiscal policy used in conjunction with monetary policy to defend the band, are also examined.