An arbitrage free trilateral target zone model

Jørgensen, Bjørn N.; Mikkelsen, Hans Ole

doi:10.1016/0261-5606(95)00050-x

Cited by 7 publications

(4 citation statements)

References 15 publications

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“…But another interpretation is also possible. Some of the recent target-zone literature, such as the work of Jorgensen and Mikkelsen (1996), Pill (1996), and Serrat (2000) have emphasized the fact that the earlier literature has not fully appreciated the empirical implications of another important institution detail. Speci cally, these works argued that the fact that the Deutsche mark/French franc (DM/FF) was part of a multilateral grid system of target rates has important implications for the unconditionaldensities of the bivariate exchangerates.…”

Section: Commentmentioning

confidence: 97%

Testing Target-Zone Models Using Efficient Method of Moments

Chung

Tauchen

2001

Journal of Business & Economic Statistics

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Section: Commentmentioning

confidence: 97%

Testing Target-Zone Models Using Efficient Method of Moments

Chung

Tauchen

2001

Journal of Business & Economic Statistics

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“…In particular, within the literature we can identify two main streams of research. On one hand, many papers develop stochastic models aiming at explaining the dynamics of exchange rates within a given target zone (see [9,18,32,28,33,48], among others). Target zone models have been pioneered in [32] where it is assumed that the "fundamental" (and not observed) exchange rate is a Brownian motion, which is instantaneously reflected at exogenously given upper and lower barriers: this intrinsically defines a singular stochastic control problem, whose value function is the exchange rate really observed in the market.…”

Section: Introductionmentioning

confidence: 99%

“…In the subsequent papers (see e.g. [9,18,28,33,48] and references therein), the authors assume that exchange rates fluctuate stochastically within an exogenously given interval according to a stochastic differential equation parametrized by a set of free parameters, and possibly satisfying reflecting boundary conditions, or with diffusion coefficient vanishing near the boundaries of the interval. The parameters are then calibrated in such a way that the model can fit the data on exchange rates, e.g.…”

Section: Introductionmentioning

confidence: 99%

On the singular control of exchange rates

Ferrari

Vargiolu

2019

Ann Oper Res

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Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads to a proportional cost whose instantaneous marginal value depends on the current level of the exchange rate. The central bank aims at minimizing the total expected costs of interventions on the exchange market, plus a total expected holding cost. We formulate this problem as an infinite time-horizon stochastic control problem with controls that have paths which are locally of bounded variation. The exchange rate evolves as a general linearly controlled one-dimensional diffusion, and the two nondecreasing processes giving the minimal decomposition of a bounded-variation control model the cumulative amount of foreign currency that has been purchased and sold by the central bank. We provide a complete solution to this problem by finding the explicit expression of the value function and a complete characterization of the optimal control. At each instant of time, the optimally controlled exchange rate is kept within a band whose size is endogenously determined as part of the solution to the problem. We also study the expected exit time from the band, and the sensitivity of the width of the band with respect to the model's parameters in the case when the exchange rate evolves (in absence of any intervention) as an Ornstein-Uhlenbeck process, and the marginal costs of controls are constant. The techniques employed in the paper are those of the theory of singular stochastic control and of one-dimensional diffusions.

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“…For evidence that the standard bilateral model is at odds with the data see for example Flood, Rose and Mathieson (1991). The importance of considering the multilateral nature of target zones has also been highlighted in the empirical papers of Honohan (1993), Pill (1994) and Jorgensen and Mikkelsen (1996).…”

Section: Introductionmentioning

confidence: 99%

Exchange Rate Dynamics in a Multilateral Target Zone

Serrat

2000

Rev Econ Studies

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This paper presents a model of exchange rate behaviour in a multilateral target zone. The model produces new economic insights beyond the well-known bilateral model of Krugman (1991), which is obtained as a special case. The paper also introduces a new class of stochastic processes in economics, namely multidimensional reflected diffusion processes.Two main features characterize the economics of exchange rates in a multilateral target zone. (i) The restrictions on interventions imposed by cross-currency constraints: when one country changes its money supply, say because its exchange rate with a second country has hit its band, all exchange rates involving the currency of that particular country will be affected, regardless of their position within their respective bands. (ii) Cooperation in sharing the intervention burden: in general, the exchange rate between any two countries will depend on the fundamentals of third countries in a multilateral target zone. This is because if the monetary authorities intervene together, a shock in the fundamentals of any country will induce a revision of the expectation of future interventions of other countries.The model reverts the counterfactual predictions of the bilateral model that the exchange rate steady-state density should be U-shaped and that its volatility should be a decreasing function of the distance of the exchange rate to the limits of its band. Thus, accounting for the multilateral feature of real-world target zones allows us to reconcile target zone models with the most salient empirical features of exchange rate behaviour.

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An arbitrage free trilateral target zone model

Cited by 7 publications

References 15 publications

Testing Target-Zone Models Using Efficient Method of Moments

Testing Target-Zone Models Using Efficient Method of Moments

On the singular control of exchange rates

Exchange Rate Dynamics in a Multilateral Target Zone

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