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Didier Sornette - One of the best experts on this subject based on the ideXlab platform.
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Currency Target Zones as Mirrored Options
The Journal of Derivatives, 2019Co-Authors: Sandro Claudio Lera, Matthias Leiss, Didier SornetteAbstract: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.
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an explicit mapping of currency Target Zone models to option prices
Social Science Research Network, 2017Co-Authors: Sandro Claudio Lera, Didier SornetteAbstract:Currency Target Zones have been under scrutiny for the past three decades, which led to the development of two broad classes of quantitative models: Phenomenological ones that explicitly take into consideration the market’s perception of the bounded exchange rate, and more mechanical ones that rely on put and call options. Until now, the two models have only been compared qualitatively. Here, we derive, for the first time, a quantitative link between these two approaches. Specifically, we show how the former approach has to be generalized in order to recover the second one. This mapping lets us relate the phenomenological parameter of the first approach to economically well-known quantities.
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quantitative modelling of the eur chf exchange rate during the Target Zone regime of september 2011 to january 2015
Journal of International Money and Finance, 2016Co-Authors: Sandro Claudio Lera, Didier SornetteAbstract:Krugman (1991)'s Target Zone model for exchange rate dynamics has become the reference of a large part of this literature. Despite its simplicity and elegance, empirical evidence has been lacking, not least because it is difficult to capture the predicted non-linear relationship between the observable exchange rate and the non-observable fundamental value. This is why we propose a different approach. By inverting locally the relation between exchange rate and fundamental value, we derive analytical expressions for the conditional volatility and the probability density as a function of the exchange rate. This allows us to examine Krugman's prediction directly from historical data, and, furthermore, enables us to test the smooth pasting condition, which is intimately related to the no-arbitrage condition. Concretely, we study the performance of the euro/Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015, when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. We show that the data are well explained by the theory and conclude that Krugman's Target Zone model holds after all, but apparently only under extreme and sustained pressure that pushes continuously the exchange rate very close to the boundary of the Target Zone.
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currency Target Zone modeling an interplay between physics and economics
Physical Review E, 2015Co-Authors: Sandro Claudio Lera, Didier SornetteAbstract:We study the performance of the euro-Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Within the general framework built on geometric Brownian motions and based on the analogy between Brownian motion in finance and physics, the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. Nonparametric empirical estimates of drift and volatility show that the predicted first-order analogy between economics and physics is incorrect. The clue is to realize that the random-walk nature of financial prices results from the continuous anticipation of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank's stated commitment to enforce the barrier, traders' anticipation of this action leads to a vanishing drift together with a volatility of the exchange rate that depends on the distance to the barrier. This effect is described by Krugman's model [P. R. Krugman, Target Zones and exchange rate dynamics, Q. J. Econ. 106, 669 (1991)]. We present direct quantitative empirical evidence that Krugman's theoretical model provides an accurate description of the euro-Swiss franc Target Zone. Motivated by the insights from the economic model, we revise the initial economics-physics analogy and show that, within the context of hindered diffusion, the two systems can be described with the same mathematics after all. Using a recently proposed extended analogy in terms of a colloidal Brownian particle embedded in a fluid of molecules associated with the underlying order book, we derive that, close to the restricting boundary, the dynamics of both systems is described by a stochastic differential equation with a very small constant drift and a linear diffusion coefficient. As a side result, we present a simplified derivation of the linear hydrodynamic diffusion coefficient of a Brownian particle close to a wall.
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quantitative modelling of the eur chf exchange rate during the Target Zone regime of september 2011 to january 2015
2015Co-Authors: Sandro Claudio Lera, Didier SornetteAbstract:Krugman (1991)’s Target Zone model has become the reference of a large part of this literature. Despite its simplicity and elegance, empirical evidence has been lacking. Deriving from Krugman’s model analytical expressions for the conditional volatility and density distribution close to the Target Zone limit, we present clear and direct evidence that the bounded EUR/CHF exchange rate between September 2011 and January 2015 was quantitatively well described by Krugman’s model. Krugman’s Target Zone model holds after all, but apparently only under extreme and sustained pressure that pushes continuously the exchange rate very close to the boundary of the Target Zone.
Lars E O Svensson - One of the best experts on this subject based on the ideXlab platform.
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How Long do Unilateral Target Zones Last
Journal of International Economics, 1994Co-Authors: Bernard Dumas, Lars E O SvenssonAbstract:Abstract We examine the expected survival time of a unilateral exchange rate Target Zone, when constraints on monetary policy prevent the central bank from exclusively focusing on defending the Target Zone. Generally the width of the Target Zone has a negligible effect on the expected survival time, and the dominant determinants are reserve levels and the degree of real and monetary divergence between the country in question and the rest of the world. For seemingly realistic parameters, the expected survival time is fairly long: a few decades rather than a few years.
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stochastic devaluation risk and the empirical fit of Target Zone models
The Review of Economic Studies, 1993Co-Authors: Giuseppe Bertola, Lars E O SvenssonAbstract:In our model, an exchange rate fluctuates between given boundaries for random lengths of time and jumps discretely when devaluations occur. We provide explicit solutions for the stochastic processes followed by the exchange rate and by the expected rate of depreciation when the likelihood and the size of devaluations vary stochastically over time. The model produces realistic patterns of covariation between exchange rates and interest rate differentials, and provides interesting interpretations of available empirical evidence. We also specify a technique for inferrring the risk of devaluation from Target-Zone data.
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stochastic devaluation risk and the empirical fit of Target Zone models
The Review of Economic Studies, 1993Co-Authors: Giuseppe Bertola, Lars E O SvenssonAbstract:In the model of this paper, an exchange rate fluctuates between given boundaries for random lengths of time and jumps discretely when devaluation occur. We provide explicit solutions for the stochastic processes followed by the exchange rate and by the expected rate of depreciation when the likelihood and the size of devaluations vary stochastically over time. The model produces realistic patterns of covariation between exchange rates and interest rate differentials, and provides interesting interpretations of available empirical evidence. We also specify how to infer devaluation risk from Target Zone data.
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the foreign exchange risk premium in a Target Zone with devaluation risk
Journal of International Economics, 1992Co-Authors: Lars E O SvenssonAbstract:Abstract The foreign exchange risk premium in an exchange rate Target Zone is derived, when the exchange rate is heteroskedastic within the band and there is a separate devaluation risk. The risk premium is then the sum of two separate risk premia, arising from uncertainty about exchange rate movements within the band and from uncertainty about devaluations. Both real and nominal risk premia are considered. Real and nominal risk premia from movements within the band are very small. Real and nominal risk premia from devaluations are larger but still relatively small proportions of the interest rate differential.
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the term structure of interest rate differentials in a Target Zone theory and swedish data
Journal of Monetary Economics, 1991Co-Authors: Lars E O SvenssonAbstract:Abstract The term structure of interest rate differentials is derived in a model of a small open economy with a Target Zone exchange rate regime. For given time to maturity the interest rate differential is decreasing in the exchange rate, and for given exchange rate the interest rate differential's absolute value and its instantaneous variability are both decreasing in the time to maturity. Devaluation/realignment risks are incorporated and imply upward shifts of the interest rate differentials. Several implications of the theory are found to be broadly consistent with data on Swedish exchange rates and interest differentials for the period 1986–1989.
Peter Walker - One of the best experts on this subject based on the ideXlab platform.
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Target Zone for balancing of total knee arthroplasties using load sensor technology a proof of concept
Orthopaedic Proceedings, 2018Co-Authors: Patrick Meere, G Salvadore, L Chu, Peter WalkerAbstract:INTRODUCTION Soft tissue balancing in knee arthroplasty remains an art. To make it a science reliable quantification and reference values for soft tissue tension and contact loads are necessary. This study intends to prove the concept of a compartmental load safe Target Zone as a clinical tool for balancing total knee arthroplasties by studying the relationship between post- balancing compartmental load distribution and patient satisfaction at 6 months. MATERIALS AND METHODS In this prospective non-randomised clinical series of 102 patients (110 knees), medial and lateral loads were recorded intra-operatively using a tibial liner load sensor system. All knees were balanced using specific algorithm sequences with a goal of equal distribution between compartments. A safe Target Zone area was defined on a scatterplot graph displaying lateral versus medial loads. Individual points on the graft were coded with their satisfaction score at 6 months. RESULTS Eighty-two (82) cases satisfied the study criteria and ...
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Target Zone for balancing of total knee arthroplasties using load sensor technology a proof of concept
Journal of Bone and Joint Surgery-british Volume, 2017Co-Authors: Patrick Meere, G Salvadore, L Chu, Peter WalkerAbstract:INTRODUCTION Soft tissue balancing in knee arthroplasty remains an art. To make it a science reliable quantification and reference values for soft tissue tension and contact loads are necessary. This study intends to prove the concept of a compartmental load safe Target Zone as a clinical tool for balancing total knee arthroplasties by studying the relationship between post- balancing compartmental load distribution and patient satisfaction at 6 months. MATERIALS AND METHODS In this prospective non-randomised clinical series of 102 patients (110 knees), medial and lateral loads were recorded intra-operatively using a tibial liner load sensor system. All knees were balanced using specific algorithm sequences with a goal of equal distribution between compartments. A safe Target Zone area was defined on a scatterplot graph displaying lateral versus medial loads. Individual points on the graft were coded with their satisfaction score at 6 months. RESULTS Eighty-two (82) cases satisfied the study criteria and were analysed. The boundaries of the safe Zone were defined by combining absolute and relative load values. Fifty-seven (57) knees fitted in the defined Zone and 25 lied outside. Excellent satisfaction scores were 4.2 times more likely to be in the safe Zone. Poor scores were twice more likely to lie outside the Zone. In the Zone the median satisfaction score was 36/40, whereas outside the Zone it fell to 31/40. DISCUSSION Load balancing of knee arthroplasty is a useful clinical tool. Early studies by a developing group showed increased satisfaction rates. One problem remains the subjectivity of testing at the time of surgery. Other studies have also pointed to the difficulty in defining a Target Zone for balancing. Using specific ligamentous balance algorithms it is now possible to predictably achieve a balanced load differential within 15 lbs between compartments. In this paper, we have demonstrated in a prospective series that a Target Zone can be defined as an area rather than a single ideal value. Within this Zone satisfaction scores reach 90–95%. Of all excellent results there are 4.2 more within the Zone than outside. Balancing a knee arthroplasty to medial and lateral compartment load values defined by a safe Target Zone can therefore be predictive of patient satisfaction.
W. Jos Jansen - One of the best experts on this subject based on the ideXlab platform.
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INSIDE THE IMPOSSIBLE TRIANGLE: MONETARY POLICY AUTONOMY IN A CREDIBLE Target Zone
Contemporary Economic Policy, 2008Co-Authors: W. Jos JansenAbstract:"This paper examines the trade-off between exchange rate stability and monetary autonomy for a Target Zone. Using the guilder-mark Target Zone in the pre-Economic and Monetary Union period as a case study, we empirically estimate how much policy discretion the Dutch central bank still enjoyed and how much had been ceded to the German central bank. The sum of these two measures is an estimate of the policy autonomy under a free float. We find that the narrow guilder-mark Target Zone still permitted a modest degree of policy independence. This result suggests that intermediate exchange rate regimes may offer an attractive trade-off compared to the corner solutions (free float and monetary union), which is consistent with the "fear of floating" phenomenon. "("JEL "E52, F33, F41, F42) Copyright (c) 2008 Western Economic Association International.
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Inside the Impossible Triangle:Monetary Policy Autonomy in a Credible Target Zone
Social Science Research Network, 2003Co-Authors: W. Jos JansenAbstract:This paper examines the trade-off between exchange rate stability and monetary autonomy for a Target Zone. Using the guilder-mark Target Zone in the pre-EMU period as a case study, we empirically estimate how much policy discretion the Dutch central bank still enjoyed and how much had been ceded to the German central bank. The sum of these two measures is an estimate of the policy autonomy under a free float. We find that the narrow guilder-mark Target Zone still permitted a modest degree of policy independence. This result suggests that intermediate exchange rate regimes may offer an attractive trade-off compared to the corner solutions (free float and monetary union), which is consistent with the ‘fear of floating’ phenomenon.
Sandro Claudio Lera - One of the best experts on this subject based on the ideXlab platform.
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Currency Target Zones as Mirrored Options
The Journal of Derivatives, 2019Co-Authors: Sandro Claudio Lera, Matthias Leiss, Didier SornetteAbstract: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.
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an explicit mapping of currency Target Zone models to option prices
Social Science Research Network, 2017Co-Authors: Sandro Claudio Lera, Didier SornetteAbstract:Currency Target Zones have been under scrutiny for the past three decades, which led to the development of two broad classes of quantitative models: Phenomenological ones that explicitly take into consideration the market’s perception of the bounded exchange rate, and more mechanical ones that rely on put and call options. Until now, the two models have only been compared qualitatively. Here, we derive, for the first time, a quantitative link between these two approaches. Specifically, we show how the former approach has to be generalized in order to recover the second one. This mapping lets us relate the phenomenological parameter of the first approach to economically well-known quantities.
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quantitative modelling of the eur chf exchange rate during the Target Zone regime of september 2011 to january 2015
Journal of International Money and Finance, 2016Co-Authors: Sandro Claudio Lera, Didier SornetteAbstract:Krugman (1991)'s Target Zone model for exchange rate dynamics has become the reference of a large part of this literature. Despite its simplicity and elegance, empirical evidence has been lacking, not least because it is difficult to capture the predicted non-linear relationship between the observable exchange rate and the non-observable fundamental value. This is why we propose a different approach. By inverting locally the relation between exchange rate and fundamental value, we derive analytical expressions for the conditional volatility and the probability density as a function of the exchange rate. This allows us to examine Krugman's prediction directly from historical data, and, furthermore, enables us to test the smooth pasting condition, which is intimately related to the no-arbitrage condition. Concretely, we study the performance of the euro/Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015, when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. We show that the data are well explained by the theory and conclude that Krugman's Target Zone model holds after all, but apparently only under extreme and sustained pressure that pushes continuously the exchange rate very close to the boundary of the Target Zone.
-
currency Target Zone modeling an interplay between physics and economics
Physical Review E, 2015Co-Authors: Sandro Claudio Lera, Didier SornetteAbstract:We study the performance of the euro-Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Within the general framework built on geometric Brownian motions and based on the analogy between Brownian motion in finance and physics, the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. Nonparametric empirical estimates of drift and volatility show that the predicted first-order analogy between economics and physics is incorrect. The clue is to realize that the random-walk nature of financial prices results from the continuous anticipation of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank's stated commitment to enforce the barrier, traders' anticipation of this action leads to a vanishing drift together with a volatility of the exchange rate that depends on the distance to the barrier. This effect is described by Krugman's model [P. R. Krugman, Target Zones and exchange rate dynamics, Q. J. Econ. 106, 669 (1991)]. We present direct quantitative empirical evidence that Krugman's theoretical model provides an accurate description of the euro-Swiss franc Target Zone. Motivated by the insights from the economic model, we revise the initial economics-physics analogy and show that, within the context of hindered diffusion, the two systems can be described with the same mathematics after all. Using a recently proposed extended analogy in terms of a colloidal Brownian particle embedded in a fluid of molecules associated with the underlying order book, we derive that, close to the restricting boundary, the dynamics of both systems is described by a stochastic differential equation with a very small constant drift and a linear diffusion coefficient. As a side result, we present a simplified derivation of the linear hydrodynamic diffusion coefficient of a Brownian particle close to a wall.
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quantitative modelling of the eur chf exchange rate during the Target Zone regime of september 2011 to january 2015
2015Co-Authors: Sandro Claudio Lera, Didier SornetteAbstract:Krugman (1991)’s Target Zone model has become the reference of a large part of this literature. Despite its simplicity and elegance, empirical evidence has been lacking. Deriving from Krugman’s model analytical expressions for the conditional volatility and density distribution close to the Target Zone limit, we present clear and direct evidence that the bounded EUR/CHF exchange rate between September 2011 and January 2015 was quantitatively well described by Krugman’s model. Krugman’s Target Zone model holds after all, but apparently only under extreme and sustained pressure that pushes continuously the exchange rate very close to the boundary of the Target Zone.
