A Jump‐diffusion Model for Exchange Rates in a Target Zone

We propose a simple jump‐diffusion model for an exchange rate target zone. The model captures most stylized facts from the existing target zone models while remaining analytically tractable. The model is based on a modified two‐limit version of the COX, INGERSOLL and ROSS (1985) model. In the model the exchange rate is kept within the band because the variance decreases as the exchange rate approaches the upper or lower limits of the band. We also consider an extension of the model with parity adjustments, which are modeled as Poisson jumps. Estimation of the model is by GMM based on conditional moments. We derive prices of currency options in our model, assuming that realignment jump risk is idiosyncratic. Throughout, we apply the theory to EMS exchange rate data. We show that, after the EMS crisis of 1993, currencies remain in an implicit target zone which is narrower than the officially announced target zones.

[1]  C. Ball,et al.  Target zone modelling and estimation for European Monetary System exchange rates , 1994 .

[2]  P. Protter.  Stochastic integration and differential equations , 1990 .

[3]  G. Bertola,et al.  Stochastic Devaluation Risk and the Empirical Fit of Target Zone Models , 1991 .

[4]  Kenneth Rogoff,et al.  The Mirage of Fixed Exchange Rates , 1995 .

[5]  Lars E. O. Svensson.  The Foreign Exchange Risk Premium in a Target Zone with Devaluation Risk , 1990 .

[6]  D. Duffie,et al.  A Yield-factor Model of Interest Rates , 1996 .

[7]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[8]  M. Garman.,et al.  Foreign currency option values , 1983 .

[9]  Wolfgang Wefelmeyer,et al.  Quasi-likelihood models and optimal inference , 1996 .

[10]  Lars E.O. Svensson,et al.  An Interpretation of Recent Research on Exchange Rate Target Zones , 1992 .

[11]  P. Söderlind,et al.  Target Zone Models and the Intervention Policy: The Swedish Case , 1994 .

[12]  V. P. Godambe.  The foundations of finite sample estimation in stochastic processes , 1985 .

[13]  Bernard Dumas,et al.  Realignment Risk and Currency Option Pricing in Target Zones , 1993 .

[14]  Siegel's paradox and the pricing of currency options , 1995 .

[15]  Robert P. Flood,et al.  An Empirical Exploration of Exchange Rate Target-Zones , 1990, SSRN Electronic Journal.

[16]  F. Diebold,et al.  The Distribution of Exchange Rate Volatility , 1999 .

[17]  J. Grabbe.  The pricing of call and put options on foreign exchange , 1983 .

[18]  É. Renault.  Econometric Models of Option Pricing Errors , 1996 .

[19]  C. Gouriéroux,et al.  PSEUDO MAXIMUM LIKELIHOOD METHODS: THEORY , 1984 .

[20]  P. H. Kevin Chang,et al.  Arbitrage-Based Tests of Target-Zone Credibility: Evidence from ERM Cross-Rate Options , 1998 .

[21]  Lars E. O. Svensson.  Assessing Target Zone Credibility: Mean Reversion and Devaluation Expectations in the Erm 1979-1992 , 1991 .

[22]  J. Harrison,et al.  Martingales and stochastic integrals in the theory of continuous trading , 1981 .

[23]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[24]  B. Werker,et al.  On the Pricing of Options in Incomplete Markets , 1996 .

[25]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[26]  Philip A. Stork,et al.  AN EMS TARGET ZONE MODEL IN DISCRETE TIME , 1998 .

[27]  Giuseppe Bertola,et al.  Target Zones and Realignments , 1990 .

[28]  Stephen Gray,et al.  Target Zones and Exchange Rates: An Empirical Investigation , 1996 .

[29]  P. Krugman,et al.  Target Zones and Exchange Rate Dynamics , 1991 .

[30]  Lars E. O. Svensson,et al.  Assessing Target Zone Credibility: Mean Reversion and Devaluation Expectations in the EMS , 1991, SSRN Electronic Journal.

[31]  W. Newey,et al.  Semiparametric Efficiency Bounds , 1990 .

[32]  Franz C. Palm,et al.  The message in weekly exchange rates in the European Monetary System: mean reversion , 1993 .