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Estimation and arbitrage opportunities for exchange rate baskets

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  • Mercurio, Danilo
  • Torricelli, Costanza

Abstract

This paper analyzes short term portfolio investment opportunities in a capital market where a currency is defined as a currency basket, i.e. a linear combination of foreign currencies. In line with the mean-variance hedging approach, we determine a self-financed optimal investment strategy which minimizes an expected quadratic cost function. In order to implement such a strategy an estimate of the basket weights is required. To this end we suggest an adaptive nonparametric procedure, which, if compared with standard procedures, provides very satisfactory results both on simulated and real data. We apply the optimal investment strategy to the case of the Thai Bath basket. The basket weights are computed with the adaptive estimator. We also implement a recursive estimator, a rolling estimator and the Ka1man filter which serve as benchmark models. The different estimators are compared with profit based criteria.

Suggested Citation

  • Mercurio, Danilo & Torricelli, Costanza, 2001. "Estimation and arbitrage opportunities for exchange rate baskets," SFB 373 Discussion Papers 2001,37, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200137
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    References listed on IDEAS

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    1. Liptser, R. & Spokoiny, Vladimir G., 1999. "Deviation probability bound for martingales with applications to statistical estimation," SFB 373 Discussion Papers 1999,85, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Danilo Mercurio & Costanza Torricelli, 2003. "Estimation and arbitrage opportunities for exchange rate baskets," Applied Economics, Taylor & Francis Journals, vol. 35(15), pages 1689-1698.
    3. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
    4. Christoffersen, Peter F & Giorgianni, Lorenzo, 2000. "Interest-Rate Arbitrage in Currency Baskets: Forecasting Weights and Measuring Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 242-253, April.
    5. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    6. Cooley, Thomas F & Prescott, Edward C, 1973. "An Adaptive Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 364-371, June.
    7. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    8. Canarellsal, Giorgio & Pollard, Stephen K. & Lai, Kon S., 1990. "Cointegration between exchange rates and relative prices: another view," European Economic Review, Elsevier, vol. 34(7), pages 1303-1322, November.
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    Cited by:

    1. Hsin-Hung Chen & Hsien-Tang Tsai & Dennis Lin, 2011. "Optimal mean-variance portfolio selection using Cauchy-Schwarz maximization," Applied Economics, Taylor & Francis Journals, vol. 43(21), pages 2795-2801.
    2. Danilo Mercurio & Costanza Torricelli, 2003. "Estimation and arbitrage opportunities for exchange rate baskets," Applied Economics, Taylor & Francis Journals, vol. 35(15), pages 1689-1698.

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    More about this item

    Keywords

    exchange rates; mean-variance hedging; adaptive estimation;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • F37 - International Economics - - International Finance - - - International Finance Forecasting and Simulation: Models and Applications

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