Foreign Exchange (FX)



This chapter discusses, including detailed mathematical descriptions, various foreign exchange trading strategies. These include FX momentum strategies based on moving averages after high-frequency noise is removed from the time series of foreign exchange rates using the Hodrick–Prescott filter known as the Whittaker–Henderson method in actuarial sciences, FX carry trades based on deviations from the Uncovered Interest Rate Parity also known as the forward discount puzzle, where low interest rate currencies are borrowed and high interest rate currencies are bought, together with their zero-cost variations known as the high-minus-low carry, the dollar carry strategy, which bets on or against the U.S. dollar vs. a basket of foreign currencies and is correlated with the state of the U.S. economy, momentum and carry combinations, and triangular foreign exchange arbitrage, which involves three currency pairs and can be extended to more than three currency pairs.


Moving average High-frequency noise Time series Foreign exchange rate Hodrick–Prescott filter Whittaker–Henderson method FX carry trades Uncovered Interest Rate Parity Forward discount puzzle High-minus-low carry Dollar carry trade Triangular arbitrage Currency pair Multi-currency arbitrage Covered Interest Rate Parity Forward contract Forward discount Forward premium Risk-free arbitrage Foreign currency Sample covariance matrix Bid Ask Interest rate Cross-sectional trade 


  1. Accominotti, O., & Chambers, D. (2014). Out-of-Sample Evidence on the Returns to Currency Trading (Working Paper). Available online:
  2. Ahmerkamp, J. D., & Grant, J. (2013). The Returns to Carry and Momentum Strategies (Working Paper). Available online:
  3. Aiba, Y., & Hatano, N. (2006). A Microscopic Model of Triangular Arbitrage. Physica A: Statistical Mechanics and Its Applications, 371(2), 572–584.CrossRefGoogle Scholar
  4. Aiba, Y., Hatano, N., Takayasu, H., Marumo, K., & Shimizu, T. (2002). Triangular Arbitrage as an Interaction Among Foreign Exchange Rates. Physica A: Statistical Mechanics and Its Applications, 310(3–4), 467–479.CrossRefGoogle Scholar
  5. Aiba, Y., Hatano, N., Takayasu, H., Marumo, K., & Shimizu, T. (2003). Triangular Arbitrage and Negative Auto-Correlation of Foreign Exchange Rates. Physica A: Statistical Mechanics and Its Applications, 324(1–2), 253–257.CrossRefGoogle Scholar
  6. Akram, Q. F., Rime, D., & Sarno, L. (2008). Arbitrage in the Foreign Exchange Market: Turning on the Microscope. Journal of International Economics, 76(2), 237–253.CrossRefGoogle Scholar
  7. Anker, P. (1999). Uncovered Interest Parity, Monetary Policy and Time-Varying Risk Premia. Journal of International Money and Finance, 18(6), 835–851.CrossRefGoogle Scholar
  8. Avdjiev, S., Du, W., Koch, C., & Shin, H. S. (2016). The Dollar, Bank Leverage and the Deviation from Covered Interest Parity (Working Paper). Available online:
  9. Ayuso, J., & Restoy, F. (1996). Interest Rate Parity and Foreign Exchange Risk Premia in the ERM. Journal of International Money and Finance, 15(3), 369–382.CrossRefGoogle Scholar
  10. Baba, N., & Packer, F. (2009). Interpreting Deviations from Covered Interest Parity During the Financial Market Turmoil of 2007–08. Journal of Banking & Finance, 33(11), 1953–1962.CrossRefGoogle Scholar
  11. Bacchetta, P., & van Wincoop, E. (2006). Incomplete Information Processing: A Solution to the Forward Discount Puzzle. American Economic Review, 96(3), 552–576.CrossRefGoogle Scholar
  12. Bacchetta, P., & van Wincoop, E. (2010). Infrequent Portfolio Decisions: A Solution to the Forward Discount Puzzle. American Economic Review, 100(3), 870–904.CrossRefGoogle Scholar
  13. Baillie, R. T., & Osterberg, W. P. (2000). Deviations from Daily Uncovered Interest Rate Parity and the Role of Intervention. Journal of International Financial Markets, Institutions and Money, 10(4), 363–379.CrossRefGoogle Scholar
  14. Bakshi, G., & Panayotov, G. (2013). Predictability of Currency Carry Trades and Asset Pricing Implications. Journal of Financial Economics, 110(1), 139–163.CrossRefGoogle Scholar
  15. Baxter, M., & King, R. (1999). Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time-Series. Review of Economics and Statistics, 81(4), 575–593.CrossRefGoogle Scholar
  16. Bekaert, G., Wei, M., & Xing, Y. (2007). Uncovered Interest Rate Parity and the Term Structure. Journal of International Money and Finance, 26(6), 1038–1069.CrossRefGoogle Scholar
  17. Beyaert, A., García-Solanes, J., & Pérez-Castejón, J. J. (2007). Uncovered Interest Parity with Switching Regimes. Economic Modelling, 24(2), 189–202.CrossRefGoogle Scholar
  18. Bilson, J. F. O. (1981). The “Speculative Efficiency” Hypothesis. Journal of Business, 54(3), 435–451.CrossRefGoogle Scholar
  19. Boulos, N., & Swanson, P. E. (1994). Interest Rate Parity in Times of Turbulence: The Issue Revisited. Journal of Financial and Strategic Decisions, 7(2), 43–52.Google Scholar
  20. Bruder, B., Dao, T.-L., Richard, R.-J., & Roncalli, T. (2013). Trend Filtering Methods for Momentum Strategies (Working Paper). Available online:
  21. Brunnermeier, M. K., Nagel, S., & Pedersen, L. H. (2008). Carry Trades and Currency Crashes. NBER Macroeconomics Annual, 23(1), 313–347.CrossRefGoogle Scholar
  22. Burnside, C., Eichenbaum, M., Kleshchelski, I., & Rebelo, S. (2011). Do Peso Problems Explain the Returns to the Carry Trade? Review of Financial Studies, 24(3), 853–891.CrossRefGoogle Scholar
  23. Burnside, C., Eichenbaum, M., & Rebelo, S. (2007). The Returns to Currency Speculation in Emerging Markets. American Economic Review, 97(2), 333–338.CrossRefGoogle Scholar
  24. Burnside, C., Eichenbaum, M., & Rebelo, S. (2008). Carry Trade: The Gains of Diversification. Journal of the European Economic Association, 6(2/3), 581–588.CrossRefGoogle Scholar
  25. Burnside, C., Eichenbaum, M., & Rebelo, S. (2011). Carry Trade and Momentum in Currency Markets. Annual Review of Financial Economics, 3, 511–535.CrossRefGoogle Scholar
  26. Chaboud, A. P., & Wright, J. H. (2005). Uncovered Interest Parity: It Works, but Not for Long. Journal of International Economics, 66(2), 349–362.CrossRefGoogle Scholar
  27. Chiang, T. C., & Jiang, C. X. (1995). Foreign Exchange Returns over Short and Long Horizons. International Review of Economics & Finance, 4(3), 267–282.CrossRefGoogle Scholar
  28. Choi, M. S. (2011). Momentary Exchange Rate Locked in a Triangular Mechanism of International Currency. Applied Economics, 43(16), 2079–2087.CrossRefGoogle Scholar
  29. Clarida, R. H., Davis, J. M., & Pedersen, N. (2009). Currency Carry Trade Regimes: Beyond the Fama Regression. Journal of International Money and Finance, 28(8), 1375–1389.CrossRefGoogle Scholar
  30. Clinton, K. (1988). Transactions Costs and Covered Interest Arbitrage: Theory and Evidence. Journal of Political Economy, 96(2), 358–370.CrossRefGoogle Scholar
  31. Coffey, N., Hrung, W. B., & Sarkar, A. (2009). Capital Constraints, Counterparty Risk, and Deviations from Covered Interest Rate Parity (Federal Reserve Bank of New York Staff Reports, No. 393). Available online:
  32. Cooper, I., & Priestley, R. (2008). Time-Varying Risk Premiums and the Output Gap. Review of Financial Studies, 22(7), 2801–2833.CrossRefGoogle Scholar
  33. Cosandier, P.-A., & Lang, B. R. (1981). Interest Rate Parity Tests: Switzerland and Some Major Western Countries. Journal of Banking & Finance, 5(2), 187–200.CrossRefGoogle Scholar
  34. Cross, R., & Kozyakin, V. (2015). Fact and Fictions in FX Arbitrage Processes. Journal of Physics: Conference Series, 585, 012015.Google Scholar
  35. Dao, T.-L. (2014). Momentum Strategies with the L1 Filter. Journal of Investment Strategies, 3(4), 57–82.CrossRefGoogle Scholar
  36. Deardorff, A. V. (1979). One-Way Arbitrage and Its Implications for the Foreign Exchange Markets. Journal of Political Economy, 87(2), 351–364.CrossRefGoogle Scholar
  37. Doskov, N., & Swinkels, L. (2015). Empirical Evidence on the Currency Carry Trade, 1900–2012. Journal of International Money and Finance, 51, 370–389.CrossRefGoogle Scholar
  38. Du, W., Tepper, A., & Verdelhan, A. (2018). Deviations from Covered Interest Rate Parity. Journal of Finance (forthcoming). Available online: Scholar
  39. Duffie, D. (2017, May). The Covered Interest Parity Conundrum. Risk. Available online:
  40. Ehlgen, J. (1998). Distortionary Effects of the Optimal Hodrick-Prescott Filter. Economics Letters, 61(3), 345–349.CrossRefGoogle Scholar
  41. Engel, C. (1996). The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence. Journal of Empirical Finance, 3(2), 123–192.CrossRefGoogle Scholar
  42. Fama, E. F. (1984). Forward and Spot Exchange Rates. Journal of Monetary Economics, 14(3), 319–338.CrossRefGoogle Scholar
  43. Fenn, D. J., Howison, S. D., Mcdonald, M., Williams, S., & Johnson, N. F. (2009). The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market. International Journal of Theoretical and Applied Finance, 12(8), 1105–1123.CrossRefGoogle Scholar
  44. Frachot, A. (1996). A Reexamination of the Uncovered Interest Rate Parity Hypothesis. Journal of International Money and Finance, 15(3), 419–437.CrossRefGoogle Scholar
  45. Frenkel, J. A., & Levich, R. M. (1975). Covered Interest Arbitrage: Unexploited Profits? Journal of Political Economy, 83(2), 325–338.CrossRefGoogle Scholar
  46. Frenkel, J. A., & Levich, R. M. (1981). Covered Interest Arbitrage in the 1970’s. Economics Letters, 8(3), 267–274.CrossRefGoogle Scholar
  47. Froot, K. A., & Thaler, R. H. (1990). Anomalies: Foreign Exchange. Journal of Economic Perspectives, 4(3), 179–192.CrossRefGoogle Scholar
  48. Goldstein, H. N. (1964). The Implications of Triangular Arbitrage for Forward Exchange Policy. Journal of Finance, 19(3), 544–551.Google Scholar
  49. Gradojevic, N., Gençay, R., & Erdemlioglu, D. (2017). Robust Prediction of Triangular Currency Arbitrage with Liquidity and Realized Risk Measures: A New Wavelet-Based Ultra-High-Frequency Analysis (Working Paper). Available online:
  50. Grobys, K., Heinonen, J.-P., & Kolari, J. W. (2016). Is Currency Momentum a Hedge for Global Economic Risk? (Working Paper). Available online:
  51. Hansen, L. P., & Hodrick, R. J. (1980). Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis. Journal of Political Economy, 88(5), 829–853.CrossRefGoogle Scholar
  52. Harris, R. D. F., & Yilmaz, F. (2009). A Momentum Trading Strategy Based on the Low Frequency Component of the Exchange Rate. Journal of Banking & Finance, 33(9), 1575–1585.CrossRefGoogle Scholar
  53. Harvey, J. T. (2015). Deviations from Uncovered Interest Rate Parity: A Post Keynesian Explanation. Journal of Post Keynesian Economics, 27(1), 19–35.Google Scholar
  54. Harvey, A., & Trimbur, T. (2008). Trend Estimation and the Hodrick-Prescott Filter. Journal of the Japan Statistical Society, 38(1), 41–49.CrossRefGoogle Scholar
  55. Hau, H. (2014). The Exchange Rate Effect of Multi-currency Risk Arbitrage. Journal of International Money and Finance, 47, 304–331.CrossRefGoogle Scholar
  56. Henderson, R. (1924). A New Method of Graduation. Transactions of the Actuarial Society of America, 25, 29–40.Google Scholar
  57. Henderson, R. (1925). Further Remarks on Graduation. Transactions of the Actuarial Society of America, 26, 52–57.Google Scholar
  58. Henderson, R. (1938). Mathematical Theory of Graduation. New York, NY: Actuarial Society of America.Google Scholar
  59. Hodrick, R. J. (1987). The Empirical Evidence on the Efficiency of Forward and Futures Foreign Exchange Markets. New York, NY: Harwood Academic.Google Scholar
  60. Hodrick, R. J., & Prescott, E. C. (1997). Postwar U.S. Business Cycles: An Empirical Investigation. Journal of Money, Credit and Banking, 29(1), 1–16.CrossRefGoogle Scholar
  61. Ilut, C. (2012). Ambiguity Aversion: Implications for the Uncovered Interest Rate Parity Puzzle. American Economic Journal: Macroeconomics, 4(3), 33–65.Google Scholar
  62. Ito, T., Yamada, K., Takayasu, M., & Takayasu, H. (2012). Free Lunch! Arbitrage Opportunities in the Foreign Exchange Markets (Working Paper). Available online:
  63. Joseph, A. (1952). The Whittaker-Henderson Method of Graduation. Journal of the Institute of Actuaries, 78(1), 99–114.CrossRefGoogle Scholar
  64. Joslin, S., & Konchitchki, Y. (2018). Interest Rate Volatility, the Yield Curve, and the Macroeconomy. Journal of Financial Economics, 128(2), 344–362.CrossRefGoogle Scholar
  65. Joslin, S., Priebsch, M., & Singleton, K. J. (2014). Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks. Journal of Finance, 69(3), 1197–1233.CrossRefGoogle Scholar
  66. Jurek, J. W. (2014). Crash-Neutral Currency Carry Trades. Journal of Financial Economics, 113(3), 325–347.CrossRefGoogle Scholar
  67. Lahmiri, S. (2014). Wavelet Low- and High-Frequency Components as Features for Predicting Stock Prices with Backpropagation Neural Networks. Journal of King Saud University—Computer and Information Sciences, 26(2), 218–227.CrossRefGoogle Scholar
  68. Lewis, K. (1995). Puzzles in International Financial Markets. In G. M. Grossman & K. Rogoff (Eds.), Handbook of International Economics (Vol. 3, Chapter 37). Amsterdam, The Netherlands: North-Holland.Google Scholar
  69. Liao, G. Y. (2016). Credit Migration and Covered Interest Rate Parity (Working Paper). Available online:
  70. Lustig, H., Roussanov, N., & Verdelhan, A. (2011). Common Risk Factors in Currency Markets. Review of Financial Studies, 24(11), 3731–3777.CrossRefGoogle Scholar
  71. Lustig, H., Roussanov, N., & Verdelhan, A. (2014). Countercyclical Currency Risk Premia. Journal of Financial Economics, 111(3), 527–553.CrossRefGoogle Scholar
  72. Lustig, H., & Verdelhan, A. (2007). The Cross-Section of Foreign Currency Risk Premia and US Consumption Growth Risk. American Economic Review, 97(1), 89–117.CrossRefGoogle Scholar
  73. Mancini-Griffoli, T., & Ranaldo, A. (2011). Limits to Arbitrage During the Crisis: Funding Liquidity Constraints and Covered Interest Parity (Working Paper). Available online:
  74. Mark, N. C., & Wu, Y. (2001). Rethinking Deviations From Uncovered Interest Parity: The Role of Covariance Risk and Noise. Economic Journal, 108(451), 1686–1706.CrossRefGoogle Scholar
  75. Mcelroy, T. (2008). Exact Formulas for the Hodrick-Prescott Filter. Econometrics Journal, 11(1), 208–217.CrossRefGoogle Scholar
  76. Menkhoff, L., Sarno, L., Schmeling, M., & Schrimpf, A. (2012). Currency Momentum Strategies. Journal of Financial Economics, 106(3), 660–684.CrossRefGoogle Scholar
  77. Moosa, I. A. (2001). Triangular Arbitrage in the Spot and Forward Foreign Exchange Markets. Quantitative Finance, 1(4), 387–390.CrossRefGoogle Scholar
  78. Moosa, I. A. (2003). Two-Currency, Three-Currency and Multi-Currency Arbitrage. In International Financial Operations: Arbitrage, Hedging, Speculation, Financing and Investment. Finance and Capital Markets Series (Chapter 1, pp. 1–18). London, UK: Palgrave Macmillan.CrossRefGoogle Scholar
  79. Morisawa, Y. (2009). Toward a Geometric Formulation of Triangular Arbitrage: An Introduction to Gauge Theory of Arbitrage. Progress of Theoretical Physics Supplement, 179, 209–215.CrossRefGoogle Scholar
  80. Mwangi, C. I., & Duncan, M. O. (2012). An Investigation into the Existence of Exchange Rate Arbitrage in the Mombasa Spot Market. International Journal of Humanities and Social Science, 2(21), 182–196.Google Scholar
  81. Okunev, J., & White, D. (2003). Do Momentum-Based Strategies Still Work in Foreign Currency Markets? Journal of Financial and Quantitative Analysis, 38(2), 425–447.CrossRefGoogle Scholar
  82. Olmo, J., & Pilbeam, K. (2009). The Profitability of Carry Trades. Annals of Finance, 5(2), 231–241.CrossRefGoogle Scholar
  83. Olszweski, F., & Zhou, G. (2013). Strategy Diversification: Combining Momentum and Carry Strategies Within a Foreign Exchange Portfolio. Journal of Derivatives & Hedge Funds, 19(4), 311–320.CrossRefGoogle Scholar
  84. Osu, B. O. (2010). Currency Cross Rate and Triangular Arbitrage in Nigerian Exchange Market. International Journal of Trade, Economics and Finance, 1(4), 345–348.CrossRefGoogle Scholar
  85. Popper, H. (1993). Long-Term Covered Interest Parity: Evidence from Currency Swaps. Journal of International Money and Finance, 12(4), 439–448.CrossRefGoogle Scholar
  86. Ready, R., Roussanov, N., & Ward, C. (2017). Commodity Trade and the Carry Trade: A Tale of Two Countries. Journal of Finance, 72(6), 2629–2684.CrossRefGoogle Scholar
  87. Rhee, S. G., & Chang, R. P. (1992). Intra-Day Arbitrage Opportunities in Foreign Exchange and Eurocurrency Markets. Journal of Finance, 47(1), 363–379.CrossRefGoogle Scholar
  88. Rime, D., Schrimpf, A., & Syrstad, O. (2017). Segmented Money Markets and Covered Interest Parity Arbitrage (Working Paper). Available online:
  89. Roll, R., & Yan, S. (2008). An Explanation of the Forward Premium ‘Puzzle’. European Financial Management, 6(2), 121–148.CrossRefGoogle Scholar
  90. Serban, A. F. (2010). Combining Mean Reversion and Momentum Trading Strategies in Foreign Exchange Markets. Journal of Banking & Finance, 34(11), 2720–2727.CrossRefGoogle Scholar
  91. Stambaugh, R. F. (1988). The Information in Forward Rates: Implications for Models of the Term Structure. Journal of Financial Economics, 21(1), 41–70.CrossRefGoogle Scholar
  92. Tille, C., Stoffels, N., & Gorbachev, O. (2001). To What Extent Does Productivity Drive the Dollar? Current Issues in Economics and Finance, 7(8), 1–6.Google Scholar
  93. Weinert, H. L. (2007). Efficient Computation for Whittaker-Henderson Smoothing. Computational Statistics & Data Analysis, 52(2), 959–974.CrossRefGoogle Scholar
  94. Whittaker, E. T. (1923). On a New Method of Graduations. Proceedings of the Edinburgh Mathematical Society, 41, 63–75.Google Scholar
  95. Whittaker, E. T. (1924). On the Theory of Graduation. Proceedings of the Royal Society of Edinburgh, 44, 77–83.CrossRefGoogle Scholar

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Quantigic Solutions LLCStamfordUSA
  2. 2.Universidad del CEMABuenos AiresArgentina

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