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The Geometry of the World of Currency Volatilities

Author

Listed:
  • Gueorgui S. Konstantinov

    (LBBW Asset and Wealth Management)

  • Frank J. Fabozzi

    (EDHEC Business School)

Abstract

Using empirical data and the properties they reveal, we develop a factor that captures changes of both currency implied correlation and volatilities. For this purpose, we apply the Guldin–Pappus theorem in Euclidean space for rotating triangles to construct a specific factor, which we define as gravity radius. This approach allows the construction of a portfolio index aggregating all currency pairwise trades. Our factor, which is a weighted sum of all gravity radius factors in a portfolio, exhibits characteristics that are similar to the well-known turbulence metric defined in the literature and has moderate correlation to the CBOE VIX index. This factor therefore can serve as a risk indicator. We argue that the changes in volatilities impact the gravity radius factor value considerably more than changes in correlations. Portfolio managers and risk managers can use the new metric to identify correlation and volatility changes that dynamically react to new information.

Suggested Citation

  • Gueorgui S. Konstantinov & Frank J. Fabozzi, 2022. "The Geometry of the World of Currency Volatilities," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 125-145, June.
    • Handle: RePEc:kap:compec:v:60:y:2022:i:1:d:10.1007_s10614-021-10140-7
    DOI: 10.1007/s10614-021-10140-7
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    References listed on IDEAS

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    1. Lukas Menkhoff & Lucio Sarno & Maik Schmeling & Andreas Schrimpf, 2012. "Carry Trades and Global Foreign Exchange Volatility," Journal of Finance, American Finance Association, vol. 67(2), pages 681-718, April.
    2. Asness, Cliff & Frazzini, Andrea & Gormsen, Niels Joachim & Pedersen, Lasse Heje, 2020. "Betting against correlation: Testing theories of the low-risk effect," Journal of Financial Economics, Elsevier, vol. 135(3), pages 629-652.
    3. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    4. Neely, Christopher J. & Weller, Paul A., 2013. "Lessons from the evolution of foreign exchange trading strategies," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3783-3798.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Racheva-Iotova, Boryana & Fabozzi, Frank J., 2011. "Fat-tailed models for risk estimation," Working Paper Series in Economics 30, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    7. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    8. Chen, Shu-Hsiu, 2017. "Carry trade strategies based on option-implied information: Evidence from a cross-section of funding currencies," Journal of International Money and Finance, Elsevier, vol. 78(C), pages 1-20.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Currency pairs trading; Currency management; Currency risk; Volatility; Correlations; Geometry; Risk factor;
    All these keywords.

    JEL classification:

    • F31 - International Economics - - International Finance - - - Foreign Exchange

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