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A multivariate stochastic volatility model with applications in the foreign exchange market

Author

Listed:
  • Marcos Escobar

    (Western University)

  • Christoph Gschnaidtner

    (Technische Universität München)

Abstract

The main objective of this paper is to study the behavior of a daily calibration of a multivariate stochastic volatility model, namely the principal component stochastic volatility (PCSV) model, to market data of plain vanilla options on foreign exchange rates. To this end, a general setting describing a foreign exchange market is introduced. Two adequate models—PCSV and a simpler multivariate Heston model—are adjusted to suit the foreign exchange setting. For both models, characteristic functions are found which allow for an almost instantaneous calculation of option prices using Fourier techniques. After presenting the general calibration procedure, both the multivariate Heston and the PCSV models are calibrated to a time series of option data on three exchange rates—USD-SEK, EUR-SEK, and EUR-USD—spanning more than 11 years. Finally, the benefits of the PCSV model which we find to be superior to the multivariate extension of the Heston model in replicating the dynamics of these options are highlighted.

Suggested Citation

  • Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    • Handle: RePEc:kap:revdev:v:21:y:2018:i:1:d:10.1007_s11147-017-9132-8
    DOI: 10.1007/s11147-017-9132-8
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    2. Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2020. "Affine multivariate GARCH models," Journal of Banking & Finance, Elsevier, vol. 118(C).
    3. Ospina-Forero, Luis & Granados, Oscar M., 2023. "A network analysis of the structure and dynamics of FX derivatives markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    4. Shiraya, Kenichiro & Yamakami, Tomohisa, 2024. "Constructing copulas using corrected Hermite polynomial expansion for estimating cross foreign exchange volatility," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1195-1214.
    5. Henao-Londono, Juan C. & Guhr, Thomas, 2022. "Foreign exchange markets: Price response and spread impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    6. Wang, Hang & Hu, Zhijun, 2020. "Optimal consumption and portfolio decision with stochastic covariance in incomplete markets," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

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    More about this item

    Keywords

    Stochastic volatility models; Multivariate models; PCSV model; FX options; Calibration; Triangular relation;
    All these keywords.

    JEL classification:

    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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