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On exact pricing of FX options in multivariate time-changed Lévy models

Author

Listed:
  • Roman V. Ivanov

    (Trapeznikov Institute of Control Sciences of RAS)

  • Katsunori Ano

    (Shibaura Institute of Technology)

Abstract

In this paper we discuss foreign-exchange option pricing in conditionally Gaussian models, namely in the variance-gamma and in the normal-inverse Gaussian models. It happens that in the both models closed-form pricing is attainable. The used method developes the one of the work by Madan et al. (Eur Finance Rev 2:79–105, 1998) where the price of the European call is primarily derived. The obtained formulas are based on values of the Gauss and the Appell hypergeometric functions.

Suggested Citation

  • Roman V. Ivanov & Katsunori Ano, 2016. "On exact pricing of FX options in multivariate time-changed Lévy models," Review of Derivatives Research, Springer, vol. 19(3), pages 201-216, October.
    • Handle: RePEc:kap:revdev:v:19:y:2016:i:3:d:10.1007_s11147-016-9120-4
    DOI: 10.1007/s11147-016-9120-4
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    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    3. Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
    4. Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Papers 0809.0301, arXiv.org, revised Nov 2009.
    5. Peter Carr & Roger Lee & Liuren Wu, 2012. "Variance swaps on time-changed Lévy processes," Finance and Stochastics, Springer, vol. 16(2), pages 335-355, April.
    6. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    7. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    8. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    9. Elton A. Daal & Dilip B. Madan, 2005. "An Empirical Examination of the Variance-Gamma Model for Foreign Currency Options," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2121-2152, November.
    10. Ariel Almendral & Cornelis W. Oosterlee, 2007. "On American Options Under the Variance Gamma Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 131-152.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Roman V. Ivanov, 2018. "A Credit-Risk Valuation under the Variance-Gamma Asset Return," Risks, MDPI, vol. 6(2), pages 1-25, May.
    2. Ivanov Roman V., 2018. "On risk measuring in the variance-gamma model," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 23-33, January.
    3. Roman V. Ivanov, 2024. "On Properties of the Hyperbolic Distribution," Mathematics, MDPI, vol. 12(18), pages 1-20, September.
    4. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.

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    More about this item

    Keywords

    Time-changed Lévy process; Variance-gamma process; Normal-inverse Gaussian process; Foreign-exchange option; Pricing; Hypergeometric function;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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