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Bounds and prices of currency cross-rate options

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  • Chung, San-Lin
  • Wang, Yaw-Huei

Abstract

This paper derives the pricing bounds of a currency cross-rate option using the option prices of two related dollar rates via a copula theory and presents the analytical properties of the bounds under the Gaussian framework. Our option pricing bounds are useful, because (1) they are general in the sense that they do not rely on the distribution assumptions of the state variables or on the selection of the copula function; (2) they are portfolios of the dollar-rate options and hence are potential hedging instruments for cross-rate options; and (3) they can be applied to generate bounds on deltas. The empirical tests suggest that there are persistent and stable relationships between the market prices and the estimated bounds of the cross-rate options and that our option pricing bounds (obtained from the market prices of options on two dollar rates) and the historical correlation of two dollar rates are highly informative for explaining the prices of the cross-rate options. Moreover, the empirical results are consistent with the predictions of the analytical properties under the Gaussian framework and are robust in various aspects.

Suggested Citation

  • Chung, San-Lin & Wang, Yaw-Huei, 2008. "Bounds and prices of currency cross-rate options," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 631-642, May.
    • Handle: RePEc:eee:jbfina:v:32:y:2008:i:5:p:631-642
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    Cited by:

    1. Rombouts, Jeroen V.K. & Stentoft, Lars, 2011. "Multivariate option pricing with time varying volatility and correlations," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2267-2281, September.
    2. 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.
    3. Akihiko Takahashi & Yukihiro Tsuzuki, 2016. "Rebalancing Static Super-Replications (Forthcoming in International Journal of Financial Engineering)," CARF F-Series CARF-F-384, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.
    5. Câmara, António, 2009. "Two counters of jumps," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 456-463, March.
    6. Masaaki Fujii & Yukihiro Tsuzuki, 2011. "Rebalancing Static Super-Replications," CIRJE F-Series CIRJE-F-796, CIRJE, Faculty of Economics, University of Tokyo.
    7. Akihiko Takahashi & Yukihiro Tsuzuki, 2017. "Rebalancing static super-replications," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-23, March.
    8. F. Antonelli & A. Ramponi & S. Scarlatti, 2010. "Exchange option pricing under stochastic volatility: a correlation expansion," Review of Derivatives Research, Springer, vol. 13(1), pages 45-73, April.
    9. Yukihiro Tsuzuki, 2012. "On the Optimal Super- and Sub-Hedging Strategies," CARF F-Series CARF-F-300, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2013.
    10. Akihiko Takahashi & Yukihiro Tsuzuki, 2016. "Rebalancing Static Super-Replications," CIRJE F-Series CIRJE-F-1008, CIRJE, Faculty of Economics, University of Tokyo.

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