Bounds and Prices of Currency Cross-Rate Options

32 Pages Posted: 18 Feb 2006 Last revised: 27 Feb 2019

See all articles by Chung San-Lin

Chung San-Lin

National Taiwan University

Yaw-Huei Wang

National Taiwan University; UNSW

Date Written: May1 2008


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 vari-ables or on the selection of the copula function; (2) they are portfolios of the dollar-rate op-tions 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 op-tions 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 ex-plaining 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.

Keywords: Option pricing, option bounds, exchange rates, cross-rate, correlation, copulas

JEL Classification: F3, F4, G1

Suggested Citation

San-Lin, Chung and Wang, Yaw-Huei, Bounds and Prices of Currency Cross-Rate Options (May1 2008). Journal of Banking and Finance, Vol. 32, No. 5, 2008. Available at SSRN: or

Chung San-Lin

National Taiwan University ( email )

21 Hsiu Chow Rd
Taipei, 10020

Yaw-Huei Wang (Contact Author)

National Taiwan University ( email )

Department and Graduate Institute of Finance
College of Management
Taipei, 106
+886233661092 (Phone)
+886283695581 (Fax)

UNSW ( email )

Sydney, NSW 2052

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