Jointly modeling the prices of American depository receipts, the local stock and the US dollar

Dilip B. Madan

Abstract

ABSTRACT

Options on an American depository receipt reflect the correlations between the local stock and the foreign currency price of the US dollar, while local option surfaces calibrate the marginal laws. After developing a general procedure for pricing all three sets of options from a model for the joint law on the local stock and the price of the US dollar quoted locally, we investigate the convergence of market to model. A rich joint law with thirteen parameters that builds on the work of Bhattacharyya is employed. It is observed that the Bhattacharyya model has squared correlations that rise to unity in the tails: this is a desirable feature for financial data. Such a convergence of market to model appears to have been present for Santander over the period October 2010 to March 2012.