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Review of Quantitative Finance and Accounting

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01-05-2015 | Original Research

Foreign exchange option pricing in the currency cycle with jump risks

Authors: Chien-Hsiu Lin, Shih-Kuei Lin, An-Chi Wu

Published in: Review of Quantitative Finance and Accounting | Issue 4/2015

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Abstract

This paper examines regime switching behavior and the nature of jumps in foreign exchange rates, as well as their implications in currency option pricing. Considering the characteristics of long swing as well as the short term jumps in exchange rates, we adopt the regime-switching model with jump risks to capture the movement of exchange rates in the developed and emerging countries. Our results show that ‘high-variance’ and ‘low-variance’ describes most of our sample currencies’ trajectories. The regime-switching model with jump risks is proven to capture better exchange rate changes than the regime-switching model (RSM) and the Black–Scholes model (BSM). In addition, our results show that the currency option pricing model when considering regimes of high-variance or low-variance states as well as the jump nature of exchange rates, is better than the traditional BSM and RSM.

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The Brazilian currency crisis occurred in 1999. On Jan. 13, 1999, the Brazilian Central Bank devalued the real by 8 % and on Jan. 15, 1999 the Cardoso government announced that the real would no longer be pegged to the US dollar. Immediately, it lost more than 30 % of its value, and the subsequent devaluation resulted in a further loss of 45 % of the original value.

If regime switching is ignored, that is μ ₁ = μ ₂ = μ and σ ₁ = σ ₂ = σ, the regime-switching model degenerates into the Black–Scholes model, and the parameters, μ and σ, are also estimated by the MLE method.

To save space, we did not report the full model estimation (with mean parameters) here. However, the results would be available upon request.

The detailed derivation is shown in “Appendix”.

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Title: Foreign exchange option pricing in the currency cycle with jump risks
Authors: Chien-Hsiu Lin
Shih-Kuei Lin
An-Chi Wu
Publication date: 01-05-2015
Publisher: Springer US
Published in: Review of Quantitative Finance and Accounting / Issue 4/2015
Print ISSN: 0924-865X
Electronic ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-013-0425-1

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