A multivariate stochastic volatility model with applications in the foreign exchange market

A multivariate stochastic volatility model with applications in the foreign exchange market The main objective of this paper is to study the behavior of a daily calibration of a multivariate stochastic volatility model, namely the principal component stochastic volatility (PCSV) model, to market data of plain vanilla options on foreign exchange rates. To this end, a general setting describing a foreign exchange market is introduced. Two adequate models—PCSV and a simpler multivariate Heston model—are adjusted to suit the foreign exchange setting. For both models, characteristic functions are found which allow for an almost instantaneous calculation of option prices using Fourier techniques. After presenting the general calibration procedure, both the multivariate Heston and the PCSV models are calibrated to a time series of option data on three exchange rates—USD-SEK, EUR-SEK, and EUR-USD—spanning more than 11 years. Finally, the benefits of the PCSV model which we find to be superior to the multivariate extension of the Heston model in replicating the dynamics of these options are highlighted. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Review of Derivatives Research Springer Journals

A multivariate stochastic volatility model with applications in the foreign exchange market

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Finance; Investments and Securities
ISSN
1380-6645
eISSN
1573-7144
D.O.I.
10.1007/s11147-017-9132-8
Publisher site
See Article on Publisher Site

Abstract

The main objective of this paper is to study the behavior of a daily calibration of a multivariate stochastic volatility model, namely the principal component stochastic volatility (PCSV) model, to market data of plain vanilla options on foreign exchange rates. To this end, a general setting describing a foreign exchange market is introduced. Two adequate models—PCSV and a simpler multivariate Heston model—are adjusted to suit the foreign exchange setting. For both models, characteristic functions are found which allow for an almost instantaneous calculation of option prices using Fourier techniques. After presenting the general calibration procedure, both the multivariate Heston and the PCSV models are calibrated to a time series of option data on three exchange rates—USD-SEK, EUR-SEK, and EUR-USD—spanning more than 11 years. Finally, the benefits of the PCSV model which we find to be superior to the multivariate extension of the Heston model in replicating the dynamics of these options are highlighted.

Journal

Review of Derivatives ResearchSpringer Journals

Published: Mar 20, 2017

References

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