A multivariate stochastic volatility model with applications in the foreign exchange market
| Autor: | Christoph Gschnaidtner, Marcos Escobar |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Multivariate statistics
050208 finance Stochastic volatility Series (mathematics) Calibration (statistics) 05 social sciences Economics Econometrics and Finance (miscellaneous) 01 natural sciences Heston model 010104 statistics & probability 0502 economics and business Principal component analysis Market data Econometrics Economics 0101 mathematics Foreign exchange market Finance |
| Zdroj: | Review of Derivatives Research. 21:1-43 |
| ISSN: | 1573-7144 1380-6645 |
| DOI: | 10.1007/s11147-017-9132-8 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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