The Use of Statistical Tests to Calibrate the Black-Scholes Asset Dynamics Model Applied to Pricing Options with Uncertain Volatility
A new method for calibrating the Black-Scholes asset price dynamics model is proposed. The data used to test the calibration problem included observations of asset prices over a finite set of (known) equispaced discrete time values. Statistical tests were used to estimate the statistical significanc...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2012/931609 |
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| author | Lorella Fatone Francesca Mariani Maria Cristina Recchioni Francesco Zirilli |
| author_facet | Lorella Fatone Francesca Mariani Maria Cristina Recchioni Francesco Zirilli |
| author_sort | Lorella Fatone |
| collection | DOAJ |
| description | A new method for calibrating the Black-Scholes asset price dynamics
model is proposed. The data used to test the calibration problem included observations of asset prices over a finite set of (known) equispaced discrete time values. Statistical tests were used to estimate the statistical significance of the two parameters of the Black-Scholes model: the volatility and the drift. The effects of these estimates on the option pricing problem were investigated. In particular, the pricing of an option with uncertain volatility in the Black-Scholes framework was revisited, and a statistical significance was associated with the price intervals determined using the Black-Scholes-Barenblatt equations. Numerical experiments involving synthetic and real data were presented. The real data considered were the daily closing values of the S&P500 index and the associated European call and put option prices in the year 2005. The method proposed here for calibrating the Black-Scholes dynamics model could be extended to other science and engineering models that may be expressed in terms of stochastic dynamical systems. |
| format | Article |
| id | doaj-art-045837f1253e4096a754b7ed47f8d860 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-045837f1253e4096a754b7ed47f8d8602025-02-03T01:23:27ZengWileyJournal of Probability and Statistics1687-952X1687-95382012-01-01201210.1155/2012/931609931609The Use of Statistical Tests to Calibrate the Black-Scholes Asset Dynamics Model Applied to Pricing Options with Uncertain VolatilityLorella Fatone0Francesca Mariani1Maria Cristina Recchioni2Francesco Zirilli3Dipartimento di Matematica e Informatica, Università di Camerino, Via Madonna delle Carceri 9, 62032 Camerino, ItalyCERI-Centro di Ricerca “Previsione, Prevenzione e Controllo dei Rischi Geologici”, Università di Roma “La Sapienza”, Palazzo Doria Pamphilj, Piazza Umberto Pilozzi 9, Valmontone 00038 Roma, ItalyDipartimento di Scienze Sociali “D. Serrani”, Università Politecnica delle Marche, Piazza Martelli 8, 60121 Ancona, ItalyDipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, ItalyA new method for calibrating the Black-Scholes asset price dynamics model is proposed. The data used to test the calibration problem included observations of asset prices over a finite set of (known) equispaced discrete time values. Statistical tests were used to estimate the statistical significance of the two parameters of the Black-Scholes model: the volatility and the drift. The effects of these estimates on the option pricing problem were investigated. In particular, the pricing of an option with uncertain volatility in the Black-Scholes framework was revisited, and a statistical significance was associated with the price intervals determined using the Black-Scholes-Barenblatt equations. Numerical experiments involving synthetic and real data were presented. The real data considered were the daily closing values of the S&P500 index and the associated European call and put option prices in the year 2005. The method proposed here for calibrating the Black-Scholes dynamics model could be extended to other science and engineering models that may be expressed in terms of stochastic dynamical systems.http://dx.doi.org/10.1155/2012/931609 |
| spellingShingle | Lorella Fatone Francesca Mariani Maria Cristina Recchioni Francesco Zirilli The Use of Statistical Tests to Calibrate the Black-Scholes Asset Dynamics Model Applied to Pricing Options with Uncertain Volatility Journal of Probability and Statistics |
| title | The Use of Statistical Tests to Calibrate the Black-Scholes Asset
Dynamics Model Applied to Pricing Options with Uncertain Volatility |
| title_full | The Use of Statistical Tests to Calibrate the Black-Scholes Asset
Dynamics Model Applied to Pricing Options with Uncertain Volatility |
| title_fullStr | The Use of Statistical Tests to Calibrate the Black-Scholes Asset
Dynamics Model Applied to Pricing Options with Uncertain Volatility |
| title_full_unstemmed | The Use of Statistical Tests to Calibrate the Black-Scholes Asset
Dynamics Model Applied to Pricing Options with Uncertain Volatility |
| title_short | The Use of Statistical Tests to Calibrate the Black-Scholes Asset
Dynamics Model Applied to Pricing Options with Uncertain Volatility |
| title_sort | use of statistical tests to calibrate the black scholes asset dynamics model applied to pricing options with uncertain volatility |
| url | http://dx.doi.org/10.1155/2012/931609 |
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