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. ©; 2012 Lorella Fatone et al.
The use of statistical tests to calibrate the Black-Scholes asset dynamics model applied to pricing options with uncertain volatility / Lorella, Fatone; Francesca, Mariani; Maria Cristina, Recchioni; Zirilli, Francesco. - In: JOURNAL OF PROBABILITY AND STATISTICS. - ISSN 1687-952X. - 2012:(2012), pp. 1-20. [10.1155/2012/931609]
The use of statistical tests to calibrate the Black-Scholes asset dynamics model applied to pricing options with uncertain volatility
ZIRILLI, Francesco
2012
Abstract
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. ©; 2012 Lorella Fatone et al.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.