The Use of Statistical Tests to Calibrate the Black-Scholes Asset Dynamics Model Applied to Pricing Options with Uncertain Volatility. (21st May 2012)

• Record Type: Journal Article
• Authors: Fatone, Lorella; Mariani, Francesca; Recchioni, Maria Cristina; Zirilli, Francesco
• Other Names: Thavaneswaran A. Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2012(2012)
• Publication Date: 2012-05-21
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2012/931609
• Languages: English
• ISSNs: 1687-952X

Abstract

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.