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 and Francesco Zirilli

Journal of Probability and Statistics, 2012, vol. 2012, 1-20

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:931609

DOI: 10.1155/2012/931609

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