The Use of Statistical Tests to Calibrate the Black-Scholes Asset Dynamics Model Applied to Pricing Options with Uncertain Volatility

Abstract EN

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.