An implementation of Bouchouev's method for a short time calibration of option pricing models

Abstract

We analyse the Bouchouev integral equation for the deterministic volatility function in the Black-Scholes option pricing model. We are able to reduce Bouchouev's original triple integral equation to a single integral equation and describe its numerical solution. Moreover we show empirically that the most complex term in the equation may often be safely ignored for the purposes of numerical calculations. We present a selection of numerical examples indicating the range of time values for which we would expect the equation to be valid.