A calibration algorithm for simulation-based pricing models

Don L. McLeish Department of Statistics and Actuarial Science, University of Waterloo, Waterloo,Ontario N2L 3G1, Canada Corresponding author. Email: mreesor{at}uwo.ca Email: dlmcleis{at}math.uwaterloo.ca Received on 20 February 2007. Accepted on 15 March 2007. Derivative pricing models require calibration to market conditionsin order to determine quantities such as hedging positions andthe prices of other instruments. For stochastic models and/orcomplex derivatives whose prices are not of an analytic form,prices must be computed via simulation and the calibration ismore difficult. A method to facilitate the calibration of simulation-basedpricing models is proposed. The algorithm uses a statisticallydesigned experiment to select the points at which simulationsare performed. The method is quite general as it is independentof the stochastic model for the underlying and allows for differentobjective functions that can incorporate information such asopen interest and volume. Furthermore, market prices from European-and/or American-style derivatives covering a range of strikeprices and maturities can be handled by this technique. Examplesshow the procedure is successful at calibrating well-known assetpricing models to both simulated and market data.