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IMA Journal of Management Mathematics Advance Access originally published online on May 24, 2007
IMA Journal of Management Mathematics 2007 18(4):371-393; doi:10.1093/imaman/dpm020
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© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A calibration algorithm for simulation-based pricing models

R. Mark Reesor{dagger}

Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada

Don L. McLeish{ddagger}

Department of Statistics and Actuarial Science, University of Waterloo, Waterloo,Ontario N2L 3G1, Canada

{dagger} Corresponding author. Email: mreesor{at}uwo.ca

{ddagger} Email: dlmcleis{at}math.uwaterloo.ca

Received on 20 February 2007. Accepted on 15 March 2007.

Derivative pricing models require calibration to market conditions in order to determine quantities such as hedging positions and the prices of other instruments. For stochastic models and/or complex derivatives whose prices are not of an analytic form, prices must be computed via simulation and the calibration is more difficult. A method to facilitate the calibration of simulation-based pricing models is proposed. The algorithm uses a statistically designed experiment to select the points at which simulations are performed. The method is quite general as it is independent of the stochastic model for the underlying and allows for different objective functions that can incorporate information such as open interest and volume. Furthermore, market prices from European- and/or American-style derivatives covering a range of strike prices and maturities can be handled by this technique. Examples show the procedure is successful at calibrating well-known asset pricing models to both simulated and market data.

Keywords: derivatives pricing; calibration; simulation; experimental design; regression


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