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http://ssrn.com/abstract=424461
 
 

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The Importance of the Loss Function in Option Valuation


Peter Christoffersen


University of Toronto - Rotman School of Management; Copenhagen Business School; University of Aarhus - CREATES

Kris Jacobs


University of Houston - C.T. Bauer College of Business

August 2002

EFA 2003 Annual Conference Paper No. 604

Abstract:     
Which loss function should be used when estimating and evaluating option valuation models? Many different functions have been suggested, but no standard has emerged. We do not promote a particular function, but instead emphasize that consistency in the choice of loss functions is crucial. First, for any given model, the loss function used in parameter estimation and model evaluation should be identical, otherwise suboptimal parameter estimates may be obtained. Second, when comparing models, the estimation loss function should be identical across models, otherwise unfair comparisons will be made. We illustrate the importance of these issues in an application of the so-called Practitioner Black-Scholes (PBS) model to S&P500 index options. We find reductions of over 50 percent in the root mean squared error of the PBS model outperforms a benchmark structural model when the estimation and evaluation loss functions are aligned. We also find that the PBS model outperforms a benchmark structural model when the estimation loss functions are identical across models, but otherwise not. The new PBS model with aligned loss functions thus represents a much tougher benchmark against which future structural models can be compared.

Number of Pages in PDF File: 38

Keywords: option valuation, implied volatility, practitioner Black-Scholes approach, pricing errors, loss functions, out-of-sample forecasting, parameter stability

JEL Classification: G12

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Date posted: August 3, 2003  

Suggested Citation

Christoffersen, Peter and Jacobs, Kris, The Importance of the Loss Function in Option Valuation (August 2002). EFA 2003 Annual Conference Paper No. 604. Available at SSRN: http://ssrn.com/abstract=424461 or http://dx.doi.org/10.2139/ssrn.424461

Contact Information

Peter Christoffersen (Contact Author)
University of Toronto - Rotman School of Management ( email )
105 St. George Street
Toronto, Ontario M5S 3E6 M5P 3C4
Canada
416-946-5511 (Phone)
HOME PAGE: http://www.christoffersen.com
Copenhagen Business School
Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark
University of Aarhus - CREATES
School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark
Kris Jacobs
University of Houston - C.T. Bauer College of Business ( email )
Houston, TX 77204-6021
United States
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