DP4960 Loss Functions in Option Valuation: A Framework for Model Selection

Author(s): Dennis Bams, Thorsten Lehnert, Christian C Wolff
Publication Date: March 2005
Keyword(s): estimation risk, GARCH, implied volatility, loss functions, option pricing
JEL(s): G12
Programme Areas: Financial Economics
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=4960

In this paper, we investigate the importance of different loss functions when estimating and evaluating option pricing models. Our analysis shows that it is important to take into account parameter uncertainty, since this leads to uncertainty in the predicted option price. We illustrate the effect on the out-of-sample pricing errors in an application of the ad hoc Black-Scholes model to DAX index options. Our empirical results suggest that different loss functions lead to uncertainty about the pricing error itself. At the same time, it provides a first yardstick to evaluate the adequacy of the loss function. This is accomplished through a data-driven method to deliver not just a point estimate of the pricing error, but a confidence interval.