Working Paper: CEPR ID: DP4960
Authors: Dennis Bams; Thorsten Lehnert; Christian C. Wolff
Abstract: 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.
Keywords: Estimation; Risk; GARCH; Implied Volatility; Loss Functions; Option Pricing
JEL Codes: G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| choice of loss function (C52) | out-of-sample pricing errors (C52) |
| misalignment of loss functions (L21) | misleading results in model selection (C52) |
| parameter uncertainty (C51) | uncertainty in forecasted prices (Q47) |
| uncertainty in forecasted prices (Q47) | accuracy of pricing errors (D41) |
| absolute pricing error criterion at estimation stage (C51) | uncertainty in pricing error at evaluation stage (G13) |
| choice of loss function (C52) | precision of pricing error estimates (C13) |