Are Jumps in Time Changed Lévy Models Superfluous? An Empirical Investigation
30 Pages Posted: 12 Jun 2012
Date Written: June 11, 2012
This paper provides empirical evidence that jumps in the underlying stock price process are superfluous for European option pricing in time changed Lévy models. We introduce a model with a.s. continuous sample paths and a parsimonious description in terms of free parameters. The conducted in- and out-of-sample analysis show almost no difference concerning calibration quality to the German DAX index between the continuous model and pure jump alternatives. The jump models in fact show signs of over-parameterization displayed by dramatically varying parameter estimates over time. An analysis of the resulting fitting errors also reveals no benefit from including jumps in the underlying process.
Keywords: option pricing, Lévy process, time change, model-to-market calibration, parameter stability
JEL Classification: G13
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