Are Jumps in Time Changed L évy Models Superfluous? An Empirical Investigation

Abstract

This paper provides empirical evidence that jumps in the underlying stock price process are superfluous for European option pricing in time changed Levy 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 di fference 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 benefi t from including jumps in the underlying process.