Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns

Abstract

This paper proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is based on a pure jump Levy process, wherein the jump arrival rate obeys a power law dampened by an exponential function. The model allows for different degrees of dampening for positive and negative jumps, and also different pricing for upside and downside market risks. Calibration of the model to the S&P 500 index shows that the market charges only a moderate premium on upward index movements, but the maximally allowable premium on downward index movements.

Keywords: Dampened power law, alpha-stable distribution, central limit theorem, upside movement, downside movement

JEL Classification: E43, G12, G13, C51