Momentum and Reversion in Risk Neutral Martingale Probabilities
27 Pages Posted: 16 Apr 2013 Last revised: 25 Mar 2014
Date Written: March 8, 2014
A time homogeneous, purely discontinuous, parsimonous Markov martingale model is proposed for the risk neutral dynamics of equity forward prices. Transition probabilities are in the variance gamma class with spot dependent parameters. Markov chain approximations give access to option prices. The model is estimated on option prices across strike and maturity for five days at a time. Properties of the estimated processes are described via an analysis of return quantiles, momentum functions that measure the response of tail probabilities to such moves. Momentum and reversion are also addressed via the construction of reverse conditional expectations. Term structures for the moments of marginal distributions support a decay in skewenss and excess kurtosis with maturity at rates slower than those implied by Lévy processes. Out of sample performance is additionally reported. It is observed that risk neutral dynamics by and large reflect the presence of momentum in numerous probabilities. However, there is some reversion in the upper quantiles of risk neutral return distributions.
Keywords: Variance Gamma, Markov Chains, Hunt Process, Reverse Expectations
JEL Classification: G10, G12, G13
Suggested Citation: Suggested Citation