Momentum and Reversion in Risk Neutral Martingale Probabilities

27 Pages Posted: 16 Apr 2013 Last revised: 25 Mar 2014

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: March 8, 2014

Abstract

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

Madan, Dilip B., Momentum and Reversion in Risk Neutral Martingale Probabilities (March 8, 2014). Available at SSRN: https://ssrn.com/abstract=2251300 or http://dx.doi.org/10.2139/ssrn.2251300

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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