Implied Price Processes Anchored in Statistical Realizations

25 Pages Posted: 11 Jun 2021

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

King Wang

Morgan Stanley

Date Written: June 10, 2021


It is observed that statistical and risk neutral densities of compound Poisson processes are unconstrained relative to each other. Continuous processes are too constrained and generally not consistent with market data. Pure jump limit laws deliver operational models simultaneously consistent with both data sets with the additional imposition of no measure change on the arbitrarily small moves. The measure change density must have a finite Hellinger distance from unity linking the two worlds. Models are constructed using the bilateral gamma and the CGMY models for the risk neutral specification. They are linked to the physical process by measure change models. The resulting models simultaneously calibrate statistical tail probabilities and option prices. The resulting models have up to eight or ten parameters permitting the study of risk reward relations at a finer level. Rewards measured by power variations of the up and down moves are observed to value negatively(positively) the even(odd) variations of their own side with the converse holding for the opposite side.

Keywords: Equivalent Lévy Processes, V Shaped Measure Change, Valuation Equilibria.

JEL Classification: G10, G11, G12

Suggested Citation

Madan, Dilip B. and Wang, King, Implied Price Processes Anchored in Statistical Realizations (June 10, 2021). Available at SSRN: or

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)

King Wang

Morgan Stanley ( email )

1585 Broadway
New York, NY 10036
United States

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