Two Processes for Two Prices

25 Pages Posted: 24 Jun 2013

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Wim Schoutens

KU Leuven - Department of Mathematics

Date Written: June 18, 2013

Abstract

Postulating additivity of bid and ask prices for claims comonotone with a long or short stock position, two pricing processes are identified from data on bid and ask prices for options. It is observed that there are two separate put call parity relations in place, with the ask price for call less bid prices for put delivering an ask price for the forward stock. Likewise, the ask for puts less the bid for calls identifies the bid for the forward stock. Two processes are introduced to determine bid and ask prices for claims comonotone with a long or short position in the stock. For a claim comonotone with a long position, one uses the so-called increasing process for the ask price and the so-called decreasing process for the bid price, and vice versa for a claim comonotone with a short position. As candidates for the two processes, one may employ any of the traditional one dimensional Markov processes. We illustrate the theory by using a Sato process, a model known to produce a smile conforming fit over strike and maturity. The two processes are observed to have marginals related by first order stochastic dominance. The increasing process dominates the decreasing process in this sense. These two processes are also used to construct upper and lower bounds for bid and ask prices for claims not comonotone with a long or short stock position. The two processes and their properties are illustrated with data on bid and ask prices for options on the exchange traded fund, SPY.

Keywords: comonotone, Sato process, variance gamma, Markov Martingale, variance swap

JEL Classification: G10, G11, G12

Suggested Citation

Madan, Dilip B. and Schoutens, Wim, Two Processes for Two Prices (June 18, 2013). Robert H. Smith School Research Paper, Available at SSRN: https://ssrn.com/abstract=2284437 or http://dx.doi.org/10.2139/ssrn.2284437

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)

Wim Schoutens

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
183
Abstract Views
1,197
rank
200,017
PlumX Metrics