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Illiquid Markets as a Counterparty: An Introduction to Conic Finance

39 Pages Posted: 28 Jan 2010 Last revised: 11 May 2010

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Alexander S. Cherny

Moscow State University

Date Written: May 7, 2010

Abstract

Illiquid markets as a counterparty are modeled as accepting at zero cost a convex cone of random variables containing the nonnegative cash flows. Formulas are provided for bid and ask prices in terms of this marketed cone. Additionally closed forms are obtained when parametric concave distortions introduced in Cherny and Madan (2009) define the marketed claims. Finally explicit expressions price call and put options at bid and ask. Three applications illustrate. The first estimates the movement of the cone through the financial crisis using data on bid and ask prices for S&P 500 index options. It is observed that the cone contracted significantly in 2008 and slowly opened up thereafter. The second application documents the improvements possible in terms of reduced ask prices by hedging at a flat Black-Scholes volatility even when all the underlying assumptions for replication are violated. The third application considers a number of structured products written on daily returns to an underlying asset price.

Suggested Citation

Madan, Dilip B. and Cherny, Alexander S., Illiquid Markets as a Counterparty: An Introduction to Conic Finance (May 7, 2010). Robert H. Smith School Research Paper No. RHS 06-115. Available at SSRN: https://ssrn.com/abstract=1540769 or http://dx.doi.org/10.2139/ssrn.1540769

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)

Alexander S. Cherny

Moscow State University ( email )

Faculty of Mechanics and Mathematics
Department of Probability Theory
Moscow, 119992
Russia
007 095 939 14 03 (Phone)
007 095 939 14 03 (Fax)

HOME PAGE: http://mech.math.msu.su/~cherny

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