Illiquid Markets as a Counterparty: An Introduction to Conic Finance
Dilip B. Madan
University of Maryland - Robert H. Smith School of Business
Alexander S. Cherny
Moscow State University
May 7, 2010
Robert H. Smith School Research Paper No. RHS 06-115
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.
Number of Pages in PDF File: 39
Date posted: January 28, 2010 ; Last revised: May 11, 2010
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