Collateral Smile

41 Pages Posted: 17 Mar 2012

See all articles by Markus Leippold

Markus Leippold

University of Zurich - Department of Banking and Finance; University of Zurich - Faculty of Economics, Business Administration and Information Technology

Lujing Su

Department of Banking and Finance

Date Written: March 15, 2012

Abstract

We analyze the impact of funding costs and margin requirements on prices of index options traded on the CBOE. Margin requirements are the collateral the option sellers are enforced to deposit with exchanges. Funding costs refer to the spread between borrowing rates and lending rates. Testing the Put-Call parity and bid-ask spreads of options, we find evidence of non-zero funding costs. Under a dynamic incomplete market where differential borrowing rates and lending rates are allowed, we propose a model that gives upper bounds and lower bounds for option prices in the absence of arbitrage. As we want to isolate the effect of these costs on implied volatilities, we choose the classical Black-Scholes model as starting point. We derive price bounds for European options in semi closed-form. Numerical estimations show that funding costs and margin requirements give a sensible increase to option prices which could translate into skew and smile patterns for implied volatility curves even under constant volatilities. Empirical tests show that the slopes our model generates have significant statistical power in explaining the slopes observed in the market. Hence, funding costs and collateral requirements offer an institutional explanation of the volatility smile phenomenon without leaving the constant volatility assumption.

Keywords: collateral requirements, funding costs, volatility smile, option pricing

JEL Classification: G01, G12, G13

Suggested Citation

Leippold, Markus and Su, Lujing, Collateral Smile (March 15, 2012). Swiss Finance Institute Research Paper No. 11-51; AFA 2013 San Diego Meetings Paper. Available at SSRN: https://ssrn.com/abstract=2023487 or http://dx.doi.org/10.2139/ssrn.2023487

Markus Leippold (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

University of Zurich - Faculty of Economics, Business Administration and Information Technology ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

Lujing Su

Department of Banking and Finance ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

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