The Economic Determinants of Interest Rate Option Smiles prachi deuskar

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The Economic Determinants 

of Interest Rate Option Smiles
















Journal of Banking and Finance, forthcoming 



March 2007 


We address three questions relating to the interest rate options market: 

What is the shape of the smile? What are the economic determinants of 

the shape of the smile? Do these determinants have predictive power for 

the future shape of the smile and vice versa?  We investigate these issues 

using daily bid and ask prices of euro (€) interest rate caps/floors. We 

find a clear smile pattern in interest rate options. The shape of the smile 

varies over time and is affected in a dynamic manner by yield curve 

variables and the future uncertainty in the interest rate markets; it also 

has information about future aggregate default risk. Our findings are 

useful for the pricing, hedging and risk management of these derivatives. 


JEL Classification: G10, G12, G13, G15 

Keywords: Volatility smiles; interest rate options; euro interest rate 

markets; Euribor market. 



 Department of Finance, College of Business, University of Illinois at Urbana-Champaign, 304C David 

Kinley Hall, 1407 West Gregory Drive, Urbana, IL 61801. Ph: (217) 244-0604, Fax: (217) 244-9867, E-



Department of Banking and Finance, Weatherhead School of Management, Case Western Reserve 

University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7235. Ph: (216) 368-2938, Fax: (216) 368-6249, 



Corresponding author. Department of Finance, Leonard N. Stern School of Business, New York 

University, 44, West Fourth Street #9-15, New York, NY 10012-1126. Ph: (212) 998-0348, Fax: (212) 995-

4233, E-mail: 


 We thank Viral Acharya, Menachem Brenner, Rob Engle, Peter Ritchken, the editor Giorgio Szego, and 

participants at the finance department seminars at Case Western Reserve University, Georgia State 

University, Michigan State University, University of Melbourne, SMU, the 2004 AFA meetings in San 

Diego, and the 2004 Quantitative Methods in Finance conference in Sydney, for helpful comments and 

suggestions on earlier drafts. We also thank the two referees for their excellent comments and suggestions, 

which substantially improved the content and exposition of the paper. We thank the Fixed Income Analysts 

Society for the 2004 FMA Competitive Paper Award in Fixed Income. We remain responsible for all 




1. Introduction 

Over-the-counter interest rate options such as caps/floors are among the most liquid options that 

trade in the global financial markets, with about $37 trillion of notional principal and $580 billion 

in gross market value outstanding as of June 2006.


 Given the enormous size of these markets, 

significant effort has been devoted, both in academia and in industry, to the development and 

testing of models to accurately price and hedge these claims.


 However, most of these studies 

have focused on at-the-money options, with little attention paid to the determinants of volatility 

smiles/skews in interest rate options markets.


 In this paper, we address this issue in the euro (€) 

interest rate options market by characterizing the smile, its time variation and its economic 

determinants. We also examine the information content of interest rate option smiles, in order to 

understand whether it has any statistical power in predicting specific macro-economic variables.  

Volatility smiles are an extensively documented cross-sectional feature in the equity options 

markets, ever since they were first reflected in option prices after the October 1987 stock market 

crash. Indeed, the focus of much of the research in the equity options literature has primarily been 

to relax the assumptions of the Black-Scholes valuation framework to model the volatility smile 

patterns observed in the market. The frameworks proposed have evolved from models with 

deterministically varying volatility of returns to models that incorporate either stochastic 

volatility, or jumps in the underlying price process, or both.


 In spite of their increasing 

complexity, none of these models has been successful in accurately explaining the behavior of the 

observed volatility smiles - the empirically observed smiles are typically more perceptible than 

those predicted by theory.  Effort has also been devoted to explaining the volatility smile in 



 BIS Quarterly Review, December 2006, Bank for International Settlements, Basel, Switzerland. 


 These include Driessen, Klaasen and Melenberg (2003), Fan, Gupta and Ritchken (2003), Longstaff, 

Santa-Clara and Schwartz (2001), Peterson, Stapleton and Subrahmanyam (2003), and many others. 


 Gupta and Subrahmanyam (2005) and Jarrow, Li and Zhao (2006) do examine smile effects in interest 

rate options, but only from a modeling perspective. 


 See Bakshi, Cao and Chen (1997), Dumas, Fleming and Whaley (1998), Bates (2000) and several 

references therein for more on this literature.  

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