The Economic Determinants
of Interest Rate Option Smiles
*
PRACHI DEUSKAR
1
ANURAG
GUPTA
2
MARTI G. SUBRAHMANYAM
3
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.
1
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-
mail: pdeuskar@uiuc.edu.
2
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,
E-mail: anurag.gupta@case.edu.
3
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: msubrahm@stern.nyu.edu.
*
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
errors.
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.
1
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.
2
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.
3
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.
4
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
1
BIS Quarterly Review, December 2006, Bank for International Settlements, Basel, Switzerland.
2
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.
3
Gupta and Subrahmanyam (2005) and Jarrow, Li and Zhao (2006) do examine smile effects in interest
rate options, but only from a modeling perspective.
4
See Bakshi, Cao and Chen (1997), Dumas, Fleming and Whaley (1998), Bates (2000) and several
references therein for more on this literature.
1