Review of Quantitative Finance and Accounting, 23: 299–312, 2004
2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
Evaluation of Black-Scholes and GARCH Models
Using Currency Call Options Data
T. HARIKUMAR AND MARIA E. DE BOYRIE
Associate Professor, Department of Finance, MSC 3FIN, College of Business Administration & Economics,
New Mexico State University, P.O. Box 30001, Las Cruces, NM 88003, USA
SIMON J. PAK
Associate Professor, Penn State University, 30 East Swedesford Road, Malvern, PA 19355, USA
Abstract. This paper empirically examines the performance of Black-Scholes and Garch-M call option pricing
models using call options data for British Pounds, Swiss Francs and Japanese Yen. The daily exchange rates exhibit
an overwhelming presence of volatility clustering, suggesting that a richer model with ARCH/GARCH effects
might have a better ﬁt with actual prices. We perform dominant tests and calculate average percent mean squared
errors of model prices. Our ﬁndings indicate that the Black-Scholes model outperforms the GARCH models. An
implication of this result is that participants in the currency call options market do not seem to price volatility
clusters in the underlying process.
Keywords: GARCH, currency options, Black-Scholes
JEL Classiﬁcation: G12, G13, G15
Option pricing has its origins in the seminal works of Black-Scholes (1973) and Merton
(1973). Empirical testing of these models did not become possible until Feigner and Jacquil-
lat (1979) ﬁrst proposed a market for currency options. In December of 1982, American
Currency Options began trading in the Philadelphia Stock Exchange (PHLX). Today, this
exchange lists six dollar-based standardized currency option contracts, which settle in the
actual physical currency. These are Australian dollar, British Pound, Canadian Dollar, Euro,
Japanese Yen and Swiss Franc.
The Black and Scholes (1973) option-pricing model was the ﬁrst to be used in pricing
currency options; but, overtime and in practice, researchers have found that the prices
estimated by the Black-Scholes model suffer from many biases. Duan (1995) mentions that
the Black-Scholes model exhibits under pricing of out-of-the money options, under pricing
of options on low volatility securities and under pricing of short-maturity options and results
in a U-shaped implied volatility curve.
We are grateful to Dr. Jin-Chuan Duan, Dr. Stewart Mayhew and the participants of the 2003 FMA International
Meetings for valuable comments. We also thank Dr. Leigh Murray, New Mexico State University for statistical
help and Dr. Jayashree Harikumar, Los Alamos National Laboratories, New Mexico for help with MATLAB.