Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data

Abstract

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.Key words: GARCH, currency options, Black-Scholes JEL Classification: G12, G13, G15Option 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 Jacquillat (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. 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. HARIKUMAR, DE BOYRIE AND PAKIn addressing these issues, some researchers have made refinements to the Black-Scholes model. Amin and Jarrow (1991) introduce a stochastic interest rate model in which the assumption of constant interest rates, both domestic and foreign, is relaxed. Hilliard, Madura and Tucker (1991) develop a currency option-pricing model under stochastic interest rates when interest rate parity holds. Their model assumes that domestic and foreign bond prices have local variances that depend only on time and not on other state variables such as the level of short-term interest rates. The authors test their option model and find that the stochastic interest rate model with domestic and foreign short term rates, driven by Arithmetic Brownian motion, exhibit greater pricing accuracy than the constant interest rate alternative. While modeling stochastic volatility, Heston and Nandi (2000) observe ...

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

“…8, No. 3;2016et al (2004 who found that the BSM outperforms the GARCH model in respect of currency options. It is however contrary to that of Bollen and Rasiel (2003) who conclude that GARCH models are an improvement over the fixed smile model.…”

“…Bollen and Rasiel (2003) examined the performance of the regime-switching, GARCH and jump-diffusion models and concluded that all these models were superior to the BSM model when fitting option prices. On the contrary Harikumar, Boyrie, and Pak (2004) evaluated the performance of the BSM and GARCH option pricing models for call options on three currencies, viz. the sterling, the Swiss franc and the yen and found that the BSM outperformed the GARCH model.…”

Strong consistency of the empirical martingale simulation option price estimator

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Asymptotic Normality for EMS Option Price Estimator with Continuous or Discontinuous Payoff Functions

“…The applicability of the EMS approach in the pricing of some options was tested by Demir and Tutek (2004). Because of its substantial reduction of simulation errors, EMS has been employed as an important adjustment to the traditional simulation by Duan and Wei (1999), Bams et al (2004), Harikumar and Boyrie (2004), and Christoffersen et al (2006). Duan et al (2001) first showed that the EMS price estimator had an asymptotic normal distribution when the payoff is piecewise linear and continuous.…”