Pricing Foreign Currency and Cross-Currency Options Under GARCH

Duan, Jin‐Chuan; Wei, Jason Zhanshun

doi:10.3905/jod.1999.319110

Cited by 32 publications

(18 citation statements)

References 28 publications

(31 reference statements)

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“…The application of GARCH models for option valuation led to the emergence of two basic categories of models in this area: the first is the affine model of Heston and Nandi (2000) which yields a closed-form solution and the second is the non-affine model of Duan (1995) which requires numerical techniques for valuation. Duan and Wei (1999) extended the GARCH model to pricing of foreign currency options. Several papers have compared the empirical performance of GARCH models with that of the BSM model and or stochastic volatility models.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Duan (1995) was the first to apply the GARCH model for pricing options. Although there are several variants of the GARCH model we have followed the non-linear asymmetric GARCH (1,1) model adapted by Duan (1999) for pricing foreign currency options. This is because a low-order GARCH model incorporating the leverage effect has been generally found adequate for characterizing time-series (Duan, 1999).…”

Section: Black-scholes-merton Model (Bsm)mentioning

confidence: 99%

“…Although there are several variants of the GARCH model we have followed the non-linear asymmetric GARCH (1,1) model adapted by Duan (1999) for pricing foreign currency options. This is because a low-order GARCH model incorporating the leverage effect has been generally found adequate for characterizing time-series (Duan, 1999). Within Duan"s framework the underlying exchange-rate return ( ) is assumed to follow a nonlinear GARCH-M model under the physical probability measure P.…”

Section: Black-scholes-merton Model (Bsm)mentioning

confidence: 99%

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

Bhat¹,

Arekar²

2016

IJEF

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Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models -the Black-Scholes-Merton Option Pricing Model (BSM) and Duan"s NGARCH option pricing model -for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the "volatility smile". This bias of the BSM results from its assumption of a constant volatility over the option"s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Black-scholes-merton Model (Bsm)mentioning

confidence: 99%

Section: Black-scholes-merton Model (Bsm)mentioning

confidence: 99%

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

Bhat¹,

Arekar²

2016

IJEF

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“…Duan and Wei (1999) priced quantos under GARCH using simulations. Kwok and Wong (1999) went a step further and priced exotic foreign equity options in a Black-Scholes framework.…”

Section: Introductionmentioning

confidence: 99%

Pricing foreign equity options under Lévy processes

Huang

Hung

2005

J. Fut. Mark.

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This article investigates the valuation of a foreign equity option whose value depends on the exchange rate and foreign equity prices. Assuming that these underlying price processes are correlated and driven by a multidimensional Lévy process, a method suitable for solving the complex valuation problem is developed. First, to reduce the number of dimensions of the problem, the probability measure is changed to embed some dimensions of the Lévy process into the pricing measure. Second, to simplify the integral complexity of the discounted terminal payoff, the valuation problem is transformed to Fourier space. The main contribution of this study is that by combining these two methods, the multivariate valuation problem is significantly simplified, and very accurate results are obtained relatively quickly. This powerful method can also be applied to other multivariate pricing problems involving Lévy processes.

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“…Duan and Wei (1999) generalize the GARCH option model by allowing for stochastic volatility, unconditional leptokurtosis and a correlation between the lagged return and the conditional variance for both the exchange rate and the foreign stock price. The authors conclude that options on foreign currency can be valued by assuming a bivariate non-linear asymmetric GARCH (1, 1) model.…”

Section: Harikumar De Boyrie and Pakmentioning

confidence: 99%

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

Harikumar¹,

Boyrie²,

Pak³

2004

Review of Quantitative Finance and Accounting

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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 ...

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Pricing Foreign Currency and Cross-Currency Options Under GARCH

Cited by 32 publications

References 28 publications

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

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

Pricing foreign equity options under Lévy processes

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

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