A Closed-Form GARCH Option Pricing Model

Heston, Steven L.; Nandi, Saikat

doi:10.2139/ssrn.96651

Cited by 113 publications

(200 citation statements)

References 28 publications

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“…The first such limit result was demonstrated by Nelson (1990). A related result is given by Heston and Nandi (2000), who show that the continuous-time model in Heston (1993) can be obtained as the limit of the GARCH dynamic they suggest. It has become clear, however, that while these limit results are theoretically intriguing, their practical relevance may be modest.…”

Section: Introductionmentioning

confidence: 72%

“…Also, like the Heston (1993) model, it has a closed-form solution, it contains a leverage effect and it allows for volatility clustering. Heston and Nandi (2000) have demonstrated that it performs satisfactorily vis-a-vis ad-hoc benchmarks for the purpose of option valuation. Because this model also has an affine structure, we refer to it as AF-GARCH.…”

Section: Volatility Dynamics and Model Implementationmentioning

confidence: 97%

“…For practical reasons, we limit the number of models to two. The first discrete-time model we investigate is the one by Heston and Nandi (2000). This model is a natural choice, as it was designed with option valuation in mind.…”

Section: Volatility Dynamics and Model Implementationmentioning

confidence: 99%

“…This is the simplest model in the GARCH literature that contains both volatility clustering and a leverage effect. It is also the model considered by Duan (1995 Heston (1993), Heston and Nandi (2000) and Nandi (1998) Huang and Wu (2004). 10 Amin and Ng (1993), Bollerslev and Mikkelsen (1996), Engle and Mustafa (1992), and Duan, Ritchken and Sun (2002) estimate model parameters using the underlying asset returns and subsequently value options.…”

Section: Volatility Dynamics and Model Implementationmentioning

confidence: 99%

“…However, apart from the Heston (1993) model, the literature contains few if any other volatility dynamics that lead to closedform solutions. The discrete-time literature also contains a volatility dynamic that yields a closed-form solution for option prices, namely the dynamic in Heston and Nandi (2000).…”

Section: Introductionmentioning

confidence: 99%

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Comparing Discrete-Time and Continuous-Time Option Valuation Models

2005

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This paper provides an empirical comparison of four option valuation models. The first of these models is the benchmark affine stochastic volatility model in the continuous-time option valuation literature. This model yields closed-form solutions for European option prices. The second model is a discrete-time affine option valuation model that also allows for a closed form solution. The third is a non-affine discrete-time model and the fourth is a nonaffine stochastic volatility model. The latter two models do not yield closed-form solutions. Using a root mean squared dollar error criterion, the non-affine models outperform the affine stochastic volatility model by approximately 15% in-and out-of-sample. The affine discretetime model outperforms the affine continuous-time model by 10% in-sample and 6% out-ofsample The non-affine discrete time model slightly outperforms the non-affine continuous time model. These findings may suggest that the distinction between continuous-time and discrete-time models is not very relevant from an empirical perspective. The distinction between non-affine and affine volatility models is more important and non-affine models need to be studied more extensively. At the methodological level, the paper presents a new method for estimating continuous-time option valuation models that can be used in a variety of applications.JEL Classification: G12

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Section: Introductionmentioning

confidence: 72%

Section: Volatility Dynamics and Model Implementationmentioning

confidence: 97%

Section: Volatility Dynamics and Model Implementationmentioning

confidence: 99%

Section: Volatility Dynamics and Model Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Comparing Discrete-Time and Continuous-Time Option Valuation Models

2005

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Approximating American option prices in the GARCH framework

Duan

Gauthier

Sasseville

et al. 2003

Journal of Futures Markets

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This article proposes an efficient approach for computing the prices of American style options in the GARCH framework. Rubinstein's (1998) Edgeworth tree idea is combined with the analytical formulas for moments of the cumulative return under GARCH developed in Duan et al. (1999Duan et al. ( , 2002 to yield a simple recombining binomial tree for option valuation in the GARCH context. Because the resulting tree is univariate, the proposed approach represents a convenient approximation of the bivariate GARCH system. Numerical analysis is used to demonstrate the speed and accuracy of the proposed approximation.

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Implied Pricing Kernels: An Alternative Approach for Option Valuation

Ryu

Kang

Suh

2013

Journal of Futures Markets

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This study proposes a new estimation approach for option valuation (an implied pricing kernelbased approach), which estimates model parameters under the physical probability measure (Pmeasure) using a pricing kernel implied by the GARCH option pricing model. Analyzing the dataset on the KOSPI 200 options market, we examine the empirical performance of the implied pricing kernel-based approach and compare it with the performance of the classical GARCH option valuation approach (i.e., a pricing model-based approach) that estimates model parameters under the risk-neutral probability measure (Q-measure). As proposed in this study, the implied pricing kernel-based estimation approach requires approximation and discretization in order to derive the functional form of the pricing kernel. Regardless of this approximation, however, when it comes to pricing OTM calls, the implied pricing kernel-based approach performs slightly better than the pricing model-based approach that has been traditionally used for option valuation. Additional analysis based on the put option sample indicates that the implied pricing kernel-based approach clearly dominates the classical pricing model-based approach during the early stage of emergence of the KOSPI 200 options market (1999)(2000) when the market was immature. During the recent global financial crisis (2007)(2008)(2009), the pricing kernel-based approach also yields smaller pricing errors for OTM puts than the classical approach does. These empirical results imply that the new approach suggested in this study can be advantageous for option valuation, particularly when the information embedded in options prices is not sufficient for estimation and/or the market is speculative and volatile.

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A Closed-Form GARCH Option Pricing Model

Cited by 113 publications

References 28 publications

Comparing Discrete-Time and Continuous-Time Option Valuation Models

Comparing Discrete-Time and Continuous-Time Option Valuation Models

Approximating American option prices in the GARCH framework

Implied Pricing Kernels: An Alternative Approach for Option Valuation

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