An analytical approximation for the GARCH option pricing model

Duan, Jin‐Chuan; Gauthier, Geneviève; Simonato, Jean‐Guy

doi:10.21314/jcf.1999.033

Cited by 86 publications

(68 citation statements)

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“…It is similar to that referenced in Duan et al (1999) but corrects a calculation error in their proof, which is also inherent in Duan, Gauthier, Sasseville, and Simonato (2004).…”

Section: Proposition 23mentioning

confidence: 59%

“…Second, a setup with high volatility persistence is created in order to investigate the series approximation under significant deviation from the normal distribution. An analysis similar to that of Duan et al (1999) is conducted to survey the effects.…”

Section: Monte-carlo Analysismentioning

confidence: 99%

“…Sample options with price C < 0.5 were abandoned because they generate large relative errors by a small divider. The same precaution was taken in Duan et al (1999). The 95% MonteCarlo confidence regions are indicated gray, bordered by circles.…”

Section: High Volatility Persistence Scenariomentioning

confidence: 99%

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Fast Analytic Option Valuation with GARCH

Mazzoni¹

2010

JOD

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This paper introduces a new method for pricing European style call options with GARCH models. The resulting pricing formula is an explicit function of the model parameters, current spot asset price, exercise price and time to maturity. The method under consideration is remarkably fast because no numerical integration procedures are involved. Errors, resulting from approximation and series expansion, are surveyed by Monte-Carlo methods and turn out to be negligible.

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“…It is similar to that referenced in Duan et al (1999) but corrects a calculation error in their proof, which is also inherent in Duan, Gauthier, Sasseville, and Simonato (2004).…”

Section: Proposition 23mentioning

confidence: 59%

Section: Monte-carlo Analysismentioning

confidence: 99%

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Fast Analytic Option Valuation with GARCH

Mazzoni¹

2010

JOD

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“…The in-out parity relationship is again applicable to European style options. This property can then be used to speed up the calculation of the European knock-in option price by employing the analytical approximation formula developed by Duan, et al 1998 for computing the plain-vanilla option value under GARCH.…”

Section: The Knock-in Barrier Optionsmentioning

confidence: 99%

Pricing Discretely Monitored Barrier Options by a Markov Chain

Duan¹,

Dudley

Gauthier

et al. 2003

JOD

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CIRANOLe CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d=une subvention d=infrastructure du ministère de la Recherche, de la Science et de la Technologie, de même que des subventions et mandats obtenus par ses équipes de recherche. La Série Scientifique est la réalisation d=une des missions que s=est données le CIRANO, soit de développer l=analyse scientifique des organisations et des comportements stratégiques. Reproduction partielle permise avec citation du document source, incluant la notice ©. Short sections may be quoted without explicit permission, provided that full credit, including © notice, is given to the source. CIRANO is a private non-profit organization incorporated under the ISSN 1198-8177Ce document est publié dans l=intention de rendre accessibles les résultats préliminaires de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions. Cette étude propose l'utilisation de chaînes de Markov pour l'évaluation de prix d'options à barrière avec vérification à temps discrets dans des contextes de volatilité constante ou variable. La méthode utilise une chaîne de Markov homogène afin d'approcher le processus stochastique postulé pour l'actif sousjacent. Cette méthode procure un environnement naturel pour évaluer ce type d'option puisque le pas discret de la chaîne de Markov peut être adapté à la longueur de temps entre les vérifications de la barrière. Le prix du sous-jacent peut aussi être discrétisé de façon optimale par rapport à la barrière. La méthode est rapide, flexible et simple à implanter puisque le calcul de prix d'options européennes et américaines est réalisé à l'aide de multiplications matricielles. De plus, la méthode proposée est précise pour les cas difficiles où la barrière est située près de la valeur du sous-jacent. Les options « knock-in » et « knock-out » sont examinées. Différents types de barrières telles les barrières doubles ainsi que les barrières mobiles sont aussi examinés.

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“…Alternative numerical procedures have been proposed recently by various authors. For example, Duan, Gauthier and Simonato (1998) propose an analytical approximation procedure whereby European options under GARCH can be priced by matching moments of the return distribution; Duan and Simonato (1999) use a Markov chain to approximate the GARCH innovations and price options accordingly; and finally, Ritchken and Trevor (1999) develop a lattice framework for most univariate GARCH processes.…”

Section: Fx Optionsmentioning

confidence: 99%

Pricing Foreign Currency and Cross-Currency Options Under GARCH

Duan

Wei

1999

JOD

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The main objective of this paper is to propose an alternative valuation framework for pricing foreign currency and cross-currency options, which is capable of accommodating existing empirical regularities. The paper generalizes the GARCH option pricing methodology of Duan (1995) to a twocountry setting. Specifically, we assume a bivariate nonlinear GARCH system for the exchange rate and the foreign asset price, and generalize the local risk-neutral valuation principle for pricing derivatives. We define an equilibrium price measure in the two-country economy and derive the locally risk-neutralized GARCH processes for the exchange rate and the foreign asset price. Foreign currency options and cross-currency options are then valued using Monte Carlo simulations. Our setup accommodates rich empirical regularities such as stochastic volatility, fat tailed distributions and leverage effect extensively documented for financial data series. Numerical results show that our proposed model exhibits properties that are consistent with the documented empirical regularities for foreign currency options and quanto options.

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An analytical approximation for the GARCH option pricing model

Cited by 86 publications

References 0 publications

Fast Analytic Option Valuation with GARCH

Fast Analytic Option Valuation with GARCH

Pricing Discretely Monitored Barrier Options by a Markov Chain

Pricing Foreign Currency and Cross-Currency Options Under GARCH

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