The Finite Sample Properties of the GARCH Option Pricing Model PDF Download
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Author: George Dotsis
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Languages : en
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This paper explores the finite sample properties of the GARCH option pricing model proposed by Heston and Nandi (2000). Simulation results show that the maximum likelihood estimators of the GARCH process may contain substantial estimation biases, even when samples as large as 3,000 observations are used. However, we find that these biases cause significant mispricings only for short-term, out-of-the-money options. It is shown that, given an adequate estimation sample, this bias can be reduced considerably by employing the jackknife resampling method.
Author: George Dotsis
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Languages : en
Pages :
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This paper explores the finite sample properties of the GARCH option pricing model proposed by Heston and Nandi (2000). Simulation results show that the maximum likelihood estimators of the GARCH process may contain substantial estimation biases, even when samples as large as 3,000 observations are used. However, we find that these biases cause significant mispricings only for short-term, out-of-the-money options. It is shown that, given an adequate estimation sample, this bias can be reduced considerably by employing the jackknife resampling method.
Author: Steven L. Heston
Publisher:
ISBN:
Category : Capital assets pricing model
Languages : en
Pages : 44
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Author: Steven L. Heston
Publisher:
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Category :
Languages : en
Pages : 34
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This paper develops a closed-form option pricing formula for a spot asset whose variance follows a GARCH process. The model allows for correlation between returns of the spot asset and variance and also admits multiple lags in the dynamics of the GARCH process. The single factor (one lag) version of this model contains Heston's (1993) stochastic volatility model as a diffusion limit and therefore unifies the discrete GARCH and continuous-time stochastic volatility literature of option pricing. The new model provides the first option formula for a random volatility model that is solely a function of observables; all the parameters can be easily estimated from the history of asset prices, observed at discreteintervals. Empirical analysis on Samp;P500 index options shows the single factor version of the GARCH model to be a substantial improvement over the Black-Scholes (1973) model. The GARCH model continues to substantially outperform the Black-Scholes model even when the Black-Scholes model is updated every period while the parameters of the GARCH model are held constant. The improvement is due largely to the ability of the GARCH model to describe the correlation of volatility with spot returns. This allows the GARCH model to capture strike price biases in the Black-Scholes model that give rise to the skew in implied volatilities in the index options market.
Author:
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Category :
Languages : en
Pages : 74
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Author: Lishang Jiang
Publisher: World Scientific
ISBN: 9812563695
Category : Science
Languages : en
Pages : 344
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From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
Author: Shu-Ing Liu
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Category :
Languages : en
Pages : 35
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This paper proposes an option pricing model, extended from the GARCH option pricing model of Duan (1995) and the Threshold-GARCH model of Hardle and Hafner (2000). Some moment properties of the proposed model are analytically proven. For simplicity or flexibility, the risk-free rate of return is treated as an estimate rather than a constant or a stochastic process. Parameter estimations are analyzed by the Bayesian approach via suitable MCMC techniques. Numerical illustrations are presented using some Samp;P 100 or 500 stock index series and call option price series. The posterior inference results indicate that the threshold effects on the volatility structure are significant. Moreover, the out-of-sample forecasting results also reveal that the inclusion of the threshold effect will indeed enhance the forecasting ability, especially, in the case of the out-of-the-money Samp;P 100 call option.
Author: Lars Stentoft
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Languages : en
Pages :
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In this paper we propose a feasible way to price American options in a model with time-varying volatility and conditional skewness and leptokurtosis, using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk-neutral dynamics can be obtained in this model, we interpret the effect of the risk-neutralization, and we derive approximation procedures which allow for a computationally efficient implementation of the model. When the model is estimated on financial returns data the results indicate that compared to the Gaussian case the extension is important. A study of the model properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model out-performs the Gaussian case for pricing options on the three large US stocks as well as a major index. In particular, improvements are found when it comes to explaining the smile in implied standard deviations.
Author: Giovanni Barone-Adesi
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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We derive analytically the first four conditional moments of the integrated variance implied by the GARCH diffusion process. From these moments we obtain an analytical closed-form approximation formula to price European options under the GARCH diffusion model.Using Monte Carlo simulations, we show that this approximation formula is accurate for a large set of reasonable parameters. Finally, we use the closed-form option pricing solution to shed light on the qualitative properties of implied volatility surfaces induced by GARCH diffusion models.
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Languages : pt-BR
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Este trabalho procura confirmar a hipótese de o modelo de apreçamento de opções GARCH reduzir alguns dos já amplamente estudados vieses do modelo de Black & Scholes, utilizando opções de compra da Telebras no período julho de 1995 a junho de 2000. Para isso, comparam-se os preços encontrados por intermédio do modelo GARCH com os do modelo de Black & Scholes, cotejando-os com os preços de mercado. Os resultados indicaram que o modelo GARCH foi capaz de diminuir alguns dos vieses, principalmente para opções fora-do-dinheiro com curto tempo para o vencimento. Desta forma, o modelo GARCH se mostrou uma alternativa eficaz ao modelo de Black e Scholes, sobretudo para opções com pouca liquidez, nas quais não é possível a utilização da volatilidade implícita da equação de Black e Scholes.
![Option Pricing Using GARCH Models [microform] : an Empirical Examination PDF](https://books.google.com/books/content/images/frontcover/LkggmwEACAAJ?fife=w80-h100)
Author: Sasseville, Caroline
Publisher: Montréal : Service des archives, Université de Montréal, Section Microfilm
ISBN:
Category :
Languages : en
Pages : 166
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