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Author: Arvid Voormanns
Publisher:
ISBN: 9783659963230
Category :
Languages : en
Pages : 80
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Author: Arvid Voormanns
Publisher:
ISBN: 9783659963230
Category :
Languages : en
Pages : 80
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Book Description
Author: Steven L. Heston
Publisher:
ISBN:
Category : Capital assets pricing model
Languages : en
Pages : 44
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Author: Yi Xi
Publisher:
ISBN:
Category :
Languages : en
Pages : 136
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Book Description
Option pricing is a major area in financial modeling. Option pricing is sometimes based on normal GARCH models. Normal GARCH models fail to capture the skewness and the leptokurtosis in financial data. The variant GARCH-in-mean (GARCH-M) model is widely used in the option pricing literature. It adds a heteroskedasticity term to the mwhich is interpreted as a risk premium, and also incorporates a type of asymmetry. Our goal is to compare option valuation between GARCH-M and ARMA-GARCH models with normal and non-normal, z-distributed innovations. The models are fitted to the historical return data, and risk neutral measures are based on the conditional Esscher transform and the extended Girsanov principle. We compare European Calls on the S & P 500 with the mopredictions. The TGARCH is best for ARMA-GARCH/GARCH-M models. Neither normal nor z dominates the other, but overall z-TGARCH-M (z-innovations) seems to be best, ARMA- TGARCH is surprisingly good.
Author: Szymon Kaminski
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659399978
Category :
Languages : en
Pages : 56
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Book Description
In this paper the application of several option pricing models has been tested on the basis of options traded on the Warsaw Stock Exchange. The models have been evaluated by comparing option prices estimates to prices observed on the market. The chosen models are: a few alternative versions of the Duan (1995) GARCH Option Pricing Model, and two versions of the model by Black (1976). A separate section is devoted to the impact of the implied dividend yield on prices of options. The study covers a period from January 2006 to March 2012. Results show that the most accurate models are the Black model with a volatility term structure, and the Duan GARCH Option Pricing Model with implied dividend yield and Student's T random errors.
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ISBN:
Category :
Languages : pt-BR
Pages :
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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.
Author: Lars Stentoft
Publisher:
ISBN:
Category :
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: Steven L. Heston
Publisher:
ISBN:
Category :
Languages : en
Pages : 34
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Book Description
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: Giovanni Barone-Adesi
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model's flexibility to fit market option prices. An extensive empirical analysis based on Samp;P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state-price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 113
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Book Description
Author: Mark Watson
Publisher: Oxford University Press
ISBN: 0199549494
Category : Business & Economics
Languages : en
Pages : 432
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Book Description
A volume that celebrates and develops the work of Nobel Laureate Robert Engle, it includes original contributions from some of the world's leading econometricians that further Engle's work in time series economics
