A Closed-Form GARCH Option Valuation Model

Heston, Steven L.; Nandi, Saikat

doi:10.2139/ssrn.210009

Cited by 260 publications

(499 citation statements)

References 35 publications

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“…Second, the influence of this behavior on asset liquidity and market microstructure could be analyzed in detail including an empirical analysis of the probability estimation of heuristic-driven traders. Third, the application of the proposed model in mathematical finance could reveal further interesting patterns; in particular, asymmetric stochastic volatility models (Heston and Nandi, 2000) in option pricing are found to provide better estimates on option prices and fit the "volatility smile" of the Black-Scholes implied volatilities, which regressions could be further improved by including the proposed model described in this paper. Finally, the introduction of cognitive research, such as the neuroeconomic approach, could reveal further underlying factors behind the behavioral patterns presented in this paper.…”

Section: Discussionmentioning

confidence: 90%

Microfoundations of Heteroscedasticity: A Loss-Aversion-Based Explanation of Asymmetric GARCH Models

Ormos

Timotity

2016

SSRN Journal

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This paper provides a theoretical explanation for the heteroscedasticity of asset returns. In line with existing empirical results, our model yields an asymmetric relationship between stock return and volatility. Based on the simple assumptions that investors behave according to Prospect Theory and are subject to mental accounting in a dynamic setting, we analytically derive the unit-root versions of two of the best fitting heteroscedasticity models (EGARCH and TGARCH). The model is supported by our empirical results from two different sides: first, analysis of individual trading data shows that investors indeed become risk-seeking right after losses and more risk-averse subsequent to gains; second, the parameter estimation of our volatility model yields the predicted negative relationship between abnormal returns and subsequent volatility.Keywords: Asymmetric volatility; Risk seeking; Prospect theory; TGARCH; EGARCH; Volatility dynamics; Market microstructure; Heuristic-driven trader JEL classification: C58; C93; G02; G11; G12 Acknowledgements: We gratefully acknowledge the help of Terry Odean, who provided us the individual trading dataset. We also would like to express our gratitude for the thoughtful remarks of Adam Zawadowski, which have significantly contributed to our paper. We thank Zsolt Bihary and Niklas Wagner for their comments and suggestions of at the 6th Annual Abstract This paper provides a theoretical explanation for the heteroscedasticity of asset returns. In line with existing empirical results, our model yields an asymmetric relationship between stock return and volatility. Based on the simple assumptions that investors behave according to Prospect Theory and are subject to mental accounting in a dynamic setting, we analytically derive the unit-root versions of two of the best fitting heteroscedasticity models (EGARCH and TGARCH). The model is supported by our empirical results from two different sides: first, analysis of individual trading data shows that investors indeed become risk-seeking right after losses and more risk-averse subsequent to gains; second, the parameter estimation of our volatility model yields the predicted negative relationship between abnormal returns and subsequent volatility.

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Section: Discussionmentioning

confidence: 90%

Microfoundations of Heteroscedasticity: A Loss-Aversion-Based Explanation of Asymmetric GARCH Models

Ormos

Timotity

2016

SSRN Journal

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“…The factors are actually option prices for different characteristics (call and put, m ∈ {0.8, 1, 1.2}), and τ ∈ {30, 60, 90 days}, obtained with the Heston Nandi GARCH (HNG) model. We choose it because HNG is a discrete time series model based on an asymmetric GARCH process for the spot asset price with a closed-form solution for option prices (Heston and Nandi 2000). Thus, it is simple and can be quickly implemented computationally.…”

Section: Predictor Variables and Factorsmentioning

confidence: 99%

Semi-parametric forecasts of the implied volatility surface using regression trees

Audrino

Colangelo

2009

Stat Comput

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We present a new semi-parametric model for the prediction of implied volatility surfaces that can be estimated using machine learning algorithms. Given a reasonable starting model, a boosting algorithm based on regression trees sequentially minimizes generalized residuals computed as differences between observed and estimated implied volatilities. To overcome the poor predictive power of existing models, we include a grid in the region of interest, and implement a cross-validation strategy to find an optimal stopping value for the boosting procedure. Back testing the out-of-sample performance on a large data set of implied volatilities from S&P 500 options, we provide empirical evidence of the strong predictive power of our model.

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“…2 See, for example Heston and Nandi (2000) that report significant path dependency in the volatility of the S&P 500 index returns. mentals (the state of the economy, dividends growth, etc.)…”

Section: Introductionmentioning

confidence: 99%