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Article

Ensuring More Is Better: On the Simultaneous Application of Stock and Options Data to Estimate the GARCH Options Pricing Model

Charles Chang, Hung-Wen Cheng and Cheng-Der Fuh
The Journal of Derivatives Fall 2018, 26 (1) 7-25; DOI: https://doi.org/10.3905/jod.2018.1.067
Charles Chang
is a professor in the Fanhai International School of Finance at Fudan University in Shanghai, China
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Hung-Wen Cheng
is an assistant professor in the department of financial engineering and actuarial mathematics at Soochow University in Taipei, Taiwan (R.O.C.)
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Cheng-Der Fuh
is a professor in the Fanhai International School of Finance at Fudan University in Shanghai, China
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Abstract

The most common approach in fitting option pricing models to market data is first to make an assumption about the underlying asset’s returns process and then develop an option pricing model for that process that is tested against market option prices. The returns process is estimated from historical data, option values are computed, and then compared against a cross-section of prices from the options market. Unfortunately, this often does not work well, and plainly it is inefficient in its use of the data. However, efforts to combine returns data from the asset market and prices from the options market into a single estimation have also not had much success. In this article, Chang, Cheng, and Fuh propose a new procedure to combine data from both markets in the estimation, in which options are assumed to be subject to random pricing noise relative to model values. The additional slack gives the estimator better ability to match prices in both markets. The article contrasts the performance of the full model approach with an approach that only uses stock prices or options prices to fit an option pricing model based on an underlying GARCH process. The value of the combined approach is demonstrated both theoretically as an asymptotic result in the model and also in a Monte Carlo simulation.

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The Journal of Derivatives: 26 (1)
The Journal of Derivatives
Vol. 26, Issue 1
Fall 2018
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Ensuring More Is Better: On the Simultaneous Application of Stock and Options Data to Estimate the GARCH Options Pricing Model
Charles Chang, Hung-Wen Cheng, Cheng-Der Fuh
The Journal of Derivatives Aug 2018, 26 (1) 7-25; DOI: 10.3905/jod.2018.1.067

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Ensuring More Is Better: On the Simultaneous Application of Stock and Options Data to Estimate the GARCH Options Pricing Model
Charles Chang, Hung-Wen Cheng, Cheng-Der Fuh
The Journal of Derivatives Aug 2018, 26 (1) 7-25; DOI: 10.3905/jod.2018.1.067
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