Modeling time series information into option prices: An empirical evaluation of statistical projection and GARCH option pricing model

In this paper, we demonstrate how to collect the data and compute the actual value of Black-Scholes Option Pricing Model call option prices for Coca-Cola and PepsiCo.The data for the current stock price and option price are taken from Yahoo Finance and the daily returns variance is computed from daily prices.The time to maturity is computed as the number of days remaining for the stock option.The risk-free rate is obtained from the U.S. Treasury website.

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

The Journal of Derivatives ◽

10.3905/jod.2018.1.067 ◽

2018 ◽

Keyword(s):

Option Pricing ◽

Stock Prices ◽

Options Pricing ◽

Asymptotic Result ◽

Option Prices ◽

Options Market ◽

Pricing Model ◽

Simultaneous Application ◽

Option Values ◽

Option Pricing Model

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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GARCH Generated Volatility Indices of Bitcoin and CRIX

Journal of Risk and Financial Management ◽

10.3390/jrfm13060121 ◽

2020 ◽

Vol 13 (6) ◽

pp. 121 ◽

Cited By ~ 1

Author(s):

Pierre J. Venter ◽

Eben Maré

Keyword(s):

Option Pricing ◽

Term Structure ◽

Implied Volatility ◽

Conditional Heteroskedasticity ◽

Option Prices ◽

Pricing Model ◽

European Option ◽

Short Term ◽

Market Prices ◽

Option Pricing Model

In this paper, the pricing performance of the generalised autoregressive conditional heteroskedasticity (GARCH) option pricing model is tested when applied to Bitcoin (BTCUSD). In addition, implied volatility indices (30, 60-and 90-days) of BTCUSD and the Cyptocurrency Index (CRIX) are generated by making use of the symmetric GARCH option pricing model. The results indicate that the GARCH option pricing model produces accurate European option prices when compared to market prices and that the BTCUSD and CRIX implied volatility indices are similar when compared, this is consistent with expectations because BTCUSD is highly weighted when calculating the CRIX. Furthermore, the term structure of volatility indices indicate that short-term volatility (30 days) is generally lower when compared to longer maturities. Furthermore, short-term volatility tends to increase to higher levels when compared to 60 and 90 day volatility when large jumps occur in the underlying asset.

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The Performance of Skewness and Kurtosis Adjusted Option Pricing Model in Emerging Markets

International Journal of Finance & Banking Studies (2147-4486) ◽

10.20525/ijfbs.v5i3.285 ◽

2016 ◽

Vol 5 (3) ◽

pp. 70-84

Author(s):

Özge Sezgin Alp

Keyword(s):

Emerging Markets ◽

Option Pricing ◽

Option Prices ◽

Pricing Model ◽

European Options ◽

Black Scholes Model ◽

Black Scholes ◽

Option Pricing Model ◽

Skewness And Kurtosis ◽

Pricing Formula

In this study, the option pricing performance of the adjusted Black-Scholes model proposed by Corrado and Su (1996) and corrected by Brown and Robinson (2002), is investigated and compared with original Black Scholes pricing model for the Turkish derivatives market. The data consist of the European options written on BIST 30 index extends from January 02, 2015 to April 24, 2015 for given exercise prices with maturity April 30, 2015. In this period, the strike prices are ranging from 86 to 124. To compare the models, the implied parameters are derived by minimizing the sum of squared deviations between the observed and theoretical option prices. The implied distribution of BIST 30 index does not significantly deviate from normal distribution. In addition, pricing performance of Black Scholes model performs better in most of the time. Black Scholes pricing Formula, Carrado-Su pricing Formula, Implied Parameters

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EFFECTS OF RETURN PREDICTABILITY ON OPTION PRICES WITH STOCHASTIC VOLATILITY FOR THE MARKET PORTFOLIO

Annals of Financial Economics ◽

10.1142/s2010495205500053 ◽

2005 ◽

Vol 01 (01) ◽

pp. 0550005

Author(s):

MELANIE CAO

Keyword(s):

Option Pricing ◽

Interest Rates ◽

Stochastic Volatility ◽

Return Predictability ◽

Option Prices ◽

Pricing Model ◽

Stochastic Interest Rates ◽

Market Portfolio ◽

Stochastic Interest ◽

Option Pricing Model

I examine the effects of return predictability on option prices for the market portfolio in the presence of stochastic volatility and/or stochastic interest rates. The analysis is implemented in an equilibrium framework where a consistent option pricing model is derived with the return predictability and stochastic volatility and the precise link between the actual and the risk neutral measures is endogenized. The equilibrium analysis indicates that the return predictability is induced by the mean-reverting and heteroskedastic features of aggregate dividends. It is shown that risk-neutral option pricing model with the stochastic volatility and/or stochastic interest rates can be consistent with return predictability. Numerical results suggest that (i) models with either perfect predictability or no predictability will significantly overprice long-term options across different strike prices when the return of the underlying exhibits modest predictability; (ii) the stochastic volatility does not affect option prices in a significant way when asset return predictability is properly reflected in the actual stock price process; (iii) when return predictability is correctly specified, the effects of stochastic interest rates are not uniform.

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Univariate and Multivariate GARCH Models Applied to Bitcoin Futures Option Pricing

Journal of Risk and Financial Management ◽

10.3390/jrfm14060261 ◽

2021 ◽

Vol 14 (6) ◽

pp. 261

Author(s):

Pierre J. Venter ◽

Eben Maré

Keyword(s):

Option Pricing ◽

Multivariate Garch ◽

Garch Models ◽

Symmetric Model ◽

Option Prices ◽

Pricing Model ◽

Market Prices ◽

Futures Options ◽

Option Pricing Model ◽

Multivariate Garch Models

In this paper, the Heston–Nandi futures option pricing model is applied to Bitcoin futures options. The model prices are compared to market prices to give an indication of the pricing performance. In addition, a multivariate Bitcoin futures option pricing methodology based on a multivatiate GARCH model is developed. The empirical results show that a symmetric model is a better fit when applied to Bitcoin futures returns, and also produces more accurate option prices compared to market prices for two out of three expiry dates considered.

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