Stock Return Autocorrelation and Individual Equity Option Prices

This study demonstrates empirically the impact of stock return autocorrelation on the prices of individual equity option. The option prices are characterized by the level and slope of implied volatility curves, and the stock return autocorrelation is measured by variance ratio and first-order serial return autocorrelation. Using a large sample of U.S. stocks, we show that there is a clear link between stock return autocorrelation and individual equity option prices: a higher stock return autocorrelation leads to a lower level of implied volatility (compared to realized volatility) and a steeper implied volatility curve. The stock return autocorrelation is more important in explaining the level of implied volatility curve for relatively small stocks. The relation between stock return autocorrelation and option price structure is more pronounced when market is volatile, especially during financial crisis. The stock return autocorrelation is more important in explaining the level of implied volatility curve for relatively small stocks. Thus, stock return autocorrelation can help differentiate the price structure across individual equity options.

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ANALYSIS OF MARKET VOLATILITY VIA A DYNAMICALLY PURIFIED OPTION PRICE PROCESS

Annals of Financial Economics ◽

10.1142/s2010495214500067 ◽

2014 ◽

Vol 09 (03) ◽

pp. 1450006 ◽

Cited By ~ 1

Author(s):

CHUONG LUONG ◽

NIKOLAI DOKUCHAEV

Keyword(s):

Stock Price ◽

Implied Volatility ◽

Financial Time Series ◽

Option Price ◽

Option Prices ◽

Price Process ◽

Volatility Index ◽

Quadratic Interpolation ◽

Dynamic Estimation ◽

The Impact

The paper studies methods of dynamic estimation of volatility for financial time series. We suggest to estimate the volatility as the implied volatility inferred from some artificial "dynamically purified" price process that in theory allows to eliminate the impact of the stock price movements. The complete elimination would be possible if the option prices were available for continuous sets of strike prices and expiration times. In practice, we have to use only finite sets of available prices. We discuss the construction of this process from the available option prices using different methods. In order to overcome the incompleteness of the available option prices, we suggests several interpolation approaches, including the first order Taylor series extrapolation and quadratic interpolation. We examine the potential of the implied volatility derived from this proposed process for forecasting of the future volatility, in comparison with the traditional implied volatility process such as the volatility index VIX.

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Option pricing under the fractional stochastic volatility model

ANZIAM Journal ◽

10.21914/anziamj.v63.15204 ◽

2021 ◽

Vol 63 ◽

pp. 123-142

Author(s):

Yuecai Han ◽

Zheng Li ◽

Chunyang Liu

Keyword(s):

Brownian Motion ◽

Option Pricing ◽

Fractional Brownian Motion ◽

Stochastic Volatility ◽

Option Price ◽

Stochastic Volatility Model ◽

Option Prices ◽

European Call Option ◽

Volatility Model ◽

The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

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Informed Trading in the Stock Market and Option-Price Discovery

Journal of Financial and Quantitative Analysis ◽

10.1017/s0022109020000629 ◽

2020 ◽

pp. 1-40 ◽

Cited By ~ 1

Author(s):

Pierre Collin-Dufresne ◽

Vyacheslav Fos ◽

Dmitry Muravyev

Keyword(s):

Stock Market ◽

Stock Price ◽

Implied Volatility ◽

Common Knowledge ◽

Option Price ◽

Price Volatility ◽

Informed Trading ◽

Flow Dynamics ◽

Option Prices ◽

Market Makers

Abstract When activist shareholders file Schedule 13D filings, the average stock-price volatility drops by approximately 10%. Prior to filing days, volatility information is reflected in option prices. Using a comprehensive sample of trades by Schedule 13D filers that reveals on what days and in what markets they trade, we show that on days when activists accumulate shares, option-implied volatility decreases, implied volatility skew increases, and implied volatility time slope increases. The evidence is consistent with a theoretical model where it is common knowledge that informed trading occurs only in the stock market and market makers update option prices based on stock-price and order-flow dynamics.

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OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

The ANZIAM Journal ◽

10.1017/s1446181121000225 ◽

2021 ◽

pp. 1-20

Author(s):

Y. HAN ◽

Z. LI ◽

C. LIU

Keyword(s):

Brownian Motion ◽

Option Pricing ◽

Fractional Brownian Motion ◽

Stochastic Volatility ◽

Option Price ◽

Stochastic Volatility Model ◽

Option Prices ◽

European Call Option ◽

Volatility Model ◽

The Impact

Abstract We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented.

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Correcting the Bias in the Practitioner Black-Scholes Method

Journal of Risk and Financial Management ◽

10.3390/jrfm12040157 ◽

2019 ◽

Vol 12 (4) ◽

pp. 157

Author(s):

Yun Yin ◽

Peter G. Moffatt

Keyword(s):

Linear Regression ◽

Implied Volatility ◽

Option Price ◽

Option Prices ◽

Technical Problems ◽

Black Scholes ◽

Option Values ◽

Non Linear ◽

Alternative Means ◽

Log Linear

We address a number of technical problems with the popular Practitioner Black-Scholes (PBS) method for valuing options. The method amounts to a two-stage procedure in which fitted values of implied volatilities (IV) from a linear regression are plugged into the Black-Scholes formula to obtain predicted option prices. Firstly we ensure that the prediction from stage one is positive by using log-linear regression. Secondly, we correct the bias that results from the transformation applied to the fitted values (i.e., the Black-Scholes formula) being a highly non-linear function of implied volatility. We apply the smearing technique in order to correct this bias. An alternative means of implementing the PBS approach is to use the market option price as the dependent variable and estimate the parameters of the IV equation by the method of non-linear least squares (NLLS). A problem we identify with this method is one of model incoherency: the IV equation that is estimated does not correspond to the set of option prices used to estimate it. We use the Monte Carlo method to verify that (1) standard PBS gives biased option values, both in-sample and out-of-sample; (2) using standard (log-linear) PBS with smearing almost completely eliminates the bias; (3) NLLS gives biased option values, but the bias is less severe than with standard PBS. We are led to conclude that, of the range of possible approaches to implementing PBS, log-linear PBS with smearing is preferred on the basis that it is the only approach that results in valuations with negligible bias.

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Implied volatility skews and stock return skewness and kurtosis implied by stock option prices

European Journal of Finance ◽

10.1080/135184797337543 ◽

1997 ◽

Vol 3 (1) ◽

pp. 73-85 ◽

Cited By ~ 45

Author(s):

C. J. Corrado ◽

Tie Su

Keyword(s):

Stock Return ◽

Implied Volatility ◽

Stock Option ◽

Option Prices ◽

Skewness And Kurtosis

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Machine Learning to Compute Implied Volatility from European/American Options Considering Dividend Yield

Proceedings ◽

10.3390/proceedings2020054061 ◽

2020 ◽

Vol 54 (1) ◽

pp. 61

Author(s):

Shuaiqiang Liu ◽

Álvaro Leitao ◽

Anastasia Borovykh ◽

Cornelis W. Oosterlee

Keyword(s):

Machine Learning ◽

Implied Volatility ◽

Numerical Technique ◽

American Options ◽

Option Price ◽

Inverse Function ◽

European American ◽

Option Prices ◽

Early Exercise ◽

Machine Learning Approach

Computing implied volatility from observed option prices is a frequent and challenging task in finance, even more in the presence of dividends. In this work, we employ a data-driven machine learning approach to determine the Black–Scholes implied volatility, including European-style and American-style options. The inverse function of the pricing model is approximated by an artificial neural network, which decouples the offline (training) and online (prediction) phases and eliminates the need for an iterative process to solve a minimization problem. Meanwhile, two challenging issues are tackled to improve accuracy and robustness, i.e., steep gradients of the volatility with respect to the option price and irregular early-exercise domains for American options. It is shown that deep neural networks can be used as an efficient numerical technique to compute implied volatility from European/American options. An extended version of this work can be found in .

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THE STOCHASTIC INTENSITY SSRD MODEL IMPLIED VOLATILITY PATTERNS FOR CREDIT DEFAULT SWAP OPTIONS AND THE IMPACT OF CORRELATION

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024906003597 ◽

2006 ◽

Vol 09 (03) ◽

pp. 315-339 ◽

Cited By ~ 9

Author(s):

DAMIANO BRIGO ◽

LAURENT COUSOT

Keyword(s):

Implied Volatility ◽

Option Price ◽

Credit Default Swap ◽

Analytical Approximation ◽

Market Model ◽

Model Parameters ◽

Qualitative Behavior ◽

Credit Default ◽

Default Swap ◽

The Impact

In this paper we investigate implied volatility patterns in the Shifted Square Root Diffusion (SSRD) model as functions of the model parameters. We begin by recalling the Credit Default Swap (CDS) options market model that is consistent with a market Black-like formula, thus introducing a notion of implied volatility for CDS options. We examine implied volatilities coming from SSRD prices and characterize the qualitative behavior of implied volatilities as functions of the SSRD model parameters. We introduce an analytical approximation for the SSRD implied volatility that follows the same patterns in the model parameters and that can be used to have a first rough estimate of the implied volatility following a calibration. We compute numerically the CDS-rate volatility smile for the adopted SSRD model. We find a decreasing pattern of SSRD implied volatilities in the interest-rate/intensity correlation. We check whether it is possible to assume zero correlation after the option maturity in computing the option price.

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