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

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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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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Sound Deposit Insurance Pricing Using a Machine Learning Approach

Risks ◽

10.3390/risks7020045 ◽

2019 ◽

Vol 7 (2) ◽

pp. 45 ◽

Cited By ~ 2

Author(s):

Hirbod Assa ◽

Mostafa Pouralizadeh ◽

Abdolrahim Badamchizadeh

Keyword(s):

Machine Learning ◽

Moral Hazard ◽

Deposit Insurance ◽

Implied Volatility ◽

Calibration Method ◽

Quadratic Model ◽

Learning Approach ◽

Conceptual Issue ◽

Hazard Risk ◽

Machine Learning Approach

While the main conceptual issue related to deposit insurances is the moral hazard risk, the main technical issue is inaccurate calibration of the implied volatility. This issue can raise the risk of generating an arbitrage. In this paper, first, we discuss that by imposing the no-moral-hazard risk, the removal of arbitrage is equivalent to removing the static arbitrage. Then, we propose a simple quadratic model to parameterize implied volatility and remove the static arbitrage. The process of removing the static risk is as follows: Using a machine learning approach with a regularized cost function, we update the parameters in such a way that butterfly arbitrage is ruled out and also implementing a calibration method, we make some conditions on the parameters of each time slice to rule out calendar spread arbitrage. Therefore, eliminating the effects of both butterfly and calendar spread arbitrage make the implied volatility surface free of static arbitrage.

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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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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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Stock Return Autocorrelation and Individual Equity Option Prices

Journal of Business Theory and Practice ◽

10.22158/jbtp.v9n1p51 ◽

2021 ◽

Vol 9 (1) ◽

pp. p51

Author(s):

Fei Fang

Keyword(s):

Stock Return ◽

Implied Volatility ◽

Option Price ◽

Option Prices ◽

Equity Options ◽

First Order ◽

Price Structure ◽

Clear Link ◽

Equity Option ◽

The Impact

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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