scholarly journals MEAN-REVERTING STOCHASTIC VOLATILITY

2000 ◽  
Vol 03 (01) ◽  
pp. 101-142 ◽  
Author(s):  
JEAN-PIERRE FOUQUE ◽  
GEORGE PAPANICOLAOU ◽  
K. RONNIE SIRCAR
Keyword(s):  
Stochastic Volatility ◽  
Stock Price ◽  
Implied Volatility ◽  
Asset Price ◽  
Market Price ◽  
Price Volatility ◽  
Estimation Procedure ◽  
Derivative Pricing ◽  
Volatility Risk ◽  
Index Value

We present derivative pricing and estimation tools for a class of stochastic volatility models that exploit the observed "bursty" or persistent nature of stock price volatility. An empirical analysis of high-frequency S&P 500 index data confirms that volatility reverts slowly to its mean in comparison to the tick-by-tick fluctuations of the index value, but it is fast mean-reverting when looked at over the time scale of a derivative contract (many months). This motivates an asymptotic analysis of the partial differential equation satisfied by derivative prices, utilizing the distinction between these time scales. The analysis yields pricing and implied volatility formulas, and the latter is used to "fit the smile" from European index option prices. The theory identifies the important group parameters that are needed for the derivative pricing and hedging problem for European-style securities, namely the average volatility and the slope and intercept of the implied volatility line, plotted as a function of the log-moneyness-to-maturity-ratio. The results considerably simplify the estimation procedure, and the data produces estimates of the three important parameters which are found to be stable within periods where the underlying volatility is close to being stationary. These segments of stationarity are identified using a wavelet-based tool. The remaining parameters, including the growth rate of the underlying, the correlation between asset price and volatility shocks, the rate of mean-reversion of the volatility and the market price of volatility risk can be roughly estimated, but are not needed for the asymptotic pricing formulas for European derivatives. The extension to American and path-dependent contingent claims is the subject of future work.

Informed Trading in the Stock Market and Option-Price Discovery

2020 ◽  
pp. 1-40 ◽  
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.

A Simple Model for Option Pricing with Jumping Stochastic Volatility

1998 ◽  
Vol 01 (04) ◽  
pp. 487-505 ◽  
Author(s):  
Stefano Herzel
Keyword(s):  
Implied Volatility ◽  
Market Price ◽  
Volatility Risk ◽  
Simple Modification ◽  
Closed Form Solutions ◽  
Black Scholes Model ◽  
A Value ◽  
Black Scholes ◽  
Delta Hedging ◽  
Actual Price

This paper proposes a simple modification of the Black–Scholes model by assuming that the volatility of the stock may jump at a random time τ from a value σa to a value σb. It shows that, if the market price of volatility risk is unknown, but constant, all contingent claims can be valued from the actual price C0, of some arbitrarily chosen "basis" option. Closed form solutions for the prices of European options as well as explicit formulas for vega and delta hedging are given. All such solutions only depend on σa, σb and C0. The prices generated by the model produce a "smile"-shaped curve of the implied volatility.

The Potential Impact of More Frequent Financial Reporting and Assurance: User, Preparer, and Auditor Assessments (Retracted)

2007 ◽  
Vol 4 (1) ◽  
pp. 47-67 ◽  
Author(s):  
James E. Hunton ◽  
Arnold M. Wright ◽  
Sally Wright
Keyword(s):  
Financial Reporting ◽  
Stock Price ◽  
Cost Of Capital ◽  
Market Price ◽  
Price Volatility ◽  
Financial Statements ◽  
Future Earnings ◽  
Decision Usefulness ◽  
Consensus Forecasts

The purpose of this study is to examine some of the potential impacts of more frequent financial reporting and concurrent assurance, as assessed by members of the assurer, preparer, and investor communities. Two hundred and fifteen participants (84 auditors, 30 controllers, 80 investors, as surrogated by MBA students, and 21 sell-side analysts) took part in an experiment where they received a case situation involving a company that was planning to voluntarily change from quarterly to monthly (daily) external financial statement reporting, without (with) assurance. After reading the case materials, the participants assessed the likely effects of such changes on the decision usefulness of financial statements, quality of earnings, financial reporting behavior, stock market price volatility, analysts' consensus forecasts, and cost of capital. The results indicate that monthly reporting without assurance would significantly enhance the decision usefulness of financial statements, improve the quality of earnings, and reduce managements' aggressiveness with respect to discretionary accounting accruals, estimates, and principles; further, the findings suggest stock price volatility would be lower, analyst consensus of future earnings estimates would increase, and cost of capital would decrease. Assessments of daily reporting were consistent with monthly reporting, yet significantly stronger. The inclusion of concurrent auditor assurance resulted in directionally consistent yet significantly pronounced results in both monthly and daily reporting conditions on all measures. Additionally, participants agreed that providing monthly reports would be technically and economically feasible at this time, while daily reporting would not be feasible.

scholarly journals A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Elisa Alòs ◽  
Jorge A. León ◽  
Monique Pontier ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Asset Price ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Time Behavior ◽  
Volatility Model ◽  
Jump Diffusion Model ◽  
White Type ◽  
Short Time

We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

scholarly journals A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Raúl Merino ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Stock Price ◽  
Implied Volatility ◽  
Option Price ◽  
Exponential Model ◽  
Heston Model ◽  
Call Option ◽  
Itô Calculus ◽  
Decomposition Formula ◽  
Price Decomposition

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model, extending a previous decomposition formula for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used for this purpose are nonanticipative. In particular, we also see that equivalent results can be obtained by using Functional Itô Calculus. Using the same generalizing ideas, we also extend to nonexponential models the alternative call option price decomposition formula written in terms of the Malliavin derivative of the volatility process. Finally, we give a general expression for the derivative of the implied volatility under both the anticipative and the nonanticipative cases.

scholarly journals An Empirical Analysis of Stock Price Risk in Chinese Growth Enterprises Market - A GARCH-VaR Approach

2016 ◽  
Vol 12 (22) ◽  
pp. 341
Author(s):  
Maoguo WU ◽  
Xin LUO
Keyword(s):  
Stock Price ◽  
Price Volatility ◽  
High Technology ◽  
Securities Market ◽  
Price Risk ◽  
Volatility Risk ◽  
Financing Channels ◽  
Risk Characteristics ◽  
Empirical Tests ◽  
Healthy Growth

The aim of Growth Enterprises Market (GEM) is to provide financing channels to burgeoning and high-technology companies which cannot be listed in the main board. GEM is a supplement to the main board. As an emerging securities market, GEM shows a unique volatility compared with the main board. The volatility of GEM has connections and differences with the main board market. Studying the price volatility of GEM contributes directly to the healthy growth of GEM and the main board. This paper investigates the risk characteristics of GEM and provides several measures to deal with the risk. In this paper, VaR based on GARCH model is utilized for empirical tests. Therefore, this paper studies the characteristics and the extent of volatility risk of GEM stock price systematically.

PENGARUH IT SPENDING TERHADAP KINERJA PERUSAHAAN PADA PERUSAHAAN TELEKOMUNIKASI YANG TERDAFTAR DI BURSA EFEK SELURUH ASIA TENGGARA PADA TAHUN 2009-2011

MODUS ◽  
2016 ◽  
Vol 26 (2) ◽  
pp. 93
Author(s):  
Irene Adrayani
Keyword(s):  
Stock Price ◽  
Sampling Method ◽  
Capital Expenditure ◽  
Stock Exchange ◽  
Market Price ◽  
Market Value ◽  
Company Performance ◽  
Corporate Value ◽  
Accounting Information System ◽  
Company Value

This study aims to get empirical evidence about the infuence of IT spending on corporate value by testing the efect of IT spending on corporate value by using Tobin’s Q. Te higher the stock price, the higher the company value as well as investors’ assessment. The market price of the company’s stocks refects investors’ assessment of the overall equity held. Of the stock price refects investor can provide an assessment of a company. Tobin’s Q is the ratio of the market value of the company’s assets as measured by the market value of the outstanding stocks and debt (enterprise value) to the replacement cost of the assets of the company. The sampling method is based on purposive sampling method with the purpose to obtain a sample that meets the criteria. Tis study used a sample taken from a telecommunications company listed on the Stock Exchange throughout Southeast Asia during the period of 2009-2011. The hypothesis in this study was tested using simple regression. Based on data analysis, the result that the variable IT spending does not afect the company value.Keywords: accounting information system, Tobin’s Q, IT spending, capital expenditure, company performance

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