Statistics and Its Interface

Volume 6 (2013)

Number 4

Volatility estimation by combining stock price data and option data

Pages: 427 – 433

DOI: http://dx.doi.org/10.4310/SII.2013.v6.n4.a2

Authors

Yi Liu (Department of Statistics, University of Wisconsin, Madison, Wi., U.S.A.)

Yazhen Wang (Department of Statistics, University of Wisconsin, Madison, Wi., U.S.A.)

Abstract

Volatility modeling and analysis are traditionally based on either historical price data or option data. Finance theory shows that option prices heavily depend on the underlying stocks’ prices, thus the two kinds of data are related. This paper explores the approach that combines both stock price data and option data to perform the statistical analysis of volatility. We investigate the Black-Scholes model and an exponential GARCH model and derive the relationship among the Fisher information for volatility estimation based on stock price data alone or option data alone as well as joint volatility estimation for combining stock price data and option data. Under the Black-Scholes model an asymptotic theory for the joint estimation is established, and a simulation study is conducted to check finite sample performances of the proposed joint estimation.

Keywords

Black-Scholes model, diffusion, GARCH model, option data, stock data, volatility estimation

2010 Mathematics Subject Classification

Primary 62M10. Secondary 62F10, 62F12, 91B25, 91B84.

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