Volatility smile

About: Volatility smile is a research topic. Over the lifetime, 8702 publications have been published within this topic receiving 318440 citations.

On the Estimation of Security Price Volatilities from Historical Data

Abstract: This paper examines the problem of estimating capital asset price volatility parameters from the most available forms of public data. While many varieties of such data are possible, we shall consider here only those which are truly universal in their accessibility to investors, namely, data appearing in the financial pages of the newspaper. In particular, we shall consider volatility estimators which are based upon the historical opening, closing, high, and low prices and transaction volume. Alternative estimators of volatility may be constructed from such data as significant news events, "fundamental" information regarding a company's prospects, and other forms of publicly available data, but these will not be considered here. Any parameter-estimation procedure must begin with a maintained hypothesis regarding the structural model within which estimation is to be made. Our structural model is given exposition in Section II. Section III discusses the "classical" Improved estimators of security price volatilities are formulated. These estimators employ data of the type commonly found in the financial pages of a newspaper: the high, low, opening, and closing prices and the transaction volume. The new estimators are seen to have relative efficiencies that are considerably higher than the standard estimators.

A Jump-Diffusion Model for Option Pricing

Abstract: Brownian motion and normal distribution have been widely used in the Black--Scholes option-pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called "volatility smile" in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jump-diffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path-dependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.

Alternative Models for Conditional Stock Volatility

Abstract: This paper compares several statistical models for monthly stock return volatility. The focus is on U.S. data from 1834-19:5 because the post-1926 data have been analyzed in more detail by others. Also, the Great Depression had levels of stock volatility that are inconsistent with stationary models for conditional heteroskedasticity, We show the importance of nonlinearities in stock return behavior that are not captured by conventional ARCH or GARCH models. We also show the nonstationariry of stock volatility, even over the 1834-1925 period.