Journal ArticleDOI
The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing
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In this paper, the maximum likelihood estimator of the Black-Scholes call option price is derived for small sample sizes and the statistically most powerful confidence intervals for the BlackScholes Call option price are constructed.Abstract:
the market requires efficient estimation of the Assuming security price dynamics are governed by a diffusion process and given the publicly most available form of data, this paper provides the maximum likelihood estimator of security price volatility. A Monte Carlo simulation compares the small-sample properties of this and other proposed security price volatility estimators. The resultant maximum likelihood estimator of the Black-Scholes call option price formulation is also derived. For small sample sizes a Monte Carlo simulation study facilitates comparison with other proposed estimation procedures. Also, the statistically most powerful confidence intervals for the BlackScholes call option price are constructed. * We would like to thank the participants of the Statistics Department Seminar and Finance Department Workshop at the University of Michigan for their helpful comments. We are especially grateful to Fred Hoppe, Adrian Tschoegl, and an anonymous referee for their insightful suggestions. Any remaining errors are our responsibility.read more
Citations
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Answering the skeptics: yes, standard volatility models do provide accurate forecasts*
TL;DR: In this article, a voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models and it has been shown that volatility models produce strikingly accurate inter-daily forecasts for the latent volatility factor that would be of interest in most financial applications.
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Forecasting Volatility in Financial Markets: A Review
Abstract: Financial market volatility is an important input for investment, option pricing, and financial market regulation. The emphasis of this review article is on forecasting instead of modelling; it compares the volatility forecasting findings in 93 papers published and written in the last two decades. Provided in this paper as well are volatility definitions, insights into problematic issues of forecast evaluation, data frequency, extreme values and the measurement of "actual" volatility. We compare volatility forecasting performance of two main approaches; historical volatility models and volatility implied from options. Forecasting results are compared across different asset classes and geographical regions.
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Range-Based Estimation of Stochastic Volatility Models
TL;DR: In this paper, the authors proposed using the price range in the estimation of stochastic volatility models and showed that range-based volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise.
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Volatility forecast comparison using imperfect volatility proxies
TL;DR: In this article, the authors derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some useful special cases of this class of robust loss functions.
Posted Content
Volatility Forecast Comparison using Imperfect Volatility Proxies
TL;DR: The authors derive necessary and sufficient conditions on functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some interesting special cases of this class of robust loss functions.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Journal ArticleDOI
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Journal ArticleDOI
The Monte Carlo method.
N. Metropolis,Stanislaw M. Ulam +1 more
TL;DR: In this paper, the authors present a statistical approach to the study of integro-differential equations that occur in various branches of the natural sciences, such as biology and chemistry.
Journal ArticleDOI
On estimating the expected return on the market: An exploratory investigation
TL;DR: In this article, three models of equilibrium expected market returns which reflect the dependence of the market return on the interest rate were analyzed and the non-negativity restriction of the expected excess return was explicity included as part of the specification.
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The Extreme Value Method for Estimating the Variance of the Rate of Return
TL;DR: In this paper, the authors compared the traditional and extreme value methods and concluded that the extreme value method is about 21/2-5 times better, depending on how you choose to measure the difference.