A modified Corrado-Miller implied volatility estimator

• Autorzy: Płuciennik P.
• Języki publikacji: EN

Abstrakty

EN

The implied volatility, i.e. volatility calculated on the basis of option price is a very important parameter in financial econometrics. Usually, it is calculated from the Black-Scholes option pricing formula, but it doesn't have any analytical solution. There are many ways to find it numerically. Unfortunately, all fast estimators give non rigorous results for deep-in or deep-out-of-the-rnoney options. In this paper there are compared some estimators of implied volatility and there are estimated errors for many cases of option price, strike price and real volatility. Furthermore, to reduce error using least squares surface approximation, a new estimator basing on the Corrado-Miller estimator is constructed. There are shown some cases in which the modified Corrado-Miller estimator gives more exact results.

Słowa kluczowe

EN

Black-Scholes formula; Corrado-Miller estimator; implied volatility; surface approximation

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2007
• Tom: Nr 38
• Strony: 115--124
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Płuciennik P.

• Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Umultowska 87, 61-614 Poznań, Poland,

Bibliografia

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• [3] HALLERBACH W.G., An Improved Estimator For Black-Scholes-Merton Implied Volatility, Report Seńes reference number ERS-2004-05Ą-F&A, 2004.
• [4] HULL J., WHITE A., The pricing of options on assets with stochastic volatilities, Journal of Finance, 42(1987), 281-300.
• [5] KELLY M.A., Faster Implied Volatilities via the Implicit Function Theorem, The Financial Review, 2005.
• [6] Li S., The estimation of implied volatility from the Black-Scholes model: some new formulas and their applications, Discussion Paper 1Ą1, Queensland University of Technology, 2003.
• [7] MANASTER S., KOEHLER G., The calculation of implied variances from the Black-Scholes model: A Note, Journal of Finance, 37(1982), 227-230.
• [8] ZunZun.com Interactive 2-Dimensional and 3-Dimensional Data Modeling