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On Estimation of Volatility Surface and Prediction of Future Spot Volatility

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Author Info
Fima Klebaner
Truc Le
Robert Liptser
Abstract

A stochastic process v ( t ) is considered as a model for asset's spot volatility. A new approach is introduced for predicting future spot volatility and future volatility surface using a finite set of observed option prices. When the volatility parameter &sgr; 2 in the Black--Scholes formulais represented by the integrated volatility , then the local volatility surface can be estimated. The main idea is to linearize the expressions for implied volatility by using a result on Normal correlation. This linearization is obtained by introducing various ad hoc approximations.

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Publisher Info
Article provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 13 (2006)
Issue (Month): 3 (September)
Pages: 245-263
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Handle: RePEc:taf:apmtfi:v:13:y:2006:i:3:p:245-263

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  2. Laurence K. Eisenberg & Robert A. Jarrow, 1991. "Option pricing with random volatilities in complete markets," Working Paper 91-16, Federal Reserve Bank of Atlanta.
  3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  5. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 293-326. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Vyacheslav Abramov & Fima Klebaner, 2007. "Estimation and Prediction of a Non-Constant Volatility," Asia-Pacific Financial Markets, Springer, vol. 14(1), pages 1-23, March. [Downloadable!] (restricted)
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