This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Preference-free option pricing with path-dependent volatility: A closed-form approach

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Steven L. Heston
Saikat Nandi
Abstract

This paper shows how one can obtain a continuous-time preference-free option pricing model with a path-dependent volatility as the limit of a discrete-time GARCH model. In particular, the continuous-time model is the limit of a discrete-time GARCH model of Heston and Nandi (1997) that allows asymmetry between returns and volatility. For the continuous-time model, one can directly compute closed-form solutions for option prices using the formula of Heston (1993). Toward that purpose, we present the necessary mappings, based on Foster and Nelson (1994), such that one can approximate (arbitrarily closely) the parameters of the continuous-time model on the basis of the parameters of the discrete-time GARCH model. The discrete-time GARCH parameters can be estimated easily just by observing the history of asset prices. ; Unlike most option pricing models that are based on the absence of arbitrage alone, a parameter related to the expected return/risk premium of the asset does appear in the continuous-time option formula. However, given other parameters, option prices are not at all sensitive to the risk premium parameter, which is often imprecisely estimated.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help file. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.frbatlanta.org/frbatlanta/filelegacydocs/wp9820.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 98-20.

Download reference. The following formats are available: HTML, plain text, BibTeX, RIS (EndNote), ReDIF
Length:
Date of creation: 1998
Date of revision:
Handle: RePEc:fip:fedawp:98-20

Contact details of provider:
Postal: 1000 Peachtree St., N.E., Atlanta, Georgia 30309
Phone: 404-521-8500
Email:
Web page: http://www.frbatlanta.org/
More information through EDIRC

Order Information:
Email:

For technical questions regarding this item, or to correct its listing, contact: (Diane Rosenberger).

Related research
Keywords: Options (Finance)

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July. [Downloadable!] (restricted)
  2. 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)
  3. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January. [Downloadable!] (restricted)
    Other versions:
  4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June. [Downloadable!] (restricted)
  5. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  6. 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)
  7. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
  8. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December. [Downloadable!] (restricted)
  9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
Full references

Cited by:
(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. Carey, Alexander, 2008. "Natural volatility and option pricing," MPRA Paper 6709, University Library of Munich, Germany. [Downloadable!]
Statistics
Access and download statistics

Did you know? You can use convenient plug-ins to search directly IDEAS from your browser.

This page was last updated on 2008-7-28.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.