Preference-free option pricing with path-dependent volatility: A closed-form approach
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.
|Date of creation:||1998|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.frbatlanta.org/Email:
More information through EDIRC
|Order Information:|| Email: |
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.:
- Nelson, Daniel B & Foster, Dean P, 1994.
"Asymptotic Filtering Theory for Univariate ARCH Models,"
Econometric Society, vol. 62(1), pages 1-41, January.
- Daniel B. Nelson & Dean P. Foster, 1994. "Asypmtotic Filtering Theory for Univariate Arch Models," NBER Technical Working Papers 0129, National Bureau of Economic Research, Inc.
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- 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.
- 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.
- 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.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- 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.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
When requesting a correction, please mention this item's handle: RePEc:fip:fedawp:98-20. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Meredith Rector)
If references are entirely missing, you can add them using this form.