Simple approximations for option pricing under mean reversion and stochastic volatility
This paper provides simple approximations for evaluating option prices and implied volatilities under stochastic volatility. Simple recursive formulae are derived that can easily be implemented in spreadsheets. The traditional random walk assumption, dominating in the analysis of financial markets, is compared with mean reversion which is often more relevant in commodity markets. Deterministic components in the mean and volatility are taken into consideration to allow for seasonality, another frequent aspect of commodity markets. The stochastic volatility is suitably modelled by GARCH. An application to electricity options shows that the choice between a random walk and a mean reversion model can have strong effects for predictions of implied volatilities even if the two models are statistically close to each other.
|Date of creation:||08 Jul 2003|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 31 10 4081111
Web page: http://www.eur.nl/ese
More information through EDIRC
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.:
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Aydinli, Gökhan, 2002. "Net based spreadsheets in quantitative finance," SFB 373 Discussion Papers 2002,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-73, July.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- 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.
- Hafner, Christian M. & Herwartz, Helmut, 1999.
"Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis,"
SFB 373 Discussion Papers
1999,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
- G. William Schwert, 1988.
"Why Does Stock Market Volatility Change Over Time?,"
NBER Working Papers
2798, National Bureau of Economic Research, Inc.
- Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-53, December.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- 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.
When requesting a correction, please mention this item's handle: RePEc:ems:eureir:1720. 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: (RePub)
If references are entirely missing, you can add them using this form.