Real World Pricing for a Modified Constant Elasticity of Variance Model
AbstractThis paper considers a modified constant elasticity of variance (MCEV) model. This model uses the familiar constant elasticity of variance form for the volatility of the growth optimal portfolio (GOP) in a continuous market. It leads to a GOP that follows the power of a time-transformed squared Bessel process. This paper derives analytic real-world prices for zero-coupon bonds, instantaneous forward rates and options on the GOP that are both theoretically revealing and computationally efficient. In addition, the paper examines options on exchange prices and options on zero-coupon bonds under the MCEV model. The semi-analytic prices derived for options on zero-coupon bonds can subsequently be used to price interest rate caps and floors.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 237.
Date of creation: 01 Nov 2008
Date of revision:
benchmark approach; real-world pricing; growth optimal portfolio; constant elasticity of variance; zero-coupon bonds; exchange prices; interest rate caps and floors;
Other versions of this item:
- Shane Miller & Eckhard Platen, 2010. "Real-World Pricing for a Modified Constant Elasticity of Variance Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(2), pages 147-175.
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-03-14 (All new papers)
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.:
- 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.
- Boyle, Phelim P. & Tian, Yisong “Sam”, 1999. "Pricing Lookback and Barrier Options under the CEV Process," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 241-264, June.
- Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(04), pages 533-554, November.
- Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
- 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.
- MacBeth, James D & Merville, Larry J, 1980. " Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
- Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
- Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
- Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
- Chin Yang & Anthony Loviscek & Hui Cheng & Ken Hung, 2012. "A Note on Allen’s Arc Elasticity with Arithmetic, Geometric and Harmonic Means," Atlantic Economic Journal, International Atlantic Economic Society, vol. 40(2), pages 161-171, June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford).
If references are entirely missing, you can add them using this form.