Bivariate Normal Mixture Spread Option Valuation
This paper explores the properties of a European spread option valuation method for correlated assets when the marginal distribution each asset return is assumed to be a mixture of normal distributions. In this ‘bivariate normal mixture’ (BNM) approach no-arbitrage option values are just weighted sums of different 2GBM values based on two correlated lognormal diffusions, and likewise for their sensitivities. The main advantage of this approach is that BNM option values are consistent with the volatility smiles for each asset and an implied correlation ‘frown’, both of which are often observed when spread options are priced under the 2GBM assumptions. It is simple to perform an extensive consideration of model values for varying strike, and for different asset volatility and correlation structures. We compare BNM valuations with those based on the ‘2GBM’ assumption of two correlated lognormal diffusions and explain the differences between the BNM values and the 2GBM values of spread options as a weighted sum of six second order 2GBM value sensitivities. We also investigate the BNM sensitivities and these, like the option values, can sometimes be significantly different from those obtained under the 2GBM model. Finally, we show how the correlation frown that is implied by this model is affected as we change the parameters in the bivariate normal mixture density of the asset returns.
|Date of creation:||Dec 2003|
|Date of revision:|
|Publication status:||Published in Quantitative Finance 2004, 4:6, 1-12|
|Contact details of provider:|| Postal: PO Box 218, Whiteknights, Reading, Berks, RG6 6AA|
Phone: +44 (0) 118 378 8226
Fax: +44 (0) 118 975 0236
Web page: http://www.henley.reading.ac.uk/
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.:
- Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-96, Winter.
- 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.
- Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, 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.
- Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Alexander, Carol, 2004. "Normal mixture diffusion with uncertain volatility: Modelling short- and long-term smile effects," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2957-2980, December.
- Damiano Brigo, 2008. "The general mixture-diffusion SDE and its relationship with an uncertain-volatility option model with volatility-asset decorrelation," Papers 0812.4052, arXiv.org.
When requesting a correction, please mention this item's handle: RePEc:rdg:icmadp:icma-dp2003-15. 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: (Marie Pearson)
If references are entirely missing, you can add them using this form.