Bivariate Normal Mixture Spread Option Valuation
AbstractThis 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.
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Bibliographic InfoPaper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2003-15.
Length: 28 pages
Date of creation: Dec 2003
Date of revision:
Publication status: Published in Quantitative Finance 2004, 4:6, 1-12
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More information through EDIRC
spread option; implied correlation; bivariate normal mixture density;
Other versions of this item:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
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