RND (version 1.2)

dmln: Density of Mixture Lognormal

Description

mln is the probability density function of a mixture of two lognormal densities.

Usage

dmln(x, alpha.1, meanlog.1, meanlog.2, sdlog.1, sdlog.2)

Arguments

x

value at which the denisty is to be evaluated

alpha.1

proportion of the first lognormal. Second one is 1 - alpha.1

meanlog.1

mean of the log of the first lognormal

meanlog.2

mean of the log of the second lognormal

sdlog.1

standard deviation of the log of the first lognormal

sdlog.2

standard deviation of the log of the second lognormal

Value

Details

mln is the density f(x) = alpha.1 * g(x) + (1 - alpha.1) * h(x), where g and h are densities of two lognormals with parameters (mean.log.1, sdlog.1) and (mean.log.2, sdlog.2) respectively.

References

B. Bahra (1996): Probability distribution of future asset prices implied by option prices. Bank of England Quarterly Bulletin, August 1996, 299-311

P. Soderlind and L.E.O. Svensson (1997) New techniques to extract market expectations from financial instruments. Journal of Monetary Economics, 40, 383-429

E. Jondeau and S. Poon and M. Rockinger (2007): Financial Modeling Under Non-Gaussian Distributions Springer-Verlag, London

Examples

#
# A bimodal risk neutral density!
#

mln.alpha.1   = 0.4
mln.meanlog.1 = 6.3
mln.meanlog.2 = 6.5
mln.sdlog.1   = 0.08
mln.sdlog.2   = 0.06

k  = 300:900
dx = dmln(x = k, alpha.1 = mln.alpha.1, meanlog.1 = mln.meanlog.1, 
         meanlog.2 = mln.meanlog.2, 
         sdlog.1 = mln.sdlog.1, sdlog.2 = mln.sdlog.2)
plot(dx ~ k, type="l")