Description Usage Arguments Details Value Author(s) References Examples
mln
is the probability density function of a mixture of two lognormal densities.
1 | dmln(x, alpha.1, meanlog.1, meanlog.2, sdlog.1, sdlog.2)
|
x |
value at which the denisty is to be evaluated |
alpha.1 |
proportion of the first lognormal. Second one is 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 |
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.
out |
density value at x |
Kam Hamidieh
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | #
# 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")
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