price.mln.option: Price Options on Mixture of Lognormals
In RND: Risk Neutral Density Extraction Package

Description Usage Arguments Details Value Author(s) References Examples

mln.option.price gives the price of a call and a put option at a strike when the risk neutral density is a mixture of two lognormals.

1	price.mln.option(r, te, y, k, alpha.1, meanlog.1, meanlog.2, sdlog.1, sdlog.2)

`r`	risk free rate
`te`	time to expiration
`y`	dividend yield
`k`	strike
`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

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.

`call`	call price
`put`	put price
`s0`	current value of the asset as implied by the mixture distribution

Kam Hamidieh

F. Gianluca and A. Roncoroni (2008) Implementing Models in Quantitative Finance: Methods and Cases

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

#
# Try out a range of options
#

r  = 0.05
te = 60/365
k  = 700:1300
y  = 0.02
meanlog.1 = 6.80
meanlog.2 = 6.95
sdlog.1   = 0.065
sdlog.2   = 0.055
alpha.1   = 0.4


mln.prices = price.mln.option(r = r, y = y, te = te, k = k, alpha.1 = alpha.1, 
  meanlog.1 = meanlog.1, meanlog.2 = meanlog.2, sdlog.1 = sdlog.1, sdlog.2 = sdlog.2)

par(mfrow=c(1,2))
plot(mln.prices$call ~ k)
plot(mln.prices$put  ~ k)
par(mfrow=c(1,1))