MOE: Mother of All Extractions
In RND: Risk Neutral Density Extraction Package

Description Usage Arguments Details Value Author(s) References Examples

MOE function extracts the risk neutral density based on all models and summarizes the results.

1 2	MOE(market.calls, call.strikes, market.puts, put.strikes, call.weights = 1, put.weights = 1, lambda = 1, s0, r, te, y, file.name = "myfile")

`market.calls`	market calls (most expensive to cheapest)
`call.strikes`	strikes for the calls (smallest to largest)
`market.puts`	market calls (cheapest to most expensive)
`put.strikes`	strikes for the puts (smallest to largest)
`call.weights`	Weights for the calls (must be in the same order of calls)
`put.weights`	Weights for the puts (must be in the same order of puts)
`lambda`	Penalty parameter to enforce the martingale condition
`s0`	Current asset value
`r`	risk free rate
`te`	time to expiration
`y`	dividend yield
`file.name`	File names where analysis is to be saved. SEE DETAILS!

The MOE function in a few key strokes extracts the risk neutral density via various methods and summarizes the results.

This function should only be used for European options.

NOTE: Three files will be produced: filename will have the pdf version of the results. file.namecalls.csv will have the predicted call values. file.nameputs.csv will have the predicted put values.

`bsm.mu`	mean of log(S(T)), when S(T) is lognormal
`bsm.sigma`	SD of log(S(T)), when S(T) is lognormal
`gb.a`	extracted power parameter, when S(T) is assumed to be a GB rv
`gb.b`	extracted scale paramter, when S(T) is assumed to be a GB rv
`gb.v`	extracted first beta paramter, when S(T) is assumed to be a GB rv
`gb.w`	extracted second beta parameter, when S(T) is assumed to be a GB rv
`mln.alpha.1`	extracted proportion of the first lognormal. Second one is 1 - `alpha.1` in mixture of lognormals
`mln.meanlog.1`	extracted mean of the log of the first lognormal in mixture of lognormals
`mln.meanlog.2`	extracted mean of the log of the second lognormal in mixture of lognormals
`mln.sdlog.1`	extracted standard deviation of the log of the first lognormal in mixture of lognormals
`mln.sdlog.2`	extracted standard deviation of the log of the second lognormal in mixture of lognormals
`ew.sigma`	volatility when using the Edgeworth expansions
`ew.skew`	normalized skewness when using the Edgeworth expansions
`ew.kurt`	normalized kurtosis when using the Edgeworth expansions
`a0`	extracted constant term in the quadratic polynomial of Shimko method
`a1`	extracted coefficient term of k in the quadratic polynomial of Shimko method
`a2`	extracted coefficient term of k squared in the quadratic polynomial of Shimko method

Kam Hamidieh

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

###
### You should see that all methods extract the same density!
###

r     = 0.05
te    = 60/365
s0    = 1000
sigma = 0.25
y     = 0.02

strikes     = seq(from = 500, to = 1500, by = 5)
bsm.prices  = price.bsm.option(r =r, te = te, s0 = s0, 
              k = strikes, sigma = sigma, y = y)

calls   = bsm.prices$call
puts    = bsm.prices$put

###
### See where your results will go...
###

getwd()


###
###  Running this may take 1-2 minutes...
###
### MOE(market.calls = calls, call.strikes = strikes, market.puts = puts, 
###    put.strikes = strikes, call.weights = 1, put.weights = 1, 
###    lambda = 1, s0 = s0, r = r, te = te, y = y, file.name = "myfile")
###
### You may get some warning messages.  This happens because the
###    automatic initial value selection sometimes picks values
###    that produce NaNs in the generalized beta density estimation.
###    These messages are often inconsequential.
###