MOE {RND}

Mother of All Extractions

Description

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

Usage

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

Arguments

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!

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.

Value

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

Author(s)

Kam Hamidieh

References

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

Examples

###
### 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.
###