Description Usage Arguments Details Value Author(s) References Examples
extract.gb.density
extracts the generalized beta density from market options.
1 2 3 |
initial.values |
initial values for the optimization |
r |
risk free rate |
te |
time to expiration |
y |
dividend yield |
s0 |
current asset value |
market.calls |
market calls (most expensive to cheapest) |
call.strikes |
strikes for the calls (smallest to largest) |
call.weights |
weights to be used for calls |
market.puts |
market calls (cheapest to most expensive) |
put.strikes |
strikes for the puts (smallest to largest) |
put.weights |
weights to be used for puts |
lambda |
Penalty parameter to enforce the martingale condition |
hessian.flag |
if F, no hessian is produced |
cl |
list of parameter values to be passed to the optimization function |
This function extracts the generalized beta density implied by the options.
a |
extracted power parameter |
b |
extracted scale paramter |
v |
extracted first beta paramter |
w |
extracted second beta parameter |
converge.result |
Did the result converge? |
hessian |
Hessian matrix |
Kam Hamidieh
R.M. Bookstaber and J.B. McDonald (1987) A general distribution for describing security price returns. Journal of Business, 60, 401-424
X. Liu and M.B. Shackleton and S.J. Taylor and X. Xu (2007) Closed-form transformations from risk-neutral to real-world distributions Journal of Business, 60, 401-424
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 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | #
# create some GB based calls and puts
#
r = 0.03
te = 50/365
k = seq(from = 800, to = 1200, by = 10)
a = 10
b = 1000
v = 2.85
w = 2.85
y = 0.01
s0 = exp((y-r)*te) * b * beta(v + 1/a, w - 1/a)/beta(v,w)
s0
call.strikes = seq(from = 800, to = 1200, by = 10)
market.calls = price.gb.option(r = r, te = te, y = y, s0 = s0,
k = call.strikes, a = a, b = s0, v = v, w = w)$call
put.strikes = seq(from = 805, to = 1200, by = 10)
market.puts = price.gb.option(r = r, te = te, y = y, s0 = s0,
k = put.strikes, a = a, b = s0, v = v, w = w)$put
#
# Extraction...should match the a,b,v,w above. You will also get warning messages.
# Weigths are automatically set to 1.
#
extract.gb.density(r=r, te=te, y = y, s0=s0, market.calls = market.calls,
call.strikes = call.strikes, market.puts = market.puts,
put.strikes = put.strikes, lambda = 1, hessian.flag = FALSE)
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