Description Usage Arguments Details Value Author(s) References Examples
dshimko
is the probability density function implied by the Shimko method.
1 | dshimko(r, te, s0, k, y, a0, a1, a2)
|
r |
risk free rate |
te |
time to expiration |
s0 |
current asset value |
k |
strike at which volatility to be computed |
y |
dividend yield |
a0 |
constant term in the quadratic polynomial |
a1 |
coefficient term of k in the quadratic polynomial |
a2 |
coefficient term of k squared in the quadratic polynomial |
The implied volatility is modeled as: σ(k) = a_0 + a_1 k + a_2 k^2
density value at x
Kam Hamidieh
D. Shimko (1993) Bounds of probability. Risk, 6, 33-47
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 | #
# a0, a1, a2 values come from Shimko's paper.
#
r = 0.05
y = 0.02
a0 = 0.892
a1 = -0.00387
a2 = 0.00000445
te = 60/365
s0 = 400
k = seq(from = 250, to = 500, by = 1)
sigma = 0.15
#
# Does it look like a proper density and intergate to one?
#
dx = dshimko(r = r, te = te, s0 = s0, k = k, y = y, a0 = a0, a1 = a1, a2 = a2)
plot(dx ~ k, type="l")
#
# sum(dx) should be about 1 since dx is a density.
#
sum(dx)
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