compute.implied.volatility {RND}

Compute Impied Volatility

Description

compute.implied.volatility extracts the implied volatility for a call option.

Usage

compute.implied.volatility(r, te, s0, k, y, call.price, lower, upper)

Arguments

r

risk free rate

te

time to expiration

s0

current asset value

k

strike of the call option

y

dividend yield

call.price

call price

lower

lower bound of the implied volatility to look for

upper

upper bound of the implied volatility to look for

Details

The simple R uniroot function is used to extract the implied volatility.

Value

sigma

extratced implied volatility

Author(s)

Kam Hamidieh

References

J. Hull (2011) Options, Futures, and Other Derivatives and DerivaGem Package Prentice Hall, Englewood Cliffs, New Jersey, 8th Edition

R. L. McDonald (2013) Derivatives Markets Pearson, Upper Saddle River, New Jersey, 3rd Edition

Examples

#
# Create prices from BSM with various sigma's
#

r     =  0.05
y     =  0.02
te    =  60/365
s0    =  400

sigma.range = seq(from = 0.1, to = 0.8, by = 0.05)
k.range     = floor(seq(from = 300, to = 500, length.out = length(sigma.range)))
bsm.calls   = numeric(length(sigma.range))

for (i in 1:length(sigma.range))
{
  bsm.calls[i] = price.bsm.option(r = r, te = te, s0 = s0, k = k.range[i], 
                                  sigma = sigma.range[i], y = y)$call
}
bsm.calls
k.range

#
# Computed implied sigma's should be very close to sigma.range.
#

compute.implied.volatility(r = r, te = te, s0 = s0, k = k.range, y = y, 
                          call.price = bsm.calls, lower = 0.001, upper = 0.999)
sigma.range