compute.implied.volatility: Compute Impied Volatility

In RND: Risk Neutral Density Extraction Package

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

RND documentation built on May 1, 2019, 10:52 p.m.