price.bsm.option {RND}

Price BSM Option

Description

bsm.option.price computes the BSM European option prices.

Usage

price.bsm.option(s0, k, r, te, sigma, y)

Arguments

s0

current asset value

k

strike

r

risk free rate

te

time to expiration

sigma

volatility

y

dividend yield

Details

This function implements the classic Black-Scholes-Merton option pricing model.

Value

d1

value of (log(s0/k) + (r - y + (sigma^2)/2) * te)/(sigma * sqrt(te))

d2

value of d1 - sigma * sqrt(te)

call

call price

put

put price

Author(s)

Kam Hamidieh

References

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

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

#
# call should be 4.76, put should be 0.81, from Hull 8th, page 315, 316
#

r     = 0.10
te    = 0.50
s0    = 42
k     = 40
sigma = 0.20
y     = 0

bsm.option = price.bsm.option(r =r, te = te, s0 = s0, k = k, sigma = sigma, y = y)
bsm.option

#
# Make sure put-call parity holds, Hull 8th, page 351
#

(bsm.option$call - bsm.option$put) - (s0 * exp(-y*te) - k * exp(-r*te))