price.bsm.option: Price BSM Option

In RND: Risk Neutral Density Extraction Package

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))

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