BS_Simple: Black-Scholes formula

In QFRM: Pricing of Vanilla and Exotic Option Contracts

Description

Black-Scholes (aka Black-Scholes-Merton, BS, BSM) formula for simple parameters

Usage

BS_Simple(S0 = 42, K = 40, r = 0.1, q = 0, ttm = 0.5, vol = 0.2)

Arguments

S0	The spot price of the underlying security
K	The srike price of the underlying (same currency as S0)
r	The annualized risk free interest rate, as annual percent / 100 (i.e. fractional form. 0.1 is 10 percent per annum)
q	The annualized dividiend yield, same units as r
ttm,	The time to maturity, fraction of a year (annualized)
vol	The volatility, in units of standard deviation.

Details

Uses BS formula to calculate call/put option values and elements of BS model

Value

a list of BS formula elements and BS price, such as d1 for d_1, d2 for d_2, Nd1 for N(d_1), Nd2 for N(d_2), NCallPxBS for BSM call price, PutPxBS for BSM put price

Author(s)

Robert Abramov, Department of Statistics, Rice University, Spring 2015

References

Hull, J.C., Options, Futures and Other Derivatives, 9ed, 2014. Prentice Hall. ISBN 978-0-13-345631-8, http://www-2.rotman.utoronto.ca/~hull/ofod. http://amzn.com/0133456315 http://www.theresearchkitchen.com/archives/106

Examples

#See Hull p.339, Ex.15.6.
(o <- BS_Simple(S0=42,K=40,r=.1,q=0,ttm=.5,vol=.2))$Px$Call #returns 4.759422
o$Px$Put # returns 0.8085994 as the price of the put

BS_Simple(100,90,0.05,0,2,0.30)
BS_Simple(50,60,0.1,.2,3,0.25)
BS_Simple(90,90,0.15,0,.5,0.20)
BS_Simple(15,15,.01,0.0,0.5,.5)

Example output

[1] 4.759422
[1] 0.8085994
$d1
[1] 0.6961714

$d2
[1] 0.2719073

$Nd1
[1] 0.7568393

$Nd2
[1] 0.6071534

$Px
$Px$Call
[1] 26.24017

$Px$Put
[1] 7.675535


$d1
[1] -0.8973676

$d2
[1] -1.33038

$Nd1
[1] 0.1847614

$Nd2
[1] 0.09169651

$Px
$Px$Call
[1] 0.9941339

$Px$Put
[1] 18.00265


$d1
[1] 0.6010408

$d2
[1] 0.4596194

$Nd1
[1] 0.7260936

$Nd2
[1] 0.6771053

$Px
$Px$Call
[1] 8.812221

$Px$Put
[1] 2.309134


$d1
[1] 0.1909188

$d2
[1] -0.1626346

$Nd1
[1] 0.5757054

$Nd2
[1] 0.4354031

$Px
$Px$Call
[1] 2.137109

$Px$Put
[1] 2.062296

QFRM documentation built on May 2, 2019, 8:26 a.m.