BS_Simple {QFRM} | R Documentation |
Black-Scholes formula
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 |
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)