This function is available in R-fiddle (here). See also its upper level page (here).
In this below, we explain Black-Scholes formula.
Functions to load: Load Bl() and BS()
Usage: BS(K, T, S, vol, r, delta)
Arguments:
K: strike
T: maturity \§: spot price of underlying stock
vol: volatility
r: continuously compounding risk free interest rate
delta: dividend yield
Value: 2-D vector of call and put price.
BS model usually assumes the lognormal distribution for the stock price at time , that is,
where
-
is short rate,
is volatility,
is dividend yield,
-
for
In particular,
when
is constant volatility.
R-code is written according to the following fact:
Proposition 1 Let
and
be the call and put premium with maturity
and strike
. Then,
and
Ex. Suppose stock spot price , volatility
, interest rate is
, and no dividend (
). For strike
and maturity
years, we can compute call and put prices as follows.