In this below, we explain Black-Scholes formula.
Functions to load: Load Bl() and BS()
Usage: BS(K, T, S, vol, r, delta)
T: maturity \§: spot price of underlying stock
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,
- 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,
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.