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 1Let 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.