Inputs in Black-Scholes Option Pricing Model Formula
- S0 = underlying price
- X = strike price
- σ = volatility
- r = continuously compounded risk-free interest rate
- q = continuously compounded dividend yield
- t = time to expiration
- σ = Volatility = India VIX has been taken.
- r = 10% (As per NSE Website, it is fixed.)
- q = 0.00% (Assumed No Dividend)
Note: In many resources, you can find different symbols for some of these parameters.
- The strike price is often denoted
K(here it is
- Underlying price is often denoted
S(without the zero)
- Time to expiration is often denoted
T – t(difference between expiration and now).
In the original Black and Scholes paper (The Pricing of Options and Corporate Liabilities, 1973) the parameters were denoted x (underlying price), c (strike price), v (volatility), r (interest rate), and t* – t (time to expiration).
The dividend yield was only added by Merton in Theory of Rational Option Pricing, 1973.
Call and Put Option Price Formulas
C and put option
P prices are calculated using the following formulas:
N(x) is the standard normal cumulative distribution function.
The formulas for
Original Black-Scholes vs. Merton’s Formulas
In the original Black-Scholes model, which doesn’t account for dividends, the equations are the same as above except:
- There is just
S0in place of
- There is no
qin the formula for
Therefore, if the dividend yield is zero, then
e-qt = 1 and the models are identical.
Black-Scholes Formulas for Option Greeks
… where T is the number of days per year (calendar or trading days, depending on what you are using).