Black-Scholes

The Black-Scholes model was published in 1973 by Fischer Black and Myron Scholes. This model is used to calculate the theoretical price of options using five key determinants of an option’s price, that is stock price, strike price, volatility, expiration time and risk-free rate.

Black-Scholes formula for call options is as follows:

Where,

r  = Risk-free Rate

t = Expiration Date

X = Strike Price of the option

S = Price of the Stock

σ= standard deviation

Assumptions underlying the Black Scholes formula

1. The stock pays no dividend during the option’s life

2. European style options

3. Interest rate is constant

4. Volatility is constant

5. Infinite liquidity and depth in the market

6. No commissions and transaction costs

7. Stock returns follow normal distribution