Black-Scholes is a pricing model used to determine the fair price or theoretical value for a Call or a Put option.
The quantum of speculation is more in case of stock market derivatives and proper pricing of options eliminates the opportunity for any arbitrage.
The model is used to determine the price of a European call option which simply means that the option can only be exercised on the expiration date.
Though usually accurate, the Black-Scholes model makes certain assumptions that can lead to prices that deviate from the real-world results.
The Black-Scholes model requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free interest rate, and the volatility.
The formula for Black-Scholes Model is a given below:
The variables that are used to assess risk in the options market are commonly referred to as the Greeks. Each Greek variable is a result of an imperfect assumption or relationship of the option with another underlying variable. Greeks are used by options traders and portfolio managers to understand how their options investments will behave as prices move, and to hedge their positions accordingly.
Delta is a ratio that relates changes in the price of a security such as company stock to a change in the price of a derivative of that stock.
Consider that you have a stock worth Rs. 5428 and a Call option on that stock is worth Rs.170. Further assume that the delta is 0.50. This indicates that the value of the Option is expected to rise by 0.50 Rs. for every 1 Rs. increase in the price of the
stock. If the stock price moves to Rs. 5448, then the value of the option becomes Rs.180.
The term theta refers to the rate of decline in the value of an option due to the passage of time. It can also be referred to as the time decay of an option. This means an option loses value as time moves closer to its maturity as long as everything is held constant. Theta is generally expressed as a negative number and can be thought of as the amount by which an option's value declines every day.
A theta of -6.70 means that Option will lose 6.70 on a daily basis if all other factors are held constant.
Gamma is the first derivative of delta and is used when trying to gauge the price movement of an option, relative to the amount it is in or out of the money. In that same regard, gamma is the second derivative of an option's price with respect to the underlying price. Gamma is the rate of change in an option's delta per 1-point move in the underlying asset's price