Question

Money Laureate Myron Scholes developed the model of optional Black Scholes (together with Fisher Black). Describe the above model and explain the cases ???

Answer 1

The black schools model also known as black schools Merton model is considered to be the model of price variation. This model assumes that the price of heavily traded assets follow a geometric Brownian motion with constant drift & volatility. When applied to stock option, the model incorporates constant price variation of stock, time value of money, option’s strike price & time to option expiry.

This is considered to be one of the most important concepts of modern financial theory which was developed in 1973 by fisher black, Robert Merton & Myron scholes. This is considered to be best method for determining the price of options. It requires five important variables which include the strike price of an option, the current stock price, time to expiration, risk free rate & volatility. The model assumes that there are no transaction costs or taxes, risk free interest rate constant for all maturities, absence of riskless arbitrage opportunities etc.

Black-Scholes Formula

The Black Scholes call option formula is calculated by multiplying the stock price by the cumulative standard normal probability distribution function. Thereafter, the net present value (NPV) of the strike price multiplied by the cumulative standard normal distribution is subtracted from the resulting value of the previous calculation. In mathematical notation, C = S*N (d1) - Ke^ (-r*T)*N (d2). Conversely, the value of a put option could be calculated using the formula: P = Ke^ (-r*T)*N (-d2) - S*N (-d1). In both formulas, S is the stock price, K is the strike price, r is the risk-free interest rate and T is the time to maturity. The formula for d1 is: (ln(S/K) + (r + (annualized volatility) ^2 / 2)*T) / (annualized volatility * (T^ (0.5))). The formula for d2 is: d1 - (annualized volatility)*(T^ (0.5)).