Black Scholes

The Black-Scholes Model

The Black-Scholes model is one of the most important concepts in modern financial theory. Cultivated in 1973, this model was brought into existence by Fisher Black, Robert Merton and Myron Scholes. It is still considered the most commonly used method of determining fair prices of options. This is a model of the price variation of financial instruments that can be used to determine the price of a call option. In order to specify an option’s value to the most accurate degree, a variety of assumptions must be made. Contrary to previous financial experts’ efforts, Black, Merton, and Scholes declared all assumptions invalid except for 6 vital components. There must be no arbitrage opportunity, or in other words there must be no riskless profit. All profit assumes a certain level of risk. One must be able to borrow and loan cash at a constant risk-free rate. He or she also has the right, but not the obligation, to buy or sell any amount of stock. Each transaction, however, must not incorporate any fees whatsoever. The prices of each stock follow Geometric Brownian Motion. Also, stocks must not pay out any dividends.

The market must not contain any arbitrage opportunity. It is impossible to secure a risk-free profit. Though there may be arbitrage in certain sectors of the market, this is not true for the Black-Scholes model. This is because those other segments are not secure in the long run and thus, relying on them would violate the Black-Scholes model. Therefore, this assumption must be held in order to obtain a fair option price.

The second assumption is that traders and brokers must be able to borrow and lend cash at a known and fixed risk-free rate. The risk-free rate is the compensation for systemic risk that cannot be eliminated through a well-diversified portfolio. This rate represents the interest that an investor would expect from a risk-free investment over a given period of time. By applying this assumption into...