Black-Scholes option pricing model

Black–Scholes Option Pricing Model

The Black–Scholes option pricing model is a mathematical formula that is used to calculate the fair price of a call or put option based on six key input variables: stock price, strike price, time to expiration, interest rate, divident yield and volatility. Developed by economists Fischer Black and Myron Scholes, the objective of the Black–Scholes model is to estimate the price of an option given by a buyer or a seller and then find the underlying asset’s fair value.

The Black–Scholes model is a type of mathematical equation that is widely used indirectly in pricing options, as well as other derivatives such as warrants, futures and swaps. Bloxham (2017) notes that, regardless of the sophistication of the pricing techniques used, the outcome of any option pricing model process is inherently reliant on subjective assumptions about future developments. However, for many investors, the Black–Scholes model is the best model to use to value options as the formula carries a number of known assumptions that, if applicable, are likely to be more reliable than many others.

To calculate the fair price of an option using the Black–Scholes model, the potential payoff from exercising the option has to be compared with its expected cost. The expected cost is calculated using the risk-free interest rate, the strike price and the stock price at the expiration date of the option. This cost is then discounted back to the present to find the option’s expected cost at the time of purchase.

The calculation of the potential payoff of a call option is the difference between the stock price and the strike price and the calculation of the potential payoff of a put option is the difference between the strike price and the stock price. The Black–Scholes model also makes assumptions about the volatility of the stock and the dividend payments that might be made. The volatility and dividend payments are used to adjust the expected cost of the option and the potential payoff of the option.

Once the potential payoff and the expected cost of exercising the option have been calculated, the option price is determined using the formula. Since the determination of the fair price of the option depends on a number of estimates, the Black–Scholes model does not provide an exact solution for the option price. However, it does provide an analytical solution for the expected cost of the option, which can then be used to approximate the option’s fair price.

The Black–Scholes model is widely used by financial institutions, banks and other organizations to value options and other derivatives. As a result, most derivatives exchanges, such as the Chicago Board Options Exchange (CBOE), the International Securities Exchange (ISE), and the New York Stock Exchange (NYSE), rely heavily on the Black–Scholes model to determine the fair market value of derivative contracts.

The Black–Scholes model is critically important in the pricing of derivatives and options. While the formula carries numerous assumptions, the model provides the best known pricing framework for most options and derivatives. As such, it is used extensively by financial institutions, investors, and other market participants in assessing the value of options.

Reference

Bloxham, E. (2017). Modeling the Fair Value of Options and other Derivatives: Black-Scholes and Beyond. Wiley, Hoboken, NJ.

The Black-Scholes Model of option pricing was developed by economists Fisher Black, Myron Scholes and Robert Merton in 1973 and revolutionized the options market as investors and market makers were now able to determine a pricing model for options contracts. The Black-Scholes Model is a mathematical equation that allows investors to determine the fair value of an option at a given time.

The Black-Scholes equation uses 5 key variables: stock price, strike price, volatility, time to expiration, and the cost of borrowing. The model gives a fair value for the option that takes into account a number of factors that could affect the option’s price. This includes the underlying stock’s price, the option’s strike price, the amount of volatility in the stock, the option’s time to expiration, and the cost of borrowing.

The Black-Scholes Model is one of the most popular options pricing models as it gives market makers and other investors an accurate estimate of the price of an option. By entering the key variables into the Black-Scholes equation, the user is able to determine the theoretical fair value of an option, as well as its sensitivity to the changes in the key variables. This is known as the option’s delta, gamma, theta and vega.

The Black-Scholes Model has been widely praised and is still used in options pricing today. It is used to help market makers to determine the fair price of an option, or the theoretical price of an option if all of the underlying factors that could affect its price stay the same. This allows for more accurate pricing and more efficient markets for investors of all kinds.