Options Pricing: Black-Scholes Model

The Black-Scholes formulation (also called Black-Scholes-Merton) has been the first widely used model for option pricing. It is used to compute the theoretical value of European-style choices utilizing current stock prices, expected dividends, the option’s strike price, expected interest rates, time to expiration and expected volatility.

The formulation, developed by three economists — Fischer Black, Myron Scholes and Robert Merton — is possibly the world’s most famous options pricing model. It had been released into their 1973 paper, “The Pricing of Options and Corporate Liabilities,” printed in the Journal of Political Economy. Black passed away two years prior to Scholes and Merton were awarded the 1997 Nobel Prize in Economics for their work at discovering a new system to ascertain the value of derivatives (the Nobel Prize isn’t given posthumously; nonetheless the Nobel committee confessed Black’s function at the Black-Scholes version).

The Black-Scholes model makes certain assumptions:

  • The option is European and can only be exercised at expiration.
  • No dividends are paid out during the life of the option.
  • Markets are efficient (i.e., market movements cannot be predicted).
  • There are no transaction costs in buying the option.
  • The risk-free rate and volatility of the underlying are known and constant.
  • The returns on the underlying are normally distributed.


Black-Scholes Formula

The formula, shown in Figure  takes the following variables into consideration:

  • current underlying price
  • options strike price
  • time until expiration, expressed as a percent of a year
  • implied volatility
  • risk-free interest rates

blackscholes1 - Options Pricing: Black-Scholes Model