Sunday, February 10, 2013

The Black–Scholes model

What does it mean?: Prices a derivative based on the assumption that it is riskless and that there is no arbitrage opportunity when it is priced correctly. 

History: Developed by Fischer Black and Myron Scholes, then expanded by Robert Merton. The latter two won the 1997 Nobel Prize in Economics for the discovery.   
Importance: Helped create the now multi trillion dollar derivatives market. It is argued that improper use of the formula (and its descendants) contributed to the financial crisis. In particular, the equation maintains several assumptions that do not hold true in real financial markets.  
Modern use: Variants are still used to price most derivatives, even after the financial crisis.



The Black-Scholes Model or Formula calculates an theoretical value of an option based on 6 variables. These variables are:
  • Whether the option is a call or a put
  • The current underlying stock price
  • The time left until the option's expiration date
  • The strike price of the option
  • The risk-free interest rate
  • The volatility of the stock
The Black-Scholes (1973) was originally formulated to price European-style options, and does not account for dividend payment and early exercise. The Cox-Ross-Rubenstein Binomial model (1979) is a variation on the original Black-Scholes. The Barone-Adessi & Whaley, or "Whaley" model (1987), accounts for early exercise of call options due to dividend payment and is widely used among individual investors for pricing American-style equity options.

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