Black-Scholes Model

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Description of Black-Scholes Model. Explanation.

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Definition Black-Scholes Model. Description.


Black-Scholes Model is a pricing model of financial instruments, and in particular stocks and options, derived by Fischer Black and Myron Scholes in 1973. It is based on arbitrage arguments that uses the stock price, the exercise price, the risk-free interest rate, the time to expiration, and the standard deviation (volatility) of the stock return.


The key assumptions of the model are:

  • The price of the underlying instrument is a geometric Brownian motion, in particular with constant drift and volatility.

  • It is possible to short sell the underlying stock.

  • There are no arbitrage opportunities.

  • Trading in the stock is continuous.

  • There are no transaction costs or taxes.

  • All securities are perfectly divisible (e.g. it is possible to buy 1/100th of a share).

  • The risk-free interest rate is constant, and the same for all maturity dates.


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