March 16, 2009

Black Scholes Assumptions

The Black-Scholes model of the market for an equity makes the following explicit assumptions:
  • It is possible to borrow and lend cash at a known constant risk-free interest rate.
  • The stock price follows a geometric Brownian motion with constant drift and constant volatility and they are lognormally distributed.
  • There are no transaction costs.
  • The stock does not pay a dividend (this was modified by Merton later on).
  • All securities are perfectly divisible (i.e. it is possible to buy any fraction of a share).
  • There are no restrictions on short selling.
  • Markets are efficient.

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