As everyone knows - there is no free lunch, or the cheese is free only in the mouse trap. So to say, we need to talk about the deficiences in the analysis by Black-Scholes and Merton. There were few assumptions put into the basis of the Black-Scholes model and equation.

Those are:

**A1**) There are no market imperfections, e.g., taxes,
transactions costs, shortsales constraints, and trading is continuous and
frictionless.

*Yes, this is the GREAT assumption.*

**A2**) There is unlimited riskless borrowing and lending at the
continuously compounded rate of return r; hence a
investment in such an asset over the time interval
grows to
Alternatively, if
is the date
price of a discount bond maturing at date
with face value
then for
the bond price dynamics are given by

**A3**) The stock price dynamics is given by a geometric Brownian
motion, with the solution to the following Ito stochastic differential
equation on

where is a standard Brownian motion, and at least one investor observes without an error.

**A4**) There is no arbitrage.

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