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There are two basic arguments involving delta-hedging that can be used to derive the Black–Scholes formula. One of them is used in the related Demonstration "Hedging the Black-Scholes Call Option". In that argument a self-financing portfolio is constructed that matches with probability 1 the value of the payoff of the option. In practice the portfolio is only approximately self-financing; to make it really so, infinitely many portfolio adjustments are needed. Here we construct a portfolio consisting of the option itself, stock, and a money market account, which makes the portfolio self-financing. However, again, infinitely many portfolio adjustments are needed to make the portfolio truly self-financing and "riskless". Assuming that the portfolio is self-financing and riskless, the principle of absence of arbitrage implies that it has to grow at the riskless interest rate. Writing this condition in differential form and using the Itô formula leads to the Black–Scholes equation.

This argument is given in incorrect form in many well-known books on option pricing—it ignores the money market account and incorrectly applies the Itô formula. This particular corrected version of the argument can be found in S. Stojanovic, Computational Financial Mathematics Using Mathematica, Boston: Birkhäuser, 2002, which also contains a Mathematica program implementing it (somewhat different from this Demonstration and written for an earlier version of Mathematica).