Brownian Motion, Ito's Lemma and the Black-Scholes Formula
1. The
stochastic property of an assets’ price can be described by Brownian Motion
2. Price of derivative is a function of a stochastic process.
3. Ito's
lemma provides a framework to differentiate the functions of stochastic process
and this is of particular significance to derivative pricing (before Ito's work, people did not know how
to do it).
4. Ito's lemma allows us to derive the stochastic differential equation (SDE) for the price of derivatives. Solving such SDEs gives us the derivative pricing models.
