A stochastic process where the change in the price of a derivative during each short period of time has a normal distribution. However, this change over longer periods of time is bound to follow a nonnormal distribution. The mean and variance of of the distribution are proportional to that short period of time and are not necessarily constant, but may vary over time. In other words, Ito’s Lemma represents a relationship that allows to deduce the stochastic process followed by a function of the price. The function, per se, is deduced from the stochastic process followed by the price itself. Ito’s Lemma is instrumental in the derivation of a number of option pricing models. For example, the price of a stock option can be assumed to be a function of the underlying stock’s price and time.
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