## [PDS] Chain Rule in Ito Calculus

**Chain Rule in Ito Calculus**

Given two stochastic processes and driven by different Brownian Motions and as

or alternatively, writing them in ‘short-hand’ (their SDE form) as:

Then Ito’s lemma in 2-D tells us that function will satisfy:

Given , the following will hold:

With this we can now simplify the expression for as:

**This describes the Chain Rule in Ito calculus.**

…

We can, of course, further simplify the above and write:

where is the correlation between the two Brownian Motions and .

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