Quadratic Variation - Semimartingales

Semimartingales

Quadratic variations and covariations of all semimartingales can be shown to exist. They form an important part of the theory of stochastic calculus, appearing in Itō's lemma, which is the generalization of the chain rule to the Itō integral. The quadratic covariation also appears in the integration by parts formula

which can be used to compute .

Alternatively this can be written as a Stochastic Differential Equation:

where

Read more about this topic:  Quadratic Variation