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Nusc
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Does anyone know a document that explains the construction of Ito's lemma? In most financial mathematics textbooks, it's poorly motivated.
Thanks!
Thanks!
Ito's Lemma is a mathematical formula used in finance to calculate the change in a stochastic process. It is important because it allows for the calculation of expected values of complex financial instruments, such as derivatives.
Ito's Lemma is constructed using the Taylor series expansion and the multidimensional Itô integral. It involves taking the partial derivatives of the stochastic process and using the chain rule to calculate the change in the process over a small time interval.
Ito's Lemma assumes that the stochastic process is continuous and differentiable, and that the increments of the process are normally distributed with mean 0 and constant variance. It also assumes that the process is not affected by external factors such as interest rates or market conditions.
Ito's Lemma is used in finance to calculate the expected value of a financial instrument, such as a stock price or option, over a small time interval. It is also used in risk management to calculate the potential impact of small changes in the underlying asset.
Ito's Lemma is commonly used in the pricing of options and other derivatives, as well as in the study of stochastic processes in finance. It is also used in the Black-Scholes model for option pricing and in the analysis of financial time series data.