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10
votes
5answers
684 views
Monte carlo methods for vanilla european options and Ito's lemma.
I understand that by applying Ito's lemma to the following SDE
$$dX=\mu\,X\,dt+\sigma\,X\,dW$$
one obtains a solution to the above SDE which is as follows:
$${X}\left( t\right) =\mathrm{X}\left( ...
8
votes
3answers
3k views
What is Ito's lemma used for in quantitative finance?
Further to my question asked here: prior post
and which left some points unanswered, I have reformulated the question as follows:
What is Ito's lemma used for in quantitative finance? and when is it ...
6
votes
1answer
357 views
How to perform basic integrations with the Ito integral?
From the text book Quantitative Finance for Physicists: An Introduction (Academic Press Advanced Finance) I have this excercise:
Prove that
$$
...
5
votes
3answers
435 views
How to use Itô's formula to deduce that a stochastic process is a martingale?
I'm working through different books about financial mathematics and solving some problems I get stuck.
Suppose you define an arbitrary stochastic process, for example
$ X_t := W_t^8-8t $ where $ W_t ...
5
votes
1answer
241 views
Demonstration of Ito's correction term/lemma in binomial tree
I am preparing an undergraduate QuantFinance lecture. I want to demonstrate the ideas of Ito's correction term and Ito's lemma in the most accessible manner.
My idea is to take the "working horse" of ...
4
votes
1answer
198 views
Derivation of Ito's Lemma
My question is rather intuitive than formal and circles around the derivation of Ito's Lemma. I have seen in a variety of textbooks that by applying Ito's Lemma, one can derive the exact solution of a ...
4
votes
1answer
131 views
Ito's Lemma - Integrand depends on upper limit of integration
A problem I came across while practicing using Ito's Lemma had a process with an integral whose integrand depends on the upper limit of integration (the goal is to find $dZ_{t}$):
...
3
votes
1answer
171 views
How to measure a non-normal stochastic process?
If I understand right, Itô's lemma tells us that for any process $X$ that can be adapted to an underlying standard normal Wiener measure $\mathrm dB_t$, and any twice continuously differentiable ...
