Chapter 9 (Ito’s Lemma)

[Bernadette Pieterse]

Hello,

In the practice question 8 and 9 (2023 version of notes), both questions have the same formula for the GBM. S_t = exp(mu*t + sigma*Bt)

When applying ito’s lemma the first question uses f=exp(mu*t + sigma*Bt) and gets the partial derivates as mu*St, sigma*St and sigma^2*St. This makes sense to me.

However, the second question uses St=exp(Xt) and gets all the derivatives as St. So it does not take the mu and sigma into account when calculating the partial derivatives.

Why do these questions use different approaches? Are they both fine in the exam?

Thanks in advance.

 

[John Potter]

You'll end up with the same answer either way - you can use Taylor's formula on any function you like. I would argue that they're not "different approaches" but, yes, the way Questions 8 and 9 have been answered would be equally valid in the exam,

John