## minimizing instantaneous variance

Discuss anything related to quantitative finance which is not directly connected to a particular book here.

### minimizing instantaneous variance

Hello
I've come across the phrase "instantaneous variance" in the following papers, and I'm not quite sure what it means (I have a rough idea). The author minimizes the instantaneous variance of the portfolio to find the min variance hedge ratio. I'm quite familiar with this from portfolio theory; where we used standard calculus to calculate the optimal hedge ratio. However, I've no idea how to do this using stochastic calculus; the paper mentioned below does hi in equations 6 and 7. I have added the relevant page from the paper, and my own attempted solution.

Klingler - Delta Hedging the load serving deal (Energy Risk Septerm 2006), image of the relevant page added here.

Even though I get to the same result as the author, ,my approach feels "wrong". I somehow feel that I'll need to invoke Ito's Lemma (etc.) to do this the "right way". In the note, the author even mentions (just above equation 6) "...This guves the ("formal Ito calculus") solution". So what is the "formal Ito calculus solution".

Could anyone point me in the right direction? Any lecture note, or reading or paper (at the undergraduate or graduate level) that explains this idea?

Just to summarize:

1. What is the meaning of instantaneous variance
2. Given a portfolio of an underlying asset that follows a stochastic process, how would I calculate the minimum variance hedge, using Ito's Lemma? I understand the nature of the problem, and I know how to derive it using standard calculus; the way it's presented in the standard undergraduate texts.

Thanks!
C
Attachments
my attempted solution
Klinger attempted solution.PNG (94.99 KiB) Viewed 739 times
page from the original file
Klinger load serving deals.PNG (131.71 KiB) Viewed 739 times
csharma75

Posts: 2
Joined: Thu Jan 11, 2018 10:16 pm

### Re: minimizing instantaneous variance

Hello,
Last edited by Gsain123 on Sat Jan 20, 2018 5:14 am, edited 1 time in total.
Gsain123

Posts: 1
Joined: Fri Jan 12, 2018 8:56 am

### Re: minimizing instantaneous variance

Thanks Gsain123. I'm hoping someone is able to help!
csharma75

Posts: 2
Joined: Thu Jan 11, 2018 10:16 pm