SERVING THE QUANTITATIVE FINANCE COMMUNITY

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frolloos
Posts: 1621
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### Re: Local Vol: Jim Gatheral formula

It would be useful to the community, which is a good thing. Incredible is a rather big word though.

Alan
Posts: 10321
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

Yes -- incredible should be worth $100 outrun Posts: 4573 Joined: April 29th, 2016, 1:40 pm ### Re: Local Vol: Jim Gatheral formula Here is a$1 idea:

Can you come up with a case where :
\begin{align} \frac{\partial \upsilon}{\partial y} &= 0, \frac{\partial^2 \upsilon}{\partial y^2} = -1 \\ \frac{\partial \upsilon}{\partial T} &\ne 0 \end{align}
?
maybe
$\upsilon = -\frac{1}{2} T y^2$

That would blow up result 1, but not result 2!

Alan
Posts: 10321
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: Local Vol: Jim Gatheral formula

Well, it's been a day and we have no takers at $50. I suggest raising the bounty by$50 a day until someone steps up and solves it.(Of course, with the proviso that the offer can be rescinded at any time).  :)

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: Local Vol: Jim Gatheral formula

Sounds like a good plan.
So now it's going to have a prisoners dilemma type of element / optimal waiting time, which will drive up the expected cost *and* as a result of that we'll need (at some point) a CDS on Jan to mitigate credit risk.
Maybe Jan should buy insurance protection?

LocalVolatility
Posts: 128
Joined: May 27th, 2009, 10:07 am
Location: Amsterdam
Contact:

### Re: Local Vol: Jim Gatheral formula

A few years back I worked through the details of the derivation on pages 11 - 13 in Gatheral's book. I was able to replicate his result. Attached are the notes that I took back then. Hope this helps...
Attachments
LocalVolatilityImpliedVolatility.pdf

JanStuller
Topic Author
Posts: 7
Joined: June 5th, 2017, 2:25 pm

### Re: Local Vol: Jim Gatheral formula

Really appreciate the feedback thus far. I am planning on going through your paper in detail, LocalVol, asap, ideally this weekend. Also, gonna go through Gatheral's paper one more time and also consider Outrun's \$1 idea - thanks so much to all.