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frolloos
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Re: Local Vol: Jim Gatheral formula

June 9th, 2017, 5:22 pm

It would be useful to the community, which is a good thing. Incredible is a rather big word though.
 
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Alan
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Re: Local Vol: Jim Gatheral formula

June 9th, 2017, 6:38 pm

Yes -- incredible should be worth $100  :D
 
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outrun
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Re: Local Vol: Jim Gatheral formula

June 9th, 2017, 8:28 pm

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!
 
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Alan
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Re: Local Vol: Jim Gatheral formula

June 10th, 2017, 3:57 pm

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raising the bounty by $50 a day until someone steps up and solves it.(Of course, with the proviso that the offer can be rescinded at any time).  :)
 
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outrun
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Joined: April 29th, 2016, 1:40 pm

Re: Local Vol: Jim Gatheral formula

June 10th, 2017, 4:13 pm

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?
 
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LocalVolatility
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Re: Local Vol: Jim Gatheral formula

June 11th, 2017, 2:06 am

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
(151.23 KiB) Downloaded 66 times
 
JanStuller
Topic Author
Posts: 7
Joined: June 5th, 2017, 2:25 pm

Re: Local Vol: Jim Gatheral formula

June 13th, 2017, 4:20 pm

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. 
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