hilss


Total Posts: 65 
Joined: Jun 2007 


Hello everyone,
I am using the SVI model to fit soft products (not sure if SVI is meant for commodities).
If so, I'm wondering if there's a modification to the SVI model that allows one to fit calls and puts separately. In other words, when we change the sigma parameter (smoothness of vertex), it changes the curvature of both calls and puts. Is there a way to change the curvature of the call side only (without breaking model/ATM gamma for example)?
I'm looking at the H19 (20180208) expiration in Coffee (KC  on ICE), and I can to fit the zone between the 10d put and the 15d call fine. But more OTM options seem to be a problem.
Please see the image below (H19 FuturePrice = 121 and TimeToExpiration = 0.585) Attached File: H19_KC.pdf
As an example, the H19 160 C has a 9 delta. H19 100P has a 3.5 delta.
Thank you, hilss
P.S. Not sure if this question should be under basics... sorry if I posted it in the wrong spot.




ronin


Total Posts: 414 
Joined: May 2006 


It probably should be under basics.
SVI is a five parameter model. There is no reason why it wouldn't be able to exactly interpolate through five points.
But it's 5d optimization  you can't do that by hand. Stick it in a solver.
To directly answer your question, not really. The sort of extension you are asking about would have a minimum of seven parameters. What would be next  10 parameter models, twenty parameter models, hundred parameter models? If five isn't enough, you probably need a grid interpolation instead of a parametric model.
Generally speaking, grid interpolation is anyway always better than a parametric model. Parametric models can be very unstable.

"There is a SIX am?"  Arthur 

hilss


Total Posts: 65 
Joined: Jun 2007 


Thank you for your response Ronin.
If I may ask, could you clarify what "grid interpolation" means?
hilss 



ronin


Total Posts: 414 
Joined: May 2006 


Pick a grid of strikes, including the ones for which you know the volatility.
For the strikes that you don't know the volatility for, interpolate using some spline. Then adjust spline parameters until you have removed all arbitrage from your new interpolated volatility surface.
What I meant by stability was that a small error in any of the points won't propagate very far in a grid model. But in a parametric model, a small error in one point can propagate everywhere.

"There is a SIX am?"  Arthur 

frolloos


Total Posts: 56 
Joined: Dec 2007 


To add to Ronin's reply, Fengler's paper "arbitrage free smoothing of the implied volatility surface" gives a spline based arbfree smoothing. 



hilss


Total Posts: 65 
Joined: Jun 2007 


Thank you both very much. hilss 


fomisha


Total Posts: 34 
Joined: Jul 2007 


If you need an offtheshelf solution for volatility fitting, check out Vola Dynamics: https://www.voladynamics.com/examples.html The library can robustly fit any market (carbfree) with curves which have from 3 to 14 parameters (including SVI). 


