has anyone tried to fit Gatheral's SVI parameterization? If so, have you implemented an algorithm which constrains the implied variacne surface to be a) positive and/or b)arbitrage free

QuoteOriginally posted by: frontofficequant has anyone tried to fit Gatheral's SVI parameterization? If so, have you implemented an algorithm which constrains the implied variacne surface to be a) positive and/or b)arbitrage freeWell, yes. But what do you mean? I set it up as vol, not variance, and used Excel Solver. Works like a charm, and Gatheral says it is arbitrage free.

The parameterization is suppose to be fit to variance (the square of vols) since it is the variances which are theoretically asymptotically linear in log-moneyness. It is not gauarenteed to be arb free. There are parameter restrictions to ensure this but they may have to be built into a fitting algorithm. Just wondering if anyone has done this? When I fit I find that I frequently end up with a parameterization that has arb across maturities.

QuoteOriginally posted by: frontofficequantThe parameterization is suppose to be fit to variance (the square of vols) since it is the variances which are theoretically asymptotically linear in log-moneyness. It is not gauarenteed to be arb free. There are parameter restrictions to ensure this but they may have to be built into a fitting algorithm. Just wondering if anyone has done this? When I fit I find that I frequently end up with a parameterization that has arb across maturities.Are you sure? I'm operating from memory here, but I don't think he said anything about arb across maturities. Let me think about this and come back...

QuoteOriginally posted by: PaperCutLet me think about this and come back...On second thought, I've got some other stuff to do. However, I have a feeling you are observing: 1) some subtleties2) "trading," i.e. people are actually taking the bid and hitting the offer on stuff, producing a sense that your parameterization is wrong when it's really just people giving up a little edge here and there.Good luck, bub !