June 10th, 2016, 5:52 pm
QuoteOriginally posted by: frolloosAs far as I understand it, the Arslan et al paper *assumes* that gamma, vanna and volga have associated theta costs. Is there a way to prove this? I mean in BS framekwork gamma has theta cost, and in say a stoch vol model you could argue theta cost is indeed gamma volga and vanna, but not sure how to abuse the BS framework correctly to allow additional volga and vanna theta costs, if this makes sense.I also found during implementation some dependency of the thetas on the choice of pillar options, anyone running into the same issue?Implementation works. I used gamma, vomma and vanna initially instead of dollar gamma, dollar volga and dollar vanna. Now there is negligible dependency on choice of the 3 pillar options, which is good. That said, I still don't understand why this method works, and why it only works when setting r=q=0, even though the smile taken from the index market obviously doesnt assume this. The interpolation is very good, and the put extrapolation also, where I can extrapolate all the way down to K = 50% for t = 0.5 and still match IBD quotes. but the call extrapolation is sometimes off for short maturities for instance t = 0.5, K > 120%.@mcakes: which paper are you looking at? The Arslan et al paper doesn't mention an alpha I believe. Like you I also like this framework by the way.
Last edited by
frolloos on June 9th, 2016, 10:00 pm, edited 1 time in total.