s****y 发帖数: 390 | 1 If the implied vol is only a function of strike, will it cause any problem
for local vol??
Thanks a lot for any comments! | l*****i 发帖数: 3929 | 2 I don't think the local vol can have problems in this case. It's still a fun
ction of S and t.
【在 s****y 的大作中提到】 : If the implied vol is only a function of strike, will it cause any problem : for local vol?? : Thanks a lot for any comments!
| z****u 发帖数: 185 | 3 I don't know how to explain. But the truth is if you agree the pdf of the
stock level at a future time has a fat tail, then implied vol cannot be only
a function of strike. Because this will lead to strike-dimension arbitrage
opportunities, which mean local variance will be negative.
On the other hand, you can insist on no-fat-tail and have a consistent
theoretical picture, i.e., the Black-Scholes flat skew. In this case, the
implied vol is a constant. This does not cause any problem since now t
【在 s****y 的大作中提到】 : If the implied vol is only a function of strike, will it cause any problem : for local vol?? : Thanks a lot for any comments!
| s****y 发帖数: 390 | 4 thanks for replying!
the implied vol is not constant in my case. it has skew, very sharp when K
goes zero, and looks exponentially decreasing later and after ATM strike as
well.
I think I will get a negative local variance when K is small. but you mean
it will lead to negative local variance every where along the strike??
Thanks a lot!!
only
arbitrage
【在 z****u 的大作中提到】 : I don't know how to explain. But the truth is if you agree the pdf of the : stock level at a future time has a fat tail, then implied vol cannot be only : a function of strike. Because this will lead to strike-dimension arbitrage : opportunities, which mean local variance will be negative. : On the other hand, you can insist on no-fat-tail and have a consistent : theoretical picture, i.e., the Black-Scholes flat skew. In this case, the : implied vol is a constant. This does not cause any problem since now t
| z****u 发帖数: 185 | 5 seems you are right. The arbitrage opportunity is expected to appear far OTM.
as
【在 s****y 的大作中提到】 : thanks for replying! : the implied vol is not constant in my case. it has skew, very sharp when K : goes zero, and looks exponentially decreasing later and after ATM strike as : well. : I think I will get a negative local variance when K is small. but you mean : it will lead to negative local variance every where along the strike?? : Thanks a lot!! : : only : arbitrage
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