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Quant版 - what's local vol??
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话题: vol话题: local话题: strike话题: implied话题: any
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1 (共1页)
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

1 (共1页)
进入Quant版参与讨论
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话题: vol话题: local话题: strike话题: implied话题: any