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Zero% Strike Floors

Giuseppe Trapani

Giuseppe Trapani

Joined
3/5/15
Messages
5
Points
13
Hi everybody,
I've encountered this problem and I'd love to know what you people think about it:

"In Europe we have very low rates and deflation risk, and this leads the bank to price many Floors with a strike of 0%. Also Caps with very low strikes such as 0.1% are requested"

Now:
1) Black's formula is almost useless
2) Fitting Sabr surface is quite a mess

Any suggestions? thanks in advance ^^
 
In a GBM, a zero strike call is the same thing as futures contract.

If you want to assume that negative rates are possible, then clearly GBM is not the right model, you'll have to do ABM and adjust surface models to match, which unfortunately means you have to re-derive a lot of it on your own I'm guessing.

Edit: Another way to get negative rates is a shifted GBM, where the actual process = GBM + constant.
 
Yike Lu said:
In a GBM, a zero strike call is the same thing as futures contract.

If you want to assume that negative rates are possible, then clearly GBM is not the right model, you'll have to do ABM and adjust surface models to match, which unfortunately means you have to re-derive a lot of it on your own I'm guessing.

Edit: Another way to get negative rates is a shifted GBM, where the actual process = GBM + constant.
Click to expand...


Thank you for the answer ^^
Yes we MUST assume that negative rates are possibile (EUR001M are negative most of the time for low maturities) . Indeed we are actually using shifted lognormal to be at least able to price that stuff, but the SABR calibration problem remains.

Ofc we can resort to Monte Carlo simulations of HJM multi-curve models with some stochastic volatility but I'd love to find a faster way.
 
You can't use a shifted SABR? Or maybe a shifted SVI?
 
Yike Lu said:
You can't use a shifted SABR? Or maybe a shifted SVI?
Click to expand...
I'll give it a try. I'm the only one working on it here now so it's kinda slow (since it's not my actual job to be a quant ^^)

I'll post some results (if any) once I'm done.

Thank you very much for the answers ^^
 
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