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Re: Why inflation zero floor prices to zero

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Chris Kenyon-2

Re: Why inflation zero floor prices to zero

Hi Ivan,

your observations are exactly correct:
1) in a Black world a zero floor has no value because you can't get there. A YoYInflationBlackCapFloorEngine implements this so, yes, you always get zero NPV.
2) If you use a displaced diffusion then, yes, you can see value in a zero floor. This is implemented in the UnitDisplacedBlackYoYInflationCouponPricer for coupons and there is an analogous engine for instruments.
3) Alternatively you can use a Normal process and use the BachelierYoYInflationCouponPricer for coupons (or the instrument one) and you will again see value in a zero floor.

Either way MAKE VERY SURE that you have the correct yoy inflation volatility for the pricing engine! Don't use a Black vol in a UnitDisplaced pricer/engine or you will have incorrect results. If you are starting from cap/floor prices on BBG (or wherever) you have to strip with the same type of pricer that you then price with. Of course, there is a smile in the market data on BBG :-) so ...

Usual disclaimers apply.

Best,
Chris

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Pomarico Francesco Ivan

Re: Why inflation zero floor prices to zero

Thanks again Chris,

I got another question on inflation.

I am looking at the file inflationvolatility.cpp in the testsuite and I don’t get what sort of cap and floor prices are used. Maybe there is some convention I am not aware of.

Looking on BBG quotes are in basis points from the order of tenths of bps to some hundredths of bps.

For example looking at price of zero floors on BBG quotes are from 68 bps up to 446 bps, so I expect to see prices in a range from 0.0068 up to 0.0446, but in the Quantlib inflationvolatility.cpp I see 0.851, 2.236, 3.935, 7.885, 17.92 and 47.625.

OK, prices are from different days, but magnitude has no sense for me. What did I miss?

Regards,

Ivan

From: Chris Kenyon [mailto:[hidden email]]
Sent: Wednesday, November 18, 2009 5:29 PM
To: [hidden email]; Pomarico Francesco Ivan
Subject: Re: Why inflation zero floor prices to zero

Hi Ivan,

your observations are exactly correct:
1) in a Black world a zero floor has no value because you can't get there. A YoYInflationBlackCapFloorEngine implements this so, yes, you always get zero NPV.
2) If you use a displaced diffusion then, yes, you can see value in a zero floor. This is implemented in the <a href="file:///\\Users\ckenyon\C++Libraries\QuantLib-SF-99\Docs\html\class_quant_lib_1_1_unit_displaced_black_yo_y_inflation_coupon_pricer.html">UnitDisplacedBlackYoYInflationCouponPricer for coupons and there is an analogous engine for instruments.
3) Alternatively you can use a Normal process and use the <a href="file:///\\Users\ckenyon\C++Libraries\QuantLib-SF-99\Docs\html\class_quant_lib_1_1_bachelier_yo_y_inflation_coupon_pricer.html">BachelierYoYInflationCouponPricer for coupons (or the instrument one) and you will again see value in a zero floor.

Either way MAKE VERY SURE that you have the correct yoy inflation volatility for the pricing engine! Don't use a Black vol in a UnitDisplaced pricer/engine or you will have incorrect results. If you are starting from cap/floor prices on BBG (or wherever) you have to strip with the same type of pricer that you then price with. Of course, there is a smile in the market data on BBG :-) so ...

Usual disclaimers apply.

Best,
Chris

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Chris Kenyon-2

Re: Why inflation zero floor prices to zero

I think that you are reading the mx the wrong way round: there are 6 strikes and 7 maturities, so I think you are looking at different strikes for the 5Y maturity. However, your points are still valid.

In the file the values are in bps. If you look in interpolatedyoyoptionletstripper.hpp in the function:

template <class Interpolator1D>
InterpolatedYoYOptionletStripper<Interpolator1D>::
ObjectiveFunction::ObjectiveFunction

you will see .withNominal(10000) which does the scaling back to what you are expecting. OK this is rather obscure, but it is in /experimental . The scaling should probably be before input rather than deep in the code.

The data in the test is from long ago and far away ... inflation expectations have moved a lot in the past two years. ~2007, i.e. pre-crisis, EU expected inflation was 2%~3% (see the data yoyEUrates higher up).

Usual disclaimers apply.

From: Pomarico Francesco Ivan <[hidden email]>
To: Chris Kenyon <[hidden email]>; [hidden email]
Sent: Thu, November 19, 2009 10:24:31 AM
Subject: RE: Why inflation zero floor prices to zero

Thanks again Chris,

I got another question on inflation.

I am looking at the file inflationvolatility.cpp in the testsuite and I don’t get what sort of cap and floor prices are used. Maybe there is some convention I am not aware of.

Looking on BBG quotes are in basis points from the order of tenths of bps to some hundredths of bps.

OK, prices are from different days, but magnitude has no sense for me. What did I miss?

Regards,

Ivan

From: Chris Kenyon [mailto:[hidden email]]
Sent: Wednesday, November 18, 2009 5:29 PM
To: [hidden email] ; Pomarico Francesco Ivan
Subject: Re: Why inflation zero floor prices to zero