Output zero rates can differ from the input rates by quite a bit

[StephenWong]

Hello fellow QL users,

I encountered a problem and I wonder if anyone else has seen it?

The problem can be essentially boiled down to if I feed a sequence of zero rates
into the PiecewiseYieldCurve, use that as the YieldTermStructure in a PricingEngine.
After pricing a zero coupon bond, the same sequence of zero rates I get back from
the term structure are not all identical to the inputs.

Most of the zero rates are identical except for a few in the sequence. Those seem to be
much worse than the rest. It does not matter if the sequence is at intervals of every half year or every
year, there are always a few in the sequence that differ more from the inputs than  
I would like to tolerate.


For example if I feed in the zero rates in the second column, I got the output in the third column

Yr  Input (%)   Output (%)
1    4.29        4.290  
2    4.64        4.638707       <----
3    4.79        4.789613       <----
4    4.87        4.870
5    4.92        4.920
6    4.94        4.940
7    4.96        4.960
8    4.96        4.959969
9    4.96        4.960
10   4.95        4.950

Or

Yr  Input (%)   Output (%)
0.5  4.29        4.290
1     4.64        4.640
1.5  4.79        4.790
2     4.87        4.869173         <----
2.5  4.92        4.92
3     4.94        4.939856         <----
3.5  4.96        4.959861         <----
4     4.96        4.960
4.5  4.96        4.960
5     4.95        4.950

I thought the accuracy would be a little bit better than this.
Is this not a problem?

Thanks!
Stephen.

[Luigi Ballabio]

On Thu, 2011-11-03 at 13:25 -0700, StephenWong wrote:
> The problem can be essentially boiled down to if I feed a sequence of zero
> rates
> into the PiecewiseYieldCurve, use that as the YieldTermStructure in a
> PricingEngine.
> After pricing a zero coupon bond, the same sequence of zero rates I get back
> from
> the term structure are not all identical to the inputs.

What do you mean "feeding zero rates into the PiecewiseYieldCurve"?
You don't feed zero rates in that, you feed deposit rates, swap rates,
futures... Do you mean some other class?

Luigi


--

There is no opinion so absurd that some philosopher will not
express it.
-- Marcus Tullius Cicero, "Ad familiares"



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[StephenWong]

Luigi Ballabio wrote

On Thu, 2011-11-03 at 13:25 -0700, StephenWong wrote:
> The problem can be essentially boiled down to if I feed a sequence of zero
> rates
> into the PiecewiseYieldCurve, use that as the YieldTermStructure in a
> PricingEngine.
> After pricing a zero coupon bond, the same sequence of zero rates I get back
> from
> the term structure are not all identical to the inputs.

What do you mean "feeding zero rates into the PiecewiseYieldCurve"?
You don't feed zero rates in that, you feed deposit rates, swap rates,
futures... Do you mean some other class?

Luigi

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Yes Luigi you are right! I meant feeding those rates into the PiecewiseYieldCurve through a bunch of DepositRateHelpers.

[Luigi Ballabio]

On Fri, 2011-11-04 at 06:36 -0700, StephenWong wrote:
> > What do you mean "feeding zero rates into the PiecewiseYieldCurve"?
> > You don't feed zero rates in that, you feed deposit rates, swap rates,
> > futures... Do you mean some other class?

> Yes Luigi you are right! I meant feeding those rates into the
> PiecewiseYieldCurve through a bunch of DepositRateHelpers.

Then I rather expect you won't get the same rates if you ask the curve
for zero rates.  They have different conventions.

Luigi


--

The Feynman Problem Solving Algorithm:
1) Write down the problem.
2) Think very hard.
3) Write down the solution.



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[StephenWong]

Luigi Ballabio wrote

On Fri, 2011-11-04 at 06:36 -0700, StephenWong wrote:
> > What do you mean "feeding zero rates into the PiecewiseYieldCurve"?
> > You don't feed zero rates in that, you feed deposit rates, swap rates,
> > futures... Do you mean some other class?

> Yes Luigi you are right! I meant feeding those rates into the
> PiecewiseYieldCurve through a bunch of DepositRateHelpers.

Then I rather expect you won't get the same rates if you ask the curve
for zero rates.  They have different conventions.

Luigi
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But I used the same day count convention in the DepositRateHelpers and in the YieldTermStructure::zeroRate call.

[Luigi Ballabio]

On Nov 4, 2011, at 10:43 PM, StephenWong wrote:

> Luigi Ballabio wrote:
>> On Fri, 2011-11-04 at 06:36 -0700, StephenWong wrote:
>>>> What do you mean "feeding zero rates into the PiecewiseYieldCurve"?
>>>> You don't feed zero rates in that, you feed deposit rates, swap  
>>>> rates,
>>>> futures... Do you mean some other class?
>>
>>> Yes Luigi you are right! I meant feeding those rates into the
>>> PiecewiseYieldCurve through a bunch of DepositRateHelpers.
>>
>> Then I rather expect you won't get the same rates if you ask the  
>> curve
>> for zero rates.  They have different conventions.
>>
>
> But I used the same day count convention in the DepositRateHelpers  
> and in
> the YieldTermStructure::zeroRate call.

Day count convention is not all.  Deposit rates are not compounded.  
If you don't specify a compounding convention, zero rates are  
continuously compounded.

Luigi


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[StephenWong]

Luigi Ballabio wrote

On Nov 4, 2011, at 10:43 PM, StephenWong wrote:
> Luigi Ballabio wrote:
>> On Fri, 2011-11-04 at 06:36 -0700, StephenWong wrote:
>>>> What do you mean "feeding zero rates into the PiecewiseYieldCurve"?
>>>> You don't feed zero rates in that, you feed deposit rates, swap  
>>>> rates,
>>>> futures... Do you mean some other class?
>>
>>> Yes Luigi you are right! I meant feeding those rates into the
>>> PiecewiseYieldCurve through a bunch of DepositRateHelpers.
>>
>> Then I rather expect you won't get the same rates if you ask the  
>> curve
>> for zero rates.  They have different conventions.
>>
>
> But I used the same day count convention in the DepositRateHelpers  
> and in
> the YieldTermStructure::zeroRate call.

Day count convention is not all.  Deposit rates are not compounded.  
If you don't specify a compounding convention, zero rates are  
continuously compounded.

Luigi

Thanks for the answers and your patience, Luigi! That explains why I have to choose Compounding:Simple in YieldTermStructure::zeroRate to even get those output rates that I listed. Anything else would give much worse rates.

What is the logic behind using no compounding? May be this should be added in the document/manual?

[Luigi Ballabio]

On Nov 6, 2011, at 10:26 AM, StephenWong wrote:
> Thanks for the answers and your patience, Luigi! That explains why I  
> have to
> choose Compounding:Simple in YieldTermStructure::zeroRate to even  
> get those
> output rates that I listed. Anything else would give much worse rates.
>
> What is the logic behind using no compounding?

That's the way deposit rates are defined and quoted on the market.  
It's not really a QuantLib thing...

Luigi



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