Wobbly, non-monotonic discount curve

[Pascal Haakmat]

Hi,

When I build a discount curve using PiecewiseLinearForward (i.e. the
SWIG binding for PiecewiseYieldCurve with Linear interpolator and
ForwardRate traits), I get discount values that do not monotonically
decrease. This behavior does not occur when using PiecewiseFlatForward
(i.e. a PiecewiseYieldCurve with BackwardFlat interpolator and
ForwardRate traits).

I've captured screenshots graphing discount factors and zero rates by year:

PiecewiseLinearForward: http://imgur.com/WiSiKnY
PiecewiseFlatForward: http://imgur.com/wd6tP8r

What could account for the wobbly behavior in the PiecewiseLinearForward
graph?

The input data is as follows. Quotes <1Y are passed using a
DepositRateHelper, >=1Y using a SwapRateHelper.

1D    0.0036
6M    0.0036999999999999997
1Y    0.0057
2Y    0.0077
3Y    0.009699999999999999
4Y    0.011699999999999999
5Y    0.013699999999999999
6Y    0.0157
7Y    0.0177
8Y    0.0197
9Y    0.0217
10Y    0.0237
11Y    0.0247
12Y    0.0257
13Y    0.026699999999999998
14Y    0.0277
15Y    0.0287
16Y    0.0297
17Y    0.030699999999999998
18Y    0.031700000000000006
19Y    0.0327
20Y    0.0337
25Y    0.0327
30Y    0.031700000000000006
40Y    0.030699999999999998
50Y    0.0297
60Y    0.0297
70Y    0.0297
80Y    0.0297
90Y    0.0297
100Y    0.0297

Thanks,
Pascal

------------------------------------------------------------------------------
Download BIRT iHub F-Type - The Free Enterprise-Grade BIRT Server
from Actuate! Instantly Supercharge Your Business Reports and Dashboards
with Interactivity, Sharing, Native Excel Exports, App Integration & more
Get technology previously reserved for billion-dollar corporations, FREE
http://pubads.g.doubleclick.net/gampad/clk?id=157005751&iu=/4140/ostg.clktrk
_______________________________________________
QuantLib-users mailing list
[hidden email]
https://lists.sourceforge.net/lists/listinfo/quantlib-users

[Peter Caspers-4]

Hi Pascal,

this is well explained in Hagan, West: Methods for constructing a
yield curve (in particular have a look into sections 4.4 and 4.5). You
can get the paper e.g. from here

http://www.math.ku.dk/~rolf/HaganWest.pdf

best regards
Peter

On 27 November 2014 at 17:53, Pascal Haakmat <[hidden email]> wrote:

> Hi,
>
> When I build a discount curve using PiecewiseLinearForward (i.e. the
> SWIG binding for PiecewiseYieldCurve with Linear interpolator and
> ForwardRate traits), I get discount values that do not monotonically
> decrease. This behavior does not occur when using PiecewiseFlatForward
> (i.e. a PiecewiseYieldCurve with BackwardFlat interpolator and
> ForwardRate traits).
>
> I've captured screenshots graphing discount factors and zero rates by year:
>
> PiecewiseLinearForward: http://imgur.com/WiSiKnY
> PiecewiseFlatForward: http://imgur.com/wd6tP8r
>
> What could account for the wobbly behavior in the PiecewiseLinearForward
> graph?
>
> The input data is as follows. Quotes <1Y are passed using a
> DepositRateHelper, >=1Y using a SwapRateHelper.
>
> 1D    0.0036
> 6M    0.0036999999999999997
> 1Y    0.0057
> 2Y    0.0077
> 3Y    0.009699999999999999
> 4Y    0.011699999999999999
> 5Y    0.013699999999999999
> 6Y    0.0157
> 7Y    0.0177
> 8Y    0.0197
> 9Y    0.0217
> 10Y    0.0237
> 11Y    0.0247
> 12Y    0.0257
> 13Y    0.026699999999999998
> 14Y    0.0277
> 15Y    0.0287
> 16Y    0.0297
> 17Y    0.030699999999999998
> 18Y    0.031700000000000006
> 19Y    0.0327
> 20Y    0.0337
> 25Y    0.0327
> 30Y    0.031700000000000006
> 40Y    0.030699999999999998
> 50Y    0.0297
> 60Y    0.0297
> 70Y    0.0297
> 80Y    0.0297
> 90Y    0.0297
> 100Y    0.0297
>
> Thanks,
> Pascal
>
> ------------------------------------------------------------------------------
> Download BIRT iHub F-Type - The Free Enterprise-Grade BIRT Server
> from Actuate! Instantly Supercharge Your Business Reports and Dashboards
> with Interactivity, Sharing, Native Excel Exports, App Integration & more
> Get technology previously reserved for billion-dollar corporations, FREE
> http://pubads.g.doubleclick.net/gampad/clk?id=157005751&iu=/4140/ostg.clktrk
> _______________________________________________
> QuantLib-users mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-users

------------------------------------------------------------------------------
Download BIRT iHub F-Type - The Free Enterprise-Grade BIRT Server
from Actuate! Instantly Supercharge Your Business Reports and Dashboards
with Interactivity, Sharing, Native Excel Exports, App Integration & more
Get technology previously reserved for billion-dollar corporations, FREE
http://pubads.g.doubleclick.net/gampad/clk?id=157005751&iu=/4140/ostg.clktrk
_______________________________________________
QuantLib-users mailing list
[hidden email]
https://lists.sourceforge.net/lists/listinfo/quantlib-users