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Alessio Benavoli

CMS Hull

Dear all,

I would like to know how pricing CMS swaps under Hull's model in QuantLib.

Here the case study I'm considering:

Valuation date 10-Jan-14
Maturity date 10-Jan-19
CMS payment frequency 2 years
Underlying swap payment frequency 2 years
Underlying swap tenor 5 years

The Euribor swap zero curve from 8 Jan 14 is

1 MO 0.434    8 YR 2.69399
2 MO 0.54    9 YR 2.84076
3 MO 0.713 10 YR 2.96595
4 MO 0.801 11 YR 3.08075
5 MO 0.895      12 YR 3.18222
6 MO 0.999      15 YR 3.37877
1 YR 1.07641   20 YR 3.45766
2 YR 1.25712   25 YR 3.35702
3 YR 1.52192   30 YR 3.17684
4 YR 1.80806   35 YR 3.07155
5 YR 2.08133   40 YR 2.95376
6 YR 2.31933   45 YR 2.97416
7 YR 2.52316   50 YR 2.91187

Swapoption volatility on a five year swap 0.22
Six months caplet volatility 0.15

Correlation between swap and forward rate 0.7

Do you have any suggestion about which classes should be used in QLib.
Here I'm assuming that the volatility is constant, what about if we have a volatility surface?

Thank you for the help.

Alex

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Peter Caspers-4

Re: CMS Hull

Hi Alex,

I think there is no cms pricer using the Hull model at the moment
(assuming you are referring to the formulas developed in Option
Futures and Other Derivatives, chapter Convexity, Quanto and Timing
adjustments). I guess the closest available choice would be the
AnalyticHaganPricer with modelOfYieldCurve =
GFunctionFactory::Standard or ExactYield. You can feed a
SwaptionVolatilityMatrix (i.e. an ATM volatility surface) into this
pricer.

Do you think it would be useful to have Hull's convexity-timing
adjustment for cms in QL ?

best regards
Peter

On 24 February 2014 16:17, Alessio Benavoli <[hidden email]> wrote:

> Dear all,
>
> I would like to know how pricing CMS swaps under Hull's model in QuantLib.
> Here the case study I'm considering:
>
> Valuation date 10-Jan-14
> Maturity date 10-Jan-19
> CMS payment frequency 2 years
> Underlying swap payment frequency 2 years
> Underlying swap tenor 5 years
>
> The Euribor swap zero curve from 8 Jan 14 is
> 1 MO 0.434 8 YR 2.69399
> 2 MO 0.54 9 YR 2.84076
> 3 MO 0.713 10 YR 2.96595
> 4 MO 0.801 11 YR 3.08075
> 5 MO 0.895 12 YR 3.18222
> 6 MO 0.999 15 YR 3.37877
> 1 YR 1.07641 20 YR 3.45766
> 2 YR 1.25712 25 YR 3.35702
> 3 YR 1.52192 30 YR 3.17684
> 4 YR 1.80806 35 YR 3.07155
> 5 YR 2.08133 40 YR 2.95376
> 6 YR 2.31933 45 YR 2.97416
> 7 YR 2.52316 50 YR 2.91187
>
> Swapoption volatility on a five year swap 0.22
> Six months caplet volatility 0.15
> Correlation between swap and forward rate 0.7
>
> Do you have any suggestion about which classes should be used in QLib.
> Here I'm assuming that the volatility is constant, what about if we have a
> volatility surface?
>
> Thank you for the help.
> Alex
>
> ------------------------------------------------------------------------------
> Flow-based real-time traffic analytics software. Cisco certified tool.
> Monitor traffic, SLAs, QoS, Medianet, WAAS etc. with NetFlow Analyzer
> Customize your own dashboards, set traffic alerts and generate reports.
> Network behavioral analysis & security monitoring. All-in-one tool.
> http://pubads.g.doubleclick.net/gampad/clk?id=126839071&iu=/4140/ostg.clktrk
> _______________________________________________
> QuantLib-users mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>