## Re: [Quantlib-users] swaps

 Re: [Quantlib-users] swaps From: Ferdinando Ametrano - 2002-06-19 17:07:51 ```Hi Jens you wrote: >I take the swapvaluation example and assume: > >- termstructure with constant 4% rates >- 2 year swap, 4% fixed rate, spread 0.0 > >and get the following results: > > *** 2Y swap at 4.00% > *** using constant 4% structure: > 2Y 4.00% NPV: 2346.70 > 2Y 4.00% fair spread: 0.1228% > 2Y fair fixed rate: 3.8760% > >Can somebody explain that to me? I'm sorry I cannot double check your example right now, but you might be paying too little attention to the daycount and compounding conventions. The 4% rate of a QuantLib term structure is continuos compounding: discount(t)=QL_EXP(0.04*t) and the time is measured with the daycount you provided as input (usually something smooth as act/365, not 30/360) The 4% fixed rate of a 2 year swap is simple compounding: cashflow=0.04*Nominal*t, and the time is measured with the daycount you provided as input (usually 30/360) This could easily account for the numerical results you provided. It would be different if you bootstrapped a term structure with a 2 year swap, 4% fixed rate and then the bootstrapped yield curve wouldn't re-price the same swap at 4%. This would be a real problem. Hope this helps. If not, please let me know and I'll go into the actual calculations ciao -- Nando ```

 [Quantlib-users] swaps From: Jens Thiel - 2002-06-19 16:01:27 Attachments: swapvaluation.cpp ```Hello, I have some problem here: I take the swapvaluation example and assume: - termstructure with constant 4% rates - 2 year swap, 4% fixed rate, spread 0.0 and get the following results: *** 2Y swap at 4.00% *** using constant 4% structure: 2Y 4.00% NPV: 2346.70 2Y 4.00% fair spread: 0.1228% 2Y fair fixed rate: 3.8760% Can somebody explain that to me? We are also getting "weird" results from the term structures. Jens. ```
 Re: [Quantlib-users] swaps From: Ferdinando Ametrano - 2002-06-19 17:07:51 ```Hi Jens you wrote: >I take the swapvaluation example and assume: > >- termstructure with constant 4% rates >- 2 year swap, 4% fixed rate, spread 0.0 > >and get the following results: > > *** 2Y swap at 4.00% > *** using constant 4% structure: > 2Y 4.00% NPV: 2346.70 > 2Y 4.00% fair spread: 0.1228% > 2Y fair fixed rate: 3.8760% > >Can somebody explain that to me? I'm sorry I cannot double check your example right now, but you might be paying too little attention to the daycount and compounding conventions. The 4% rate of a QuantLib term structure is continuos compounding: discount(t)=QL_EXP(0.04*t) and the time is measured with the daycount you provided as input (usually something smooth as act/365, not 30/360) The 4% fixed rate of a 2 year swap is simple compounding: cashflow=0.04*Nominal*t, and the time is measured with the daycount you provided as input (usually 30/360) This could easily account for the numerical results you provided. It would be different if you bootstrapped a term structure with a 2 year swap, 4% fixed rate and then the bootstrapped yield curve wouldn't re-price the same swap at 4%. This would be a real problem. Hope this helps. If not, please let me know and I'll go into the actual calculations ciao -- Nando ```
 Re: Re: [Quantlib-users] swaps From: Ilja Chagalov - 2002-06-20 08:50:56 ```Hi everybody! If you try to compute zero yields with the constant 4% term structure in the Jens's example (TermStructure is fed with four DepositRateHelpers: 1w, 1y, 5y, 10y and the rate is set to 4% everywhere) ... for(double t=1.0; t<=9.0;t+=1.0) std::cout << "zeroYield(" << t << ") =" << RateFormatter::toString(depoSwapTermStructure->zeroYield(t), 4) << std::endl; ... you get the following results: zeroYield(1) =3.9755% zeroYield(2) =3.7999% zeroYield(3) =3.7413% zeroYield(4) =3.7121% zeroYield(5) =3.6945% zeroYield(6) =3.5983% zeroYield(7) =3.5296% zeroYield(8) =3.4781% zeroYield(9) =3.4380% I get similar results using act/365 day counter. In my understanding it should be appr. =4% everywhere, but it looks different. Why is it so? Why is the zero yield going down as t inscreases? Greetings, Ilja ----- Original Message ----- From: "Ferdinando Ametrano" To: "Jens Thiel" ; Cc: Sent: Wednesday, June 19, 2002 7:07 PM Subject: Re: [Quantlib-users] swaps > Hi Jens > > you wrote: > >I take the swapvaluation example and assume: > > > >- termstructure with constant 4% rates > >- 2 year swap, 4% fixed rate, spread 0.0 > > > >and get the following results: > > > > *** 2Y swap at 4.00% > > *** using constant 4% structure: > > 2Y 4.00% NPV: 2346.70 > > 2Y 4.00% fair spread: 0.1228% > > 2Y fair fixed rate: 3.8760% > > > >Can somebody explain that to me? > I'm sorry I cannot double check your example right now, but you might be > paying too little attention to the daycount and compounding conventions. > The 4% rate of a QuantLib term structure is continuos compounding: > discount(t)=QL_EXP(0.04*t) > and the time is measured with the daycount you provided as input (usually > something smooth as act/365, not 30/360) > The 4% fixed rate of a 2 year swap is simple compounding: > cashflow=0.04*Nominal*t, and the time is measured with the daycount you > provided as input (usually 30/360) > This could easily account for the numerical results you provided. > > It would be different if you bootstrapped a term structure with a 2 year > swap, 4% fixed rate and then the bootstrapped yield curve wouldn't re-price > the same swap at 4%. > This would be a real problem. > > Hope this helps. If not, please let me know and I'll go into the actual > calculations > > ciao -- Nando > > > ```
 Re: Re: [Quantlib-users] swaps From: Ferdinando Ametrano - 2002-06-20 12:54:52 ```At 10:48 AM 6/20/2002 +0200, Ilja Chagalov wrote: >If you try to compute zero yields with the constant 4% term structure in the >Jens's example (TermStructure is fed with four DepositRateHelpers: 1w, 1y, >5y, 10y and the >rate is set to 4% everywhere) ... >[...] >... you get the following results: > >zeroYield(1) =3.9755% >zeroYield(2) =3.7999% >zeroYield(3) =3.7413% >zeroYield(4) =3.7121% >zeroYield(5) =3.6945% >zeroYield(6) =3.5983% >zeroYield(7) =3.5296% >zeroYield(8) =3.4781% >zeroYield(9) =3.4380% > >I get similar results using act/365 day counter. >In my understanding it should be appr. =4% everywhere, but it looks >different. >Why is it so? Why is the zero yield going down as t inscreases? the zero curve is decreasing since depo rates are simple compounding while zero rate in QuantLib are continuously compounded. I attach here a simple Excel spreadsheet with the following calculation: A B C D E ------------------------------------------------------------------- time act/365 depo rate discount=1/(1+C*B) zero=LN(1/D)/B 1w 0.019 4% 0.999233465 4.00% 1y 1.000 4% 0.961538462 3.92% 5y 5.000 4% 0.833333333 3.65% 10y 10.000 4% 0.714285714 3.36% The residual difference with the QuantLib output is because my simple example doesn't take into account the correct (act/360) deposit daycount. That is the time used in column D should be different (act/360) from the time used in column E (act/365) QuantLib::TermStructure::PiecewiseFlatForward does "interpolate" on the 4 discounts bootstrapped from the 4 deposit rates using constant _continuously_compounded_ forward rates. Namely: 0-1w 4.00% 1w-1y 3.92% 1y-5y 3.58% 5y-10y 3.08% The conclusion is that 4% flat deposit rate doesn't mean flat zero/forward, as long as the zero/forward use a different compounding rule. Besides a flat forward curve doesn't provide a flat swap (par rate) curve Market convention are a mess, I know, but this is not QuantLib fault ;-) hope this helps ciao -- Nando PS It's sometime now I'm thinking about posting a short review of "Capital Market Instruments: Analysis and Valuation" by Moorad Choudhry, Didier Joannas, Richard Pereira, Rod Pienaar. I think it is a great introductory book for someone approaching the complexity of financial market with a strong math background, that is someone who doesn't really need an introduction to finite difference or stochastic processes as much as he needs an introduction to market conventions, products, etc. ```
 Re: Re: [Quantlib-users] swaps From: Ferdinando Ametrano - 2002-06-20 17:06:37 Attachments: example.xls ```oops, I forgot the attachment. Here it is ciao -- Nando```