Re: Re: [Quantlib-users] swaps

[Ferdinando A. <fer...@am...>]

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.