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An interest rate swap is a hedging tool frequently used
by our clients. Kynex provides its own proprietary model to value these
swaps. This calculator is fully integrated into the portfolio and trade
entry systems. The model will allow you to pay fixed rate payments and
receive floating rate payments or vice versa.
Critical to the standard valuation of a swap is the
determination of the implied forward rates derived from the swap curve.
These forward rates represent today’s best estimate of current index values.
Given the US$ Swap Curve and a 3-month fixed-to-float swap, the relevant
index value is 3-month libor. Displayed below are
the mid-market values for the US$ Swap Curve as of 5pm EST on 9/25/2003
(with settle on 9/29/2003) as well as the corresponding yields, spots, and
forwards for the subsequent ten years (the graph plots these values for 30
years).
These 3-month forward rates (yellow line on the graph
and yellow background in the table) are derived using the Kynex forward
rate model. This model connects and smoothes the forward rates while
maintaining term structure as well as no arbitrage on the yields. Note that the calculated yield curve
values (light blue) are exactly equivalent to the par-yields specified at
the swap curve tenor points. It is also important to note that the yields
at the intermediate points (e.g. 12/29/2010) are derived from the
forwards. Direct interpolation of
interest rates on yield curves will produce irregular forward rates (generally
having a “saw tooth” pattern). These
derived forward rates are semi-annual, 30/360 compound interest rates.
However, they need to be adjusted to an ACT/360, simple interest rate basis
in order to be used as a future 3-month libor
rate. For example, the first forward rate should be adjusted as follows to
current 3-month libor:
100*(360/days)*(1.00/0.997126613
– 1) = 1.14, where days = 91 is the
actual number of
days between 9/29/2003 and 12/29/2003
Similarly, the 3-month forward rate five years out
should also be adjusted from 5.33701782 to:
100*(360/days)*( 0.85298143/0.84194649 –
1) = 5.184975, where days = 91
is the actual
number of days between 6/30/2008 and 9/29/2008
The Kynex interest rate-swap model makes the appropriate
adjustments in calculating the forward rates. These adjusted forward rates
give the market consensus of future 3-month libor,
and they are shown as the Projected Index values on the Flows window of the
IR Swap calculator.
However, the market consensus can be wrong. Certainly,
the forwards from the standard valuation were not close proxies five years
ago (hindsight is 20-20, but is instructive nevertheless). Consider below the mid-market values for
the US$ Swap Curve as of 5pm EST on 9/25/1998 (with settle on 9/29/1998).
If you purchased a five year, Pay-Fixed/Receive-Float
swap on 9/25/1998, you overpaid by 88.8bps (the 5 year fixed coupon was
4.237 based on the actual resets). Of course, the flip side of this is true
as well. If the interest rates rise higher than that suggested by the yield
curve at the time of valuation, the fixed payment would be under-estimated.
Kynex allows you to analyze alternate valuations by using a cap and floor.
If you believe, for example, that 3-month libor
will not go above 4.5%; you can use the Kynex swap model to cap forward
rates at 4.5% and to then recalculate the 5 year fixed swap rate.
To value a generic swap on Kynex, please click on the
Swaps tab and then IR Swap. You enter the general terms of the swap in the
upper portion of the panel on the left of the screen. Additional terms
(e.g. fixed coupon, index term of 0.25 for a float leg that resets
quarterly) are entered on the panel on the right. The Kynex model requires
certain other valuation parameters which are found on the bottom portion of
the panel on the left. For example,
the model can calculate any one of three different values of swap premium,
fixed coupon, and floating spread, given the other two. You may also select
if the principle is going to be exchanged at maturity. Kynex has defaulted this to “No” because
the DV+01 for each of the legs will be correctly measured. If this value is
set to “Yes”, the total DV+01 will remain unchanged and the swap premium
for each leg will show in familiar bond terms. If you want to see the curve
or your cash flows, click their respective buttons. You may also add a swap directly to your
portfolio by means of the “Create” button.
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