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UNIVERSITY of LIMERICK
OLLSCOIL LUIMNIGH
DEPARTMENT OF ACCOUNTING & FINANCE
KEMMY BUSINESS SCHOOL
FI6002 Interest Rate Derivatives Hedging & Trading Project Assignment
MODULE TITLE: Fixed Income Models
MODULE CODE:
FI6002
SEMESTER:
ACADEMIC YEAR:
2014-15
Spring
PERCENTAGE OF TOTAL MARKS: 40%
DURATION :
Weeks 7 - 13
LECTURER :
EXTERNAL EXAMINER:
Dr. Bernard Murphy
Prof. Don Bredin
3-person Student Group :
Part A –Swap Risk Management & Yield-Spread Arbitrage Trading Strategy (15 Marks)
Part B – Swaption Risk Management & Yield-Spread Arbitrage Trading Strategy (25 Marks)
See inside for details of the project assignment – parts A and B.
Part A (15%)
A ‘Multi-Leg FRA’ Swap Key Rate Hedge & Yield-Spread Arbitrage Trading Strategy
The equilibrium swap rate X can be specified in terms of the discrete forward-Libor rates F
which span the life of the swap and where P(t,T) denotes the current price of a discount bond
(priced off the Libor-Swap zero curve) maturing on date T,

360
denotes the
Act
360
day-count fraction for
the floating / fixed legs of the swap.
Required
(a) You are required to use Bloomberg’s multi-leg Swap Manager tool (SWPM) to delta-hedge
(against small parallel movements in the yield curve) the two ‘key-rate’ swaps linked to your
group’s assigned swaption instrument described in Part B, using as hedging instruments a
strip of single-period FRA’s for the near-dated swap (as suggested by Figures 1 & 2 overleaf)
and a simple offsetting par swap hedge for the far-dated swap.
(b) Explaining how your delta-hedged swap portfolio can be used to speculate on a non-parallel
movement in the benchmark Libor – ED Futures - Swap yield curve, use the Scenario analysis
tool in SWPM to show how your delta-hedged swap portfolio can be used to implement a
low-risk “yield-spread arbitrage” trading strategy.
Instructions
For part (a) you must first create and save as a “SWPM Deal” the delta-hedged Swap + FRA portfolio
using the SWPM Swap Manager tool. Supporting your work with well-labelled Bloomberg trading
screens, you must demonstrate using the

Risk tab in SWPM (i.e. showing the before and after stages in the construction of the ED
Futures / FRA hedge), and
that the total DV01 of your hedged swap portfolio is ‘approximately’ zero.
You must take care to synchronise the timing of the cash flow on the hedge as closely as possible
with that of the swap by using IMM “Date Types” as demonstrated in FI6002 Tutorial class.
You must also explain whether you need to be long or short (receive or pay fixed) the hedging
futures contracts (or FRA’s), and show calculations to validate the notional principal amounts
required for each of the FRA hedges.
For part (b) you should explain whether your portfolio is long or short the Libor-Swap yield-spread
(which in turn is driven by the ‘tilt’ aka ‘twist’ yield curve risk factor) implied by the maturities of the
two par swaps alluded to in part (a). You should additionally show calculations to confirm the source
and magnitude of your arbitrage trading strategy.
Figure 1 – 2Y Swap Risk Analysis (Details of Offsetting Delta Hedges in Listed Eurodollar / ED Interest Rate Futures Contracts)
Figure 2 – Details of Libor, Futures & Swap Rates used to Bootstrap the Libor-Swap Zero Curve (Mar13 ED Futures Contract has just expired)
Part B (25%)
The Swaption Key Rate Hedge – An Alternative Yield-Spread Arbitrage Trading Strategy
(i)
Black’s formula for valuing a payer interest rate swaption can reveal the key rate exposures of the
swaption instrument and hence an appropriate delta-hedging strategy :
Required
In this section of Part B you are required to first provide an intuitive explanation for the “dual” key
rate exposures of your group’s assigned swaption position, producing a ‘similar’ DV01 screenshot as
illustrated for the 5Y x 5Y payer swaption shown in Figure 3 overleaf, citing in particular any hedging
insights or intuition which might be inferred from the methodology used to “strip” zero rates from
the Libor-Swap market curve.
Figure 3 - Payer Swaption Key Rate Risk Exposures (in response to -1bp shift in Key-Maturity Rates)
(ii)
Recall that for the type of non-parallel yield curve movement depicted below
an appropriate combination of a payer + receiver swap hedge can be combined with your swaption
position so as to isolate an exposure to the tilt / slope yield curve risk-factor.
Required
(a) Carefully interpreting the valuation formulae for the various component parts of your
assigned delta-hedged swaption position (i.e. including the formulae for the payer and
receiver swaps shown above), you should explain what type(s) of reference yield curve
movement1 will generate a positive P&L for your yield spread arbitrage trading strategy (i.e.
assuming you delta-hedge your assigned swaption position using par swaps).
(b) In order to confirm that that your proprietary portfolio has isolated out an exposure to the
tilt / slope risk-factor (the swaption’s ‘vega’ exposure notwithstanding), you should create
and save as a “SWPM Deal” the delta-hedged Swaption + Swap portfolio using the SWPM
Swap Manager tool. Then supporting your work with well-labelled Bloomberg trading
screens, you must demonstrate using both the
o Risk tab in SWPM (i.e. showing the before and after stages in the construction of the
par swap payer / receiver delta hedge) – see Figure 3 above, and
o Bloomberg’s Multi Asset Risk Management System (MARS) tool – see Figure 4 below
1
For example, in the bond market you might explain how a bond trader’s expectation of an imminent positive steepening
in the Treasury Bond yield curve might be seen as a rational investor demand for more yield as maturity extends in
anticipation of an economic upturn. Analogously in the money markets, you could refer to and analyse a bank treasurer’s
perspective when contemplating an OIS-based liquidity management strategy (as explained in class) in the face of an
anticipated steepening in the money market term structure at the short or ‘policy rate’ end of the maturity spectrum.
that the total DV01 of your hedged swaption portfolio is approximately zero.
(c) Using the Scenario Screen or Market Scenario Manager function in Bloomberg’s swap and
swaption trading screens, you should select from the pre-defined menu (or manufacture a
customised scenario) a yield curve scenario (e.g. positive or negative tilt; upwards or
downwards parallel shift) and then quantitatively analyse the resulting P&L to validate the
source2 of your proprietary trading strategy’s P&L (i.e. put simply, was your position long or
short the spread and was your manufactured scenario consistent with a widening or
contraction in the ‘key-maturity’ yield-spread ?).
Figure 4. Delta-Hedged Payer Swaption Portfolio in MARS
2
The advantage of using Bloomberg’s scenario-based ‘what if’ functionality (as opposed to a historical backtest across two distinct historical dates) is that a “ceteris-paribus” or “other things equal” non-parallel
movement can be applied to the reference Libor-Swap yield curve – i.e. leaving the swaption volatility “factor”
unchanged. Consequently, any trading strategy P&L must only be due to the ‘manufactured yield-curve
outturn’. In other words, the trading P&L cannot be due to the shift or parallel movement risk-factor since this
yield-curve risk-factor is hedged-out by the hedging swaps, and moreover cannot be due to a shock from the
volatility risk-factor since, by assumption, the swaption implied volatility remains unchanged under the
Bloomberg scenario-based or ‘manufactured’ yield curve movement.