(i) IR Swap = Long floating rate note + Short fixed rate note. Cash flow at time t i = M [(r i-1 -R]Δt

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Paula Fisher
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1 Solvay Busess School Uversté Lbre de Bruxelles Swaps Adré arber Revsed September 2005 Iterest rate swap Perodc paymets (=, 2,..,) at tme t+δt, t+2δt,..t+δt,..,t= t+δt Tme of paymet : t = t + Δt Log posto: Pays fx, receves floatg Cash flow (at tme t ): Dfferece betwee a floatg rate (set at tme t - =t+ (-) Δt) ad a fxed rate R adjusted for the legth of the perod (Δt) ad multpled by otoal amout M C = M (r - - R) Δt where r(-) s the floatg rate at tme t - Decompostos ad valuato () IR Swap = Log floatg rate ote + Short fxed rate ote Value of swap = f swap = V float - V fx = M M ( R Δ t) + xed rate R set tally to acheve f = 0 () IR Swap = Portfolo of RAs Remder: or RA wth ed of terest perod at tme t ad settlemet date at t - [ r R] Δt Cash flow at tme t - = M Cash flow at tme t = M [(r - -R]Δt + r Δt RA orward sale at tme t of a zero-coupo maturg at tme t + wth face value M (+ R Δt) for a delvery prce M Value of RA f RA, = M - - M (+ R Δt) fswap = fra, = [ M M( + RΔ t) ] = M M RΔ t + = = = Note: some of the RAs have postve values, other egatve values Swaps Class ote September 2005 /4/2007

2 2 () Swap valuato based o forward rates (for gve swap rate R): f = M ( Rˆ R) t Δ swap where R ˆ s the forward terest rate (smple terest) set at tme t for a forward trasacto from - to Rˆ t + Δ = To see why, rewrte the value of a RA as: f ˆ RA, = M ( + RΔ t) = M ( R R) Δ t If the forward rate R ˆ s greater tha the swap rate R: - the value of the RA s > 0 If the forward rate R s less tha the swap rate R: - the value of the RA s < 0 (v) Swap valuato based o curret swap rate for same maturty f = M ( R R) Δt swap swap = where R swap s the curret equlbrum swap rate wth a value = 0 Note: f swap = M R Δ t = M M = swap M M ( R Δ t) + = V float - V fx Swaps Class ote September 2005 /4/2007

3 3 Iterest Rate Swap - Illustrato Notoal amout 00 mo Swap rate xed paymet It.Rate (cotuous) 4.00% 4.50% 5.00% Dsc.actor Decomposto to bods Value of floatg rate ote Value of fxed rate ote Cash flows Dsc.actor Preset value Decomposto to RAs RA=M*(T)-M(+R Dt)*(T*) 0 2 M*(T) M(+R Dt)*(T*) RAs value Valuato based o forward rates wd rates (cotuous) 4.00% 5.00% 6.00% wd rates (aual comp) 4.08% 5.3% 6.8% Ga/loss o swap Preset value Valuato based o curret swap rate loatg rate ote PV Notoal amout / Sum of dsc.factors 2.74 =Curret swap rate New Swap Old Swap Preset value Swaps Class ote September 2005 /4/2007

4 4 Currecy swap Ivolves two curreces: D (the domestc currecy) ad (the foreg currecy) Sze of cotract: M D (D), M () Ital spot exchage rate: S 0 (D/) Cash flows for domestc compay (Europea compay) Tme Outflow : M D: R D M D D: M D (+R D ) Iflow D: M D : R x M : M (+R ) Decompostos ad valuato () Cur Swap = Log foreg deomated bod + Short domestc bod Value of currecy swap f cswap = BB S 0 - B DB Itally : f cswap = 0 BB S 0 = B DB B = M R + M,, = B = M R + M D D D D, D D, = () Cur Swap = Portfolo of forward cotracts orward cotract at tme : Domestc compay buys (R M ) foreg currecy for a prce equal to (R D M D ) uts of domestc currecy Value of forward cotracts : Spot value of uderlyg asset - Preset value of delvery prce (S - PV(K)) Spot value of uderlyg asset: () Dscout the future value foreg currecy at the foreg terest rate () Multply by the spot exchage rate Value of dvdual forward cotracts: tme ( to -) : f = S 0 (R M, ) - (R D M D ) D, tme : f = S 0 (+R ) M, - (+R D ) M D, f = ( S R M R M ) + S ( + R ) M (+ R ) M cswap 0, D D D, 0, D D D, Swaps Class ote September 2005 /4/2007

5 5 () Currecy swap valuato based o forward exchage rates Implct forward exchage rates swap: for perod ( to -): ˆ RD M D = R M ( ) for perod : ˆ + RD M D = ( + R ) M Equlbrum forward exchage rates: = S0, D, Value of dvdual forward cotracts: tme ( to -) : f ˆ = RM D, tme : f = ( + R ) M ˆ, D Swaps Class ote September 2005 /4/2007

6 6 Currecy Swap- Ilustrato Old swap Year 2 3 Cash flows USD Cash flow EURO Data ItRate EURO (Cot) 2.00% 2.50% 3.00% ItRate USD (Cot) 4.00% 5.00% 6.00% EURO $ Spot Exchage Rate= 0.80 EUR/$ Decomposto to bods Value $ bod USD 324. Value $ bod EURO Cash flow USD PV USD Value EURO bod Cash flow EURO PV EURO Swap value 3.66 Decomposto to forward cotracts 2 3 Spot prce uderlyg asset PV(Delvery Prce) Value of forward cotracts Swap value 3.66 Valuato based o forward rates Maturty orw.ex.rate = S(0)*$/EURO Swap Ex.Rate Ga/Loss PresValue Swap value 3.66 Valuato based o ew swap rates Value $ bod EURO / Sum EURO =Cash flow EURO New swap Old swap Preset value Swap value 3.66 Swaps Class ote September 2005 /4/2007

May 2005 Exam Solutions

May 2005 Exam Solutions May 005 Exam Soluto 1 E Chapter 6, Level Autes The preset value of a auty-mmedate s: a s (1 ) v s By specto, the expresso above s ot equal to the expresso Choce E. Soluto C Chapter 1, Skg Fud The terest