Wih he FX basis risk he circumsances are more complicaed. Saring poin of he following analysis is he definiion of he fixed-o-floa cross currency swap in Equaion 6. Le s analyze he changes in presen value of he EUR floaing leg a a subsequen rese dae 4 " T: Equaion 9: Rese of he EUR Floaing Leg of a Cross Currency Swap N " N " N j "5 j "5 j "5 j, j j f, j 4, j, j B, B,T 4 j 4 f 4, j, j b 4,T b 4,T B 4, j B 4,T " j N b 4,T, j j "5 " N b 4,T f j j "5 4, j B 4, j j " N N S b 4,T, j, j b 4,T B 4, j B 4,T, j B 4, j j "5 j, j B 4, j The resuls above show ha he EUR floaing leg reses o one minus he curren cross currency basis spread muliplied by he floaing leg annuiy. The laer erm causes ineffeciveness in erms of hedge accouning. The srucure will be he same on each rese dae: rese o N plus a second erm depending via N " N S on he iniial spo rae and he curren cross currency basis spread b,t for he remain ing erm and he corresponding annuiy of he floaing leg in EUR. 24 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
This resul now defines he dynamic hedge accouning sraegy: In he hedged iem is defined as fixed coupon liabiliy wih he fol low ing inernal coupon: FX, cin,,t " c,t. This corresponds o he USD discoun curve used for he fixed leg of he CCS. Bu wih he possibiliy o designae porions of cash flows, he inernal coupon in can also be defined as follows: c FX, in,,t " c,t b,t j " N k " j, j B, j B,Tk Tk,Tk. Using he laer represenaion, he iniial inernal coupon coincides wih he fixed rae on he CCS. In he single-curve case he FX basis is zero and so he raes for he single currency ineres rae swap and he CCS also coincide. In T he cash flows of he hedged iem are adjused and defined as fixed coupon liabiliy wih he following coupon using he rese propery of he EUR floaing leg and he ideniy N " N S as derived above: b,t c FX, in, T,T " c,t j " N k " j S b 4,T S T j "5 N k "2 S " c,t b 4,T S T j "5 N k "2 B,Tk Tk,Tk, j B, j j Tk,Tk j, j B 4, j B T,Tk, j B 4, j Tk,Tk B T,Tk. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 25
In general erms his will lead o he following adjusmens on a rese dae of he fixed leg: Equaion 2: Dynamically Adjused Inernal Coupon for he Firs Cross Currency Swap Represenaion (FX Basis Incorporaed in Fixed Rae) for EURIBOR / LIBOR Discouning b,t c FX, in,,t " c,t j " N k " j S b,t S j # N c,t " c FX, in, S,T b,t S j # N k # j j, j B, j Tk,Tk k # B,Tk Tk,Tk FX, in,, j B, j B,Tk, j B, j Tk,Tk B,Tk Therefore he iniial coupon is dynamically adjused by he curren FX basis convered wih he hisorical currency spo rae. Please noe ha he USD discoun rae is no adjused by he FX basis by assuming he marke convenion for he muli-curve seup so ha he resricions concerning sub-libor resricions under IAS 39 are avoided. In order o show he effec of he definiion of he cash flow in T, i is insered in he presen value formula of he hedged iem: FX, HFV T :" S T N cin, T,T FX, cin,,t " S T N b T,T j "5 26 N k "2 Tk,Tk k "2 Tk,Tk S N S T k "2 j N B T,Tk B T,T Tk,Tk, j B T, j B T,Tk B T,T B T,Tk N k "2 Tk,Tk B T,Tk 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he N KPMG nework of independen Inernaional Cooperaive ( KPMG Inernaional ), FX, member firms affiliaed wih KPMG a Swiss eniy. All righs reserved. in, k k k k "2 c,t T,T B T,T B T,T
" S T N b T,T j "5 j b T,T N S S T j "5 N "N j "5 j j Tk,Tk k "2 B T,Tk B T,Tk B T,T, j B T, j Tk,Tk k "2 b T,T S N B T,Tk N Tk,Tk k "2 FX, " S T N cin,,t, j B T, j FX, cin,,t " S T N Tk,Tk S T k "2 B T,Tk B T,T, j B T, j. Rese amoun floaing side of he EUR leg If he FX basis is aken ino accoun on he EUR floaing side, a he rese dae 4 " T: N j, j j "5 j "5 " N j "5 j f 4, j, j b,t B 4, j B 4,T, j b,t B 4, j B 4,T f 4, j, j j, j b,t b,t 4 B 4, j 4 " b,t b 4,T " N j "5 j "5 j "5 j, j j, j B 4, j j, j B 4, j f 4, j, j b 4,T B 4, j B 4,T " " N b,t b 4,T j "5 " N S b,t b 4,T j, j B 4, j j "5 j, j B 4, j N. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 27
This resul now defines he dynamic hedge accouning sraegy: In he hedged iem is defined as fix coupon liabiliy wih he USD swap rae as coupon: FX, cin,,t " c,t. Alernaively he iniial definiion c FX, in,,t " c,t b,t j " N k " j, j B, j Tk,Tk B,Tk using he same raionale and consequences as above could be chosen. In T he cash flows of he hedged iem are adjused and defined as fix coupon liabiliy wih he following coupon using he rese propery of he EUR floaing leg and he ideniy N " N S as derived above: FX, cin, T,T "c,t b,t b T,T S S T j "5 N k "2 j, j B T, j Tk,Tk B T,Tk. Consequenly for arbirary : Equaion 2: Dynamically Adjused Inernal Coupon for he Second Cross Currency Swap Represenaion (FX Basis as Consan Spread on he Floaing Side) EURIBOR / LIBOR Discouning FX, cin,,t " c,t b,t b,t S S j # N k # j, j B, j Tk,Tk B,Tk This definiion of he coupon is uilized o deermine he fair changes of he hedged iem. 28 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
Table 4: Example for a USD / EUR Fixed-o-Floa Cross Currency Hedging Relaionship Terms and condiions Fixed liabiliy CCS fixed leg CCS floa leg Value dae /23/2X9 /23/2X9 /23/2X9 Mauriy /23/2X4 /23/2X4 /23/2X4 Fixed inernal rae / enor 2.336 % 2.336 % 3 M Ineres paymen frequency Semi-annually Semi-annually Quarerly Noional,.,. 78,55.53 Day coun convenion 3 / 36 3 / 36 ACT / 36 For illusraion in he following he hedge accouning example of Secion 5.2.3 is considered in he muli-curve seup using he dynamical adjusmen mehod as described above (see Table 4). The inernal coupon is deermined by he risk-equivalen bond / loan mehod, and he hedging cos measuremen mehod will be applied. Dae of incepion is he value dae of liabiliy and swap. In order o avoid calculaion repeiions only he relevan changes from he case wihou FX basis are presened firs for he measuremen of he hedging insrumen (CCS) and hen for he hedged iem including he dynamical adjusmen. Since he adjusmens of he FX basis are considered on he EUR side, i.e. he EUR discoun curve is boosrapped as described in Secion 5.3. and following he firs alernaive of valuaion for CCS of Secion 5.3.4 he valuaion of he fixed leg differs only in fixed coupon, whereas for he floaing leg differen curves for forwarding (3-monh EURIBOR) and discouning (3-monh EURIBOR including he USD FX basis) are used. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 29
A incepion =/23/2X9 he exchange rae of EUR =.2795 USD and he discoun facors derived from USD vs. 3-monh USD LIBOR swap raes for he indicaed erms (in years) shown in Table 4 are given. The given marke daa in EUR are shown in Table 42. Table 4: Example for a USD / EUR Fixed-o-Floa Cross Currency Hedging Relaionship Discoun Facors a Years o mauriy Ti Discoun facor B,Ti Years o mauriy Ti Years o mauriy j Discoun facor B, j Days per period j j, j Years o mauriy j Days per period j j, j Years o mauriy j Forward rae f 22 j, j, j Discoun facor B, j Days per period j, j Discoun facor B, j Forward rae f.5 2 2.5.974573.9735.958947 3 3.5 4 4.5 5.945949.932932.98869.95236.8997 Example for a USD / EUR Fixed-o-Floa Cross Currency Hedging Relaionship Marke Daa Forward rae f.98924 Discoun facor B,Ti Table 42:.5.9923, j.25.5.75.25.5.75.99587.9935.98586.9894.97696.97325.96979 9 9 92 92 9 9 92 2.7 % 2.38 % 2.4 % 2.45 % 2.2 % 2.7 %.75 % 2 2.25 2.5 2.75 3 3.25 3.5.96662.9679.95446.94768.9453.9333.92579 92 9 9 92 92 9 9.6 % 2.74 % 2.92 % 3.8 % 3.23 % 3.39 % 3.75 4 4.25 4.5 4.75 5.9787.9964.925.8949.8864.8777 92 92 9 9 92 9 3.7 % 3.85 % 3.64 % 3.74 % 3.85 % 3.96 % 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
Thus he value of he floaing leg according o Equaion 6 is N 2 j " j, j f, j, j B, j B, 2 " 78,55.53 9 9 2.7%.99587 2.38%.9935... 36 36 92 3.96%.8777.8777 36 " 79,49.2. Also for he fixed leg he formula of Equaion 6 using he 3-monh USD LIBOR swap rae and he FX basis can be used or, as he CCS should be zero a incepion, he fac ha also he fixed leg has o have his value wih opposie sign. S N k " c CCS,T Tk,Tk B,Tk B,T " 79,49.2. This yields: c CCS,T " 79,49.2 B,T S N k " " 79,49.2 B,T 78,55.53 B,Tk 2 k " Tk,Tk B,Tk " 2.64499%. Seing he fixed rae c CCS,T of he fair CCS o 2.64499 % by definiion resuls in a fair value of zero a incepion : FVCCS " fixed side floaing side " 79, 49.2 79, 49.2 ". Bu i should be noed ha due o he fac ha forwarding and discouning are no done on he same curve, he absolue value of each leg no longer coincides wih ha of he EUR noional N " 78,55.53. Using he marke daa for USD as in Secion 5.2.3 for he valuaion of he fixed leg wih he fixed rae c CCS,T and corresponding marke 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 22
Table 43: Dae Fair Values and Fair Value Changes of he Cross Currency Swap Fixed leg Floaing leg FV CCS FV changes CCS 79,49.2 79,49.2. 69,782.94 79,85. 9,32.6 9,32.6 2 7,773.4 78,667.63 6,894.49 2,47.68 3 8,964.64 79,4.69,949.95 8,844.44 4 76,8.48 78,852.89 2,4.4 3,99.35 daa for he EUR leg wih forwarding and discouning on differen curves as shown above leads o he fair values and resuling fair value changes of he CCS for he differen daes as shown in Table 43. I can be seen ha in he muli-curve case he floaing leg does no rese o par. A incepion he inernal coupon for he hedged iem can be chosen o be he fair USD ineres rae swap rae c,t or he fixed rae c CCS,T of he fair CCS as defined above. Wih he marke daa and calculaion saed in Secion 5.2.3 he fair value is calculaed o be EUR 78,55.53 and EUR 79,49.2 respecively. If he inernal coupon is kep consan over he period from o, he same cash flows (bu he firs one ha falls due on ha dae) are valued wih he corresponding marke daa a showing he aging effec of he conrac. Since in he dynamic sraegy a each repor dae he hedge will be de-designaed and re-designaed, his hedge fair value wih he inernal coupon corresponding o he previous period a he repor dae will be denoed by HFV,D,T. Depending on he choice of he iniial coupon, his hedge fair value a de-designaion will be EUR 68,76.48 and EUR 69,782.94 respecively. These will be rele van for he booking enries for he hedge adjusmen as demonsraed in he booking example in Secion 4.3.3. 222 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
Also a he hedge will be re-designaed wih he new dynamically adjused coupon S FX, FX, cin,,t " cin,,t b,t S j # N k # j, j B, j Tk,Tk B,Tk. Using he adjusmen formula of Equaion 8 his can be wrien as FX, cin,,t " c CCS,T S c,t c CCS,T. S Wih S ".2795, S ".4229, c,t " 2.863% and c CCS,T " 3.8973% he adjused inernal coupon is calculaed o be FX, cin,,t " 2.64499%.2795 @2.863% 3.8973%B.4229 " 2.3346%. The corresponding hedge fair value for he hedged iem wih adjused inernal coupon evaluaed a will be denoed by HFV,R,T. Since he definiion of he inernal coupon a depends only on he way he gen eral CCS for he hedging is defined, and is independen of he ini ial inernal coupon he unique value is calculaed o be EUR 68,853.37. This will be used o deermine he discreizaion effec for he period from o recognized as par of he hedge adjusmen (cf. he booking example in Secion 4.3.3). Furhermore he value will serve as ref er ence for a fair value hedge adjusmen of he subsequen period from o 2. Moreover his hedge fair value coincides wih he value uilized for effeciveness measuremen as presened in Table 45. The argumen for he laer is ha HFV,R,T includes he correcion of he marke valuaion for he previous period from o a he end of he period a which is only relevan for his period. Since is he rese dae for he hedged iem and boh legs of he hedging CCS and no amorizaion of he book value is assumed by consrucion, he changes of hedge iem and hedging insrumen as given in Table 43 exacly offse in he case when he USD swap rae is chosen as he iniial coupon: 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 223
HFV,R,T HFV,R,T " 68,853.37 78,55.53 " 9,32.6 giving an effeciveness of %. Choosing he fair rae of he CCS as he saring value of he inernal coupon of he hedged iem he change is HFV,R,T HFV,R,T " 68,853.37 79,49.2 ",565.65 giving an ineffeciveness of,565.65 9,32.6 " 3.58%. Given he marke daa a each reporing dae he dynamically adjused inernal coupon of he hedged iem and he hedge fair values HFV,D i,t (in column denoed by HFV_D relevan for he booking enries as shown in he booking example of Secion 4.3.3) and HFV,R i,t (in column denoed by HFV_R relevan for he deerminaion of he discreizaion effec recognized as par of he hedge adjusmen for he previous period as shown in he booking example of Secion 4.3.3, as reference value for he subsequen period as well as for effeciveness esing) are calculaed as shown in Table 44. In conjuncion wih he fair value changes of he hedging insrumen given in Table 43 he resuls for effeciveness measuremen shown in Table 45 are obained. In his ideal case where he erms and condiions of hedged iem and hedg ing insrumen perfecly mach and he reporing daes are chosen o be rese daes / ineres paymen daes for he hedged iem as well as for boh legs of he hedging insrumen, % effeciveness is obained. In he general case ineffeciveness will arise, as in he single-curve case, from he changes of he floaing leg beween rese daes and differ ences in he erms and condiions of hedging insrumen and hedged iem. Addiionally in he muli-curve case wih dynamical adjusmen also he difference of he ineres periods of fixed and floaing leg of he hedging insrumen will give rise o ineffeciveness82. 224 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
Table 44: Dae Dynamically Adjused Coupon and Hedge Fair Values for he Hedged Iem Fair ineres rae Fair CCS rae FX spo rae Adjused inernal coupon HFV_D HFV_R 2.336 % 2.645 %.2795 2.336 % / 2.645 % 78,55.53 / 79,49.2 78,55.53 / 79,49.2 2.86 % 3.897 %.4229 2.3346 % 68,76.48 / 69,768.94 68,853.37 2 2.2685 % 2.4385 %.435 2.4572 % 7,842. 7,26.4 3.3545 %.6755 %.2897 2.325 % 8,57.95 8,5.48 4.3363 %.639 %.352 2.325 % 76,67.33 76,4.2 Table 45: Example for a USD / EUR Fixed-o-Floa Cross Currency Hedging Relaionship Changes effeciveness measuremen Dae HFV R j HFV R j Changes hedging insrumen Effeciveness 9,32.6 /,565.65 9,32.6 % / 3.58 % 2 2,47.68 2,47.68. % 3 8,844.44 8,844.44. % 4 3,99.35 3,99.35. % As in he case of he hedge in one currency wih differen enors (refer o Secion 4.3.3) here are differences beween booking enries for he hedge adjusmen and he fair values used in he echniques for effeciveness esing83. This resuls from he dynamic adjusmen feaure based on he discree adjusmen of he inernal coupon for he hedged iem. Similarly o he booking enries derived for he single currency case in Secion 4.3.3, he discreizaion effec will be aken ino accoun in he booking enries of he example above. In his case he hedging insrumen is given by a fixed-o-floa cross currency swap involving FX risk. 82 For reasons of simpliciy he impac of counerpary credi risk on he hedging insrumen is negleced in his conex. 83 E.g. due o amorizaions, insallmen, impairmen (no par of he hedged risk) or he consideraion of clean and diry fair values. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 225
Subsequenly o he de-designaion of he hedge a each reporing dae he booked hedge adjusmens will be amorized over he remaining life ime of he hedged iem as i was demonsraed in he booking example in Secion 4.3.3. Assuming he MM feaure described a he end of he previous Secion 5.3.4 also for fixed-o-floa cross currency swaps, in order o deal wih his feaure in conex wih hedge accouning he rese can be regarded as a virual erminaion of he original cross currency swap and he sar of a new one wih same erm o mauriy and fixed rae bu noionals according o he curren FX spo rae. If he adjusmen is recognized on he hedged currency leg, an adjusmen of he hedge raio migh be necessary. For illusraion purposes a which poin he MM feaure would ener ino he formula i is assumed ha he valuaion of a cross currency swap wih his feaure may be approximaed by ha of a consan noio nal cross currency swap. In order o derive he inernal coupon for a hedging relaionship wih a fixed-o-floa cross currency swap including an MM feaure, he above argumenaion is used. Following a sim ilar reasoning as in he calculaion of he consan noional cross currency swap (observing ha he iniial spo exchange rae in his case eners ino he formula in he nominaor of he raio of spo exchange raes involved) he formula of he dynamically adjused inernal coupon akes he following form if he MM feaure is included: FX, cin,,t "c,t S S b,t adj b,t j # j, j B, j A,T. Here S adj denoes he FX spo rae of he curren or las adjusmen dae of he noional. Thus on he adjusmen daes he raio of he FX spo raes equals one. The erms involving he cross currency basis spread remain unouched since his is relaed wih he expecaion of 226 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
ineres raes in boh currencies as from he beginning of he swap, and he fixed coupon of he hedging insrumen remains he same when he noional is adjused. For a more sophisicaed derivaion of he inernal coupon in his case also he valuaion of he MM feaure should be aken ino accoun. 5.3.5.2 Cash Flow Hedge Accouning wih an FX Conrac including he FX Basis Risk Considering he example of an FX forward conrac of Secion 5.2. including he FX basis (in he EUR zero raes) firs he corresponding FX forward raes are deermined as shown in Table 46. The general approach of Secion 5.2. remains he same, only he fair value of he FX forward conrac changes as carried ou in Secion 5.3. and he discouning of he spo componen changes according o he changes in he marke daa (see Table 47). Table 46: Example of an FX Forward Conrac FX Forward Raes Inverse exchange rae S Inverse FX forward rae f USD for EUR EUR zero rae incl. FX basis dae mauriy USD zero rae dae mauriy dae mauriy 365.942.2225 %.966 %.93894 = 2/8/2X 82.32.285 %.4584 %.3528 T = 6/8/2X.468.65 %.265 %.468 Dae Days o mauriy = 6/8/2X Table 47: Dae Example of an FX Forward Conrac Marke Daa FX Forward conrac FV FX Forward conrac FV changes Spo componen Changes spo componen P & L OCI (spo) (ineres) = 6/8/2X...... = 2/8/2X 7,668.26 7,668.26 7,93.63 7,93.63 7,93.63 263.37 T = 6/8/2X 5,33.89 7,635.63 5,282.43 7,35.8 7,35.8 284.84 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 227
5.4 Oher Hedge Accouning Approaches o Avoid P & L Volailiy from FX Basis In he secions above, hedge accouning in presence of he FX basis was porrayed. Since he P & L volailiy resuling from he FX basis despie sound economic hedging relaionships in foreign currency causes per sis ing headaches for reasury deparmens of banks, he quesion arises if he model described above is he only workable solu ion o his. In he following wo approaches are briefly described wih illus raions, so for his purpose a mahemaical descripion is no considered. The wo hedge accouning approaches considered are he following: 33 In a fixed-o-floa cross currency hedge he fixed-o-floa cross currency swap is decomposed ino an ineres rae and an FX basis componen. The ineres rae componen is designaed ino a fair value hedge, while he FX basis is designaed ino a cash flow hedge. 33 A sand-alone cross currency basis swap is designaed ino a cash flow hedge relaionship. The firs hedge accouning model is schemaically illusraed in Figure 73 and described in he following: The cross currency swap is decomposed synheically ino a USD iner es rae swap and a cross currency basis swap. In order o mee he hedge accouning requiremens, he fixed rae liabiliy is correspondingly synheically represened wice: 33 The firs hedge relaionship conains fixed rae liabiliy (including noional) cash flows and a plain vanilla USD ineres rae swap. This fair value hedge corresponds o he usually applied fair value hedge; he hedged risk is he USD benchmark curve. 33 The second hedge relaionship conains he FX basis floa-o-floa derivaive (including he exchange of noional cash flows) and a 228 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
Figure 73: Synheic Decomposiion of a Cross Currency Swap and Synheic Represenaion of a Fixed Rae Liabiliy for FX Hedge Accouning Economic hedging relaionship Fixed-o-floa cross currency swap Hedging Relaionship No. : fair value hedge accouning Fixed rae liabiliy N USD ineres rae swap N Hedging Relaionship No. 2: cash flow hedge accouning ic synhe enirely Floaing rae liabiliy N Synheic decomposiion Synheic represenaion Fixed rae liabiliy N Cross-currency basis swap N synheically creaed floaing rae liabiliy. Since his model inends o designae a cash flow hedge, i requires designaing he variabi liy in he FX basis (difference beween USD LIBOR and EURIBOR) and he FX risk. For he sake of simpliciy he decom posiion of iner es and FX basis cash flows is omied. As a resul he economic hedging relaionship is subdivided for accoun ing purposes ino wo separae hedge accouning relaionships. If a consisen se of discoun curves is applied, like e.g. Equaion 4, he decomposiion of he cross currency swap is economically consisen wih he absence of arbirage principle. Oherwise off-marke valued insrumens are creaed. Alhough hedge effeciveness can be easily achieved, his approach is quesionable in view of IAS 39. According o IAS 39.74 he possibiliies of a synheic decomposiion of hedging insrumens are clearly saed. These rules refer o opions and forward insrumens, so no necessarily o one legal cross currency swap. Addi ionally according o IAS 39.76 / IG F..2 permis an eniy o designae a derivaive simulaneously as a hedging insrumen in a cash flow and fair value hedge. Bu his is no done in he approach above since he derivaive is enirely decomposed. This issue can be circumvened by 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 229
enering ino a USD ineres rae swap and a cross currency basis swap separaely. IAS 39.77 permis he designaion of wo or more deriv a ives in a hedge accouning relaionship. Bu hen he issue of he syn he ic represenaion of he fixed rae liabiliy remains. There is no much guidance in IFRS on his paricular subjec, bu IAS 39 IG C. does no allow o idenify a floaing rae insrumen in a fixed rae insru men and o designae a synheic hedged iem. Neiher is i accep able o designae a synheic insrumen as hedged iem. Therefore i is quesionable wheher he synheic represenaion of he fixed rae liabil iy as a floaing rae liabiliy mees he crieria of IAS 39 hedge accoun ing requiremens and is in our view no permied. Furhermore he derivaion of he booking enries requires care; since he USD floaing rae liabiliy is enirely synheic i does no represen a recognized liabiliy, so i canno rigger a currency ranslaion adjusmen according o IAS 2. The following approach deals wih a hedge accouning model which is applicable for sand-alone cross currency basis swaps. According o KPMG Insighs 7.7.38.4 a cash flow hedge accouning model is appli cable o floa-o-floa basis swaps if he hedged iem is represened by an asse and a liabiliy. In his case he hedged risk is represened by he variabiliy of he differences beween he floaing raes of an asse and a liabiliy (basis) as well as an FX risk84. This hedge accouning model is illusraed in Figure 74. The major seps for his hedge accouning are summarized as follows: 33 Hedged iems: Combinaion of a group of (a leas one) USD floa ing loans (asses) and (a leas one) floaing EUR funding. The enors of boh coincide wih he enor of he pay and receive floaing side of he cross currency basis swap respecively. 84 Wih respec o he booking enries, here is no necessiy o designae FX risk, since he cross currency basis swap requires he exchange in noional. These represen, as shown in Figure 6, recognized asses and liabiliies and are subjec o currency ranslaion adjusmens according o IAS 2. 23 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
Figure 74: Cash Flow Hedge Accouning Approach for a Sand-Alone Cross Currency Basis Swap Hedged iems USD LIBOR USD LIBOR floaing rae asse N Hedging insrumen USD LIBOR Cross currency basis swap Funding floaing EURIBOR EURIBOR EURIBOR 33 Homogeneiy wih respec o he variabiliy of floaing raes and FX risk has o be shown. 33 Effeciveness esing is performed by wo hypoheical derivaives: for boh he EUR funding and he USD floaing loan a hypo he ical derivaive (floa-o-fixed ineres rae swap and a floao-fixed cross currency swap respecively) is consruced and compared o he cross currency basis swap ha may be virually decomposed correspondingly. 33 According o he cash flow hedge accouning model he booking enries are deermined by uilizing he lower of es and he effecive par is recognized in OCI, while he ineffecive par is recognized in P & L. The oulined hedge accouning model unforunaely faces some pracical limiaions: 33 Ofen enors of floaing rae loans are -monh, while he liquid cross currency basis swap conains a 3-monh enor, he difference in enor giving rise o ineffeciveness. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 23
33 The major ypes of floaing rae loans are no represened by plain vanilla floaing rae loans bu by revolving credi faciliies, so because of he uncerainy of drawings, ineres cash flows, callable feaures or oher embedded opions, he hedged iem has o be facored ino a cash flow hedge of a highly probable forecas ransacion. Then expecaions of drawings and cash flows have o be esimaed, which usually requires a large daa sample and furhermore reduces he amoun subjec o hedge accouning. As a consequence only par of he cross currency basis swap can be designaed ino he cash flow hedge accouning model and a reducion of P & L volailiy is limied. 5.5 Inerim Resul When applying FX hedging he quesion arises wheher he FX basis mees he requiremens of IAS 39.AG99F and AG ( separaely ideni fiable and reliably measurable and hedged risk ). The answer is yes as a consequence of he economic raionale of muli-curve models, bu from he hedge accouning perspecive (effeciveness esing) he desig naion of FX basis risk as hedged risk is of limied relevance o he hedge accouning model. The posiive answer is based on he follow ing: According o marke convenions and o economic hedging acivi ies i is clear ha he FX basis is a liquidly raded derivaive, affecs he P & L and is aken ino accoun in economic hedging aciviies, since i represens a relevan risk facor in a bank s funding posiion. Moreover he FX basis is generally considered when banks gran loans or issue deb so i plays an inegral par in reasury aciviies. From a more echnical poin of view he FX basis shares he same fae like any oher enor basis swap or risk facor added on he discoun curve. As shown in Secion 3 he explanaory power of fair values evaluaed wih he discoun curve derived from he derivaive marke wih respec o cash marke prices (e.g. bonds) is poor apar from accidenal saisical coincidence. So consequenly i is impossible o demonsrae empirically ha enors sysemaically affec cash prices. 232 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
Bu his propery is no of relevance and even if he requiremens of hedge accouning are me, his does no ensure effecive hedges in erms of IAS 39 for he FX basis. This resuls from he fac ha benchmark curve hedging in case of he fair value hedge accouning model under IAS 39 is a single risk valuaion facor model. As shown above, he USD discoun curve canno be modeled independenly from he EUR discoun curve. The applicaion of he fair value hedge accouning model requires he definiion of one single discoun facor wheher USD or EUR and also defines he hedged risk (3-monh USD LIBOR or 3-monh EURIBOR). The siuaion does no change if FX risk is added o he hedged risk. So once defined, he discoun facor only represens one risk facor in a muli-curve seup and he oher remaining risk facors are negleced. The only way o ake ino accoun he re main ing risk facors like he FX basis is o adjus he cash flows as described above. The pracical oucome of all his is ha he hedge will be defined in such a way ha ineffeciveness is minimized. In comparison he applicaion of cash flow hedge accouning is easy. Bu he economic underpinnings of he cash flow hedge accouning model are similar o hose of fair value hedge accouning. Wih respec o he role of enor basis swaps as risk facors i is worh o noe ha, given he requiremen o value hypoheical derivaives under IAS 39 according o marke convenions (KPMG Insighs 7.7.63.3), highly effecive ness of he hedging relaionship is preserved, provided ha he erms and condiions of hedged iem and hedging insrumen are suf ficienly similar. By he required applicaion of marke convenions o evalu ae he fair value of derivaives i is generally acceped ha he fair value of he hypoheical derivaive is synheically decomposed ino is eco nomic risk facors presuming he absence of arbirage. As shown in connecion wih he boosrapping algorihm, his resuls in a recovery of marke quoes, bu in differen dynamics and consequenly in differ en P & L effecs. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 233
S ecion S ix Collaeralized Derivaive Pricing and Hedge Accouning according o IAS 39 6. 6 Inroducion Collaeralizaion and Muli-Curve Models As described before, he re-assessmen of risks by marke paricipans in volved in financial insrumens ransacions is a fac and leads o he im plemenaion of muli-curve models. Addiionally changes in marke convenions and insiuional changes wihin financial markes accel er ae he implemenaion of muli-curve models. Clearing houses85 such as SwapClear, (LCH.Clearne)86, Eurex Clearing AG (Deusche Börse AG) 87 require he uilizaion of an overnigh index for valuaion pur poses, e.g. EONIA. The increasing involvemen of clearing houses and cenral counerparies in derivaive ransacions, in order o eliminae 85 For a descripion of he economics of clearing houses refer o Pirrong, C. (2), The Economics of Cenral Clearing: Theory and Pracice, in: ISDA Discussion Paper Series No.. 86 cf. e.g. Whiall, C. (2b) LCH.Clearne re-values 28 rillion swap porfolio using OIS, in: Risk Magazine, June 2 87 cf. Eurex Clearing (22) 234 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
counerpary risk, pushes financial markes owards sandardizaion con cerning discoun curves derived from OIS raes. This developmen is closely relaed o he reamen of collaeralizaions in derivaive ransacions, since clearing houses require daily collaeral posings ( margins ) and corresponding ineres paymens on cash col laerals. In consideraion of daily exchanges of collaeral posings, an overnigh index o deermine he ineres on he collaeral posings is considered adequae. This has an immediae consequence on he valua ion of collaeralized derivaives since, in order o avoid arbirage opporuniies, he applied discoun curve has o be chosen according o he evaluaion of ineres paymens on cash collaeral. These changes in he marke environmen are accompanied by modi ficaions of he legal framework of he derivaive business beween wo counerparies acing under an ISDA Maser Agreemen (22), which represens he marke sandard for derivaive ransacions sup ple mened by a CSA. Accordingly, in such a CSA he evaluaion of he iner es as so ciaed wih cash collaeral posings of derivaive rans ac ion is changed o require he uilizaion of an overnigh index, e.g. EONIA. Currenly cash collaeral is commonly eligible and posed in seleced reference currencies (e.g. USD, EUR, GBP, JPY)88. According o his spe cific feaure commonly used under he erms and condiions in he relevan framework documens for derivaives issued by ISDA (e.g. ISDA Maser Agreemen (22), ISDA Credi Derivaive Definiions (23) and CSA), he cross currency basis spread (FX basis spread) canno be negleced in connecion wih collaeral posings, since he cash collaeral can be referenced o a differen (foreign) currency han he derivaive ransacion. Accordingly, he FX basis eners ino he dis coun curve for valuaion purposes. This feaure of differen rade and cash collaeral currencies is currenly under debae 89, since ISDA plans 88 See ISDA (2 B). 89 For a descripion refer o Sawyer, N. and Vaghela, V. (22), Sandard CSA: he dollar dominance dispue, in: Risk Magazine, January 22. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 235
o inroduce a new sandardized CSA owards an alignmen ( silo ap proach ).9 Bu his plan does no faciliae he siua ion for cross currency producs which by definiion deal wih wo currencies or deals raded in minor currencies wih collaeral posings in a reference currency, and hus for he valuaion he FX basis has o be aken ino accoun. Addiional legal changes under he ISDA Maser Agreemen (22) are he rules concerning dispues and close ous of derivaive ransacions, since hese also require he uilizaion of overnigh indices in order o deermine he close ou amoun. The feaures described represen he marke sandard for derivaive ransacions only in he inerbank marke ( collaeralized derivaive ransacions ). Corporaes also use he ISDA documenaion for deriva ives as sandard, bu no he CSA ( uncollaeralized derivaive ransacions ) due o liquidiy requiremens of collaeral posings, which are considered unfavourable for corporaes because of heir liquidiy consrains. Consequenly overnigh indices are no applied as discoun raes for hose derivaive ransacions and herefore e.g. he EURIBOR or LIBOR raes are applied. As a resul of changes in marke convenions, discoun raes for derivaive ransacions become counerpary specific and yield o a segmenaion of derivaive markes. I is also imporan o noe ha evaluaing ineres on a cash collaeral using an overnigh index does no mean e.g. ha a financial insiuion (bank) is able o (fully) fund on overnigh index basis! Wih respec o hese developmens wihin financial markes, valuaion models have o be modified in order o reflec he increased number of risk and counerpary specific facors. Addiionally discoun curves canno be derived from marke daa (e.g. swap raes) wihou aking ino accoun differen enors. For example (in he inerbank marke) EURIBOR or LIBOR discoun raes canno be derived independenly 9 See ISDA (2B) 236 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
from overnigh index raes, so a pure EURIBOR or LIBOR curve ceased o exis. According o hese circumsances financial insiuions sared o implemen muli-curve models for derivaive pricing in order o ake ino accoun he enor dependence and he collaeralizaion. Wihin hese valuaion models forwarding and discouning is performed on differen curves. In he following a muli-curve model for collaeralized derivaives and is implicaions o hedge accouning are analyzed. The secion is srucured as follows:. A brief descripion of he ineracion of funding, changes in ineres evaluaion of cash collaerals, performance measuremen of hedges and VaR evaluaions is provided. 2. Definiion and derivaion of a consisen and arbirage free seup of discoun and forward curves involving several risk facors like enor and cross currency basis spreads for collaeralized derivaives. 3. Implicaions of he muli-curve model for collaeralized derivaives o hedge accouning according o IAS 39. 6.2 Performance Measuremen of Economic Hedges Performance measuremen of banking aciviies is a complex and vas area in economic modeling. In he following we only consider a simple example in order o show he differences and relaionships beween performance measuremen, funding and ineres paymens on collaerals of derivaives. The explanaions commence in a single-curve model seup in order o reduce complexiy (for addiional explanaions please refer o Secion 4). 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 237
Figure 75: Economic Hedge Relaionship Using a 5-Year 3 M EURIBOR Ineres Rae Swap and a Bond / Loan Noional of he bond / loan Ineres paymens EURIBOR floaing side of swap OUTFLOW INFLOW Synheic, risk-equivalen bond / loan Noional floaing side of he swap Cash funding of he bond / loan YE AR Fixed paymens swap YE AR 2 Fixed paymens swap YE AR 3 Fixed paymens swap Funding coss EURIBOR YE AR 5 Fixed paymens swap Noional fixed side of he swap EURIBOR componen / inernal coupon Figure 76: YE AR 4 Fixed paymens swap Componens of a Performance Measuremen Performance measuremen Unrealized gains and losses Presen value of he synheic, risk-equivalen bond / loan Loan / liabiliy pricing Presen value of he EURIBOR ineres rae swap Presen value of funding Funding model Realized gains and losses Cos of banking aciviies Realized cash flows resuling from he bond / loan, EURIBOR ineres rae swap, ineres paymens funding Ineres paymens from collaeral posings (margins) Cos of collaeral posings = Toal performance 238 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
In Figure 75 an economic hedging relaionship is porrayed. As represened in his figure, he cash flows of he 5-year 3-monh EURIBOR ineres rae swap enirely offse he cash flows of he cash funding and he synheic and risk-equivalen loan / bond. Consequenly a ne profi or performance of zero is expeced. This conclusion ress on wo assumpions: 33 The performance of collaeral posings in connecion wih he ineres rae swap (derivaive) and he corresponding funding / replacemen coss are no considered. 33 Cash funding is carried ou on 3-monh EURIBOR. In Figure 76 he componens of performance measuremen models are illusraed. Generally hese models disinguish beween realized and unrealized gains / losses. Realized gains / losses refer o ineres paymens of he 3-monh EURIBOR ineres rae swap, funding ec. Unrealized gains / losses refer o presen value evaluaions of he finan cial insrumens included in he performance measuremen. I is impor an o noe ha he bond / loan is already decomposed ino an ineres rae risk bearing componen (= he synheic, risk-equivalen bond / loan), credi and oher margin componens. Therefore commonly per for mance measuremen includes various componens of iner nal pricings or ransfer prices in order o reflec he decom po siion of risk posiions ( division of labor ) and organizaional respon sibiliies (cre di and ineres reasury deparmens) wihin a financial insiuion. As represened in Figure 76, he ineres of collaeral posings (margins) affecs he oal performance. Therefore changes in ineres evaluaions of collaeral posings (margins) impac direcly he oal performance and he ineres or rading resul according o IFRS. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 239
Addiionally here is an indirec effec on a financial insiuions funding and he overall cos posiion. The exisence of his effec is clear bu is exen depends on he individual financial insiuions funding model. There are wo major ypes of funding models: 33 Overnigh funding ypically based on EONIA or EURIBOR ( shor erm lending ) in order o fund posiions (also ermed cos of carry ). This funding model is widely applied for rading aci viies and is usually performed by inernal deals.9 Alernaively repos can be used for shor erm funding. 33 Models of he enire capial srucure of he financial insiuion ( long erm financing ) including equiy, hybrid capial, oher deb financings, savings deposis ec. Such models require addiional economic and economeric modeling. This funding model is usually applied in reasury deparmens. Irrespecive of he funding model cash collaeral posings (margins) resuling from derivaive ransacions have o be funded on an overnigh basis resuling in coss for he financial insiuion. Consequenly here is also an indirec effec on loan and bond pricing since he oal hedging coss aler in case of changes of ineres paymens on cash collaeral. Similar economic reasoning holds in presence of FX basis risk. In he following he change in ineres paymens resuling from he changes in CSA is illusraed. 6.3 Performance Measuremen and he CSA Effec If wo paries ener ino a derivaive conrac under an ISDA Maser Agreemen (22) and a CSA deermining cash as eligible collaeral, cash collaeral is posed if he hedging derivaive has a presen value differen from zero. The counerpary wih negaive presen value of he 9 A discussion of inernal deals is beyond he scope of he aricle. 24 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
derivaive poss cash collaeral and receives ineres paymens from he counerpary. According o he ISDA Marke Review of OTC Derivaive Bilaeral Collaeralizaion Pracices (2.) from 2 he ineres rae being paid on he collaeral is agreed according o conracual feaures of he CSA. These feaures include: he ineres period, he accrued (daily) ineres, hreshold or minimum ransfer amouns. Typically cash collaeral is being (re)called on a daily basis and generally referenced o he rae index, which is represened by he overnigh funding rae for he relevan currency, e.g. Federal Funds H-5 for USD, EONIA for EUR and Serling Overnigh Inerbank Average Rae (SONIA) for GBP. This gives a variey of possible erms and condiions o deermine he ineres amoun of he collaeral, bu as repored in he ISDA Marke Review of OTC Derivaive Bilaeral Collaeralizaion Pracices, generally he simple (raher han he compounded) overnigh (ON) funding rae for he applicable currency is used accrued daily bu ypically wih a monhly paymen period. This should be seen in conex wih he possible daily calls on collaeral, he role of cenral counerparies and he plans on regulaions of he OTC marke or he developmen of a Sandard CSA. In is Margin Survey 2 ISDA repors ha on average almos 7 % (8 % for large dealers) of all OTC derivaives are collaeralized and even 79 % (88 % for large dealers) for he subse of all fixed income derivaives. 8 % of he collaeral has been posed as cash and a leas for large dealers 6 % of he porfolio reconciliaion is done on a daily basis (3 % overall). In order o illusrae he impac on differen ineres rae evaluaions for cash collaeral posings, he following simplifying assumpions are made: 33 Collaeral is posed as cash of he same currency. 33 There is no hreshold, minimum ransfer amoun, rounding amoun or oher opional feaures in he CSA and, neglecing rans acions coss, he posing of collaeral mainly has an effec on he relaed ineres paymens. 33 The posed collaeral is approximaed o be consan beween monhly reporing daes. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 24
The example in Figure 75 is coninued and he fixed rae bond / loan wih 5-year mauriy has a noional of EUR,,. The hedging insrumen is a 5-year 3-monh EURIBOR ineres rae swap wih mach ing erms and condiions. Cash funding is based on 3-monh EURIBOR. Since a single-curve model is assumed wih he 3-monh EURIBOR ineres rae swap curve as benchmark curve he EURIBOR componen (inernal coupon) of he hedged iem coincides wih he 5-year EURIBOR ineres rae swap rae consrucing he synheic and risk-equivalen loan / bond. Figure 77: FV Changes of a 3 M EURIBOR Ineres Rae Swap Based on 3 M EURIBOR Discouning, T EUR 2, 3, 4, 5, 9/2X 9/2X 7/2X 8/2X 8/2X 5/2X 6/2X 3/2X 4/2X /2X 2/2X /2X 2/2X /2X 9/2X 7/2X 8/2X 5/2X 6/2X 3/2X 4/2X 2/2X /2X /2X9 Figure 78: 2/2X9 /2X9 6, FV Changes of a 3 M EURIBOR Ineres Rae Swap Based on EONIA Discouning, T EUR 2, 3, 4, 5, 242 7/2X 5/2X 6/2X 3/2X 4/2X /2X 2/2X 2/2X /2X /2X 9/2X 7/2X 8/2X 5/2X 6/2X 4/2X 3/2X 2/2X /2X 2/2X9 /2X9 /2X9 6, 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
Figures 77 and 78 presen he monhly fair value changes of he 3-monh EURIBOR ineres rae swap discouned wih 3-monh EURIBOR and EONIA discoun curve. The figures show ha he fair value of he payer swap is negaive and herefore, according o he CSA, cash collaeral and ineres paymens are exchanged. This observaion holds rue for he case of discouning on he 3-monh EURIBOR curve in he single-curve approach as well as for collaeralized rades commonly using OIS discouning on he EONIA curve. Thus he argumen is qualiaively he same and he example may be coninued wih he swap discouned on OIS. In Table 48 he amoun of ineres paymens for cash collaeral posings referenced o he 3-monh EURIBOR are compared o hose re ferences o (simple) EONIA ineres raes. As a funding model, he 3-monh EURIBOR cash funding is assumed. Table 48: Comparison of Ineres Paymens on Cash Collaeral Posings Ineres paymens on cash collaeral posings Dae Swap fair value (OIS discouning) 3 M EURIBOR EONIA Resuling impac Funding model: 3 M EURIBOR 3 M EURIBOR EONIA /23/2X9 534,837..... 2/23/2X9 798,73 38.67 55.99 38.67. 62.68 6/23/2X 4,35,6 2,467.2,75.55 2,467.2.,39.47 7/23/2X 3,773,97 2,546.54,3.26 2,546.54.,46.27 8/23/2X 5,5,954 2,876.8,624.9 2,876.8.,25.8 9/23/2X 4,482,826 3,875.34,839.8 3,875.34. 2,35.53 /23/2X 3,56,2 3,279.93,639.97 3,279.93.,639.97 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 243
As i becomes apparen from Table 48, if he ineres evaluaion of he cash collaeral posings differs from he ineres of he funding model, here is an immediae effec on he oal performance (P & L). When assuming a 3-monh EURIBOR cash funding, impac of change in iner es evaluaions can be regarded as enor basis spread difference beween he EONIA ineres rae and he 3-monh EURIBOR. This is also illusraed in Figure 79. Addiionally i can be observed ha he impac on differences in ineres evaluaions of cash collaerals and funding is negaive. This can be regarded as an increase in funding coss and herefore affecing he funding model of he enire financial insiuion. As menioned above, in pracice for funding a differen model han 3-monh EURIBOR cash funding, e.g. funding by repos or capial, sruc ure models may be applied. A differen funding model would change he values for he funding in Table 48, bu an overall effec of changes due o differen ineres evaluaions of cash collaeral remains. Figure 79: Difference of Ineres Paymens on Cash Collaeral a 3 M EURIBOR and EONIA Rae 5 EUR 5,,5 /2X 9/2X 7/2X 8/2X 5/2X 6/2X 3/2X 4/2X /2X /2X 2/2X /2X 9/2X 7/2X 8/2X 5/2X 6/2X 3/2X 4/2X /2X 2/2X /2X9 244 2/2X9 2,5 2/2X 2, 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
6.4 Iniial Valuaion Effecs Resuling from Changes in Discoun Curves Wih he change-over from discouning on e.g. 3-monh EURIBOR o OIS discouning as he marke consensus for he correc pricing of col la eralized rades, financial insiuions have o cope wih an iniial valuaion effec when firs adoping he new valuaion mehod for exis ing collaeralized rades. In he following his iniial valuaion effec is analyzed. Firsly in general he EONIA rae is less han a EURIBOR or LIBOR rae for he same period (refer o Secion 3): reonia, reuribor, resp. reuribor,. reonia, Thus, assuming discouning on (homogeneous) discoun curves, he discoun facors derived from EONIA curves will be greaer han hose of he EURIBOR or LIBOR curve for he same ime period: BEONIA, BEURIBOR,. In he following he example of a 5-year 3-monh EURIBOR ineres rae swap as in he previous Secion 6.3 is coninued, assuming ha he payer swap has a negaive presen value (fair value) in case of 3-monh EURIBOR discouning: payer swap PVEURIBOR. In order o analyze he effec of changing discoun curves he following assumpions are made: 33 The valuaion of 3-monh EURIBOR ineres rae swap (value dae ) a he rese dae Tk is considered. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 245
33 The 3-monh EURIBOR discoun curve can be modeled independ enly from he EONIA discoun curve and he following equilibrium condiions hold: c Tk,T A Tk,T " c Tk,T AEONIA Tk,T " Tk,T " /EONIA B Tk,T Tk,T. Using he definiions above he following properies can be derived: c,t A Tk,T Tk,T PV swap EURIBOR discouning "c,t AEONIA Tk,T A Tk,T c Tk,T A Tk,T AEONIA Tk,T A Tk,T AEONIA Tk,T " c,t AEONIA Tk,T c Tk,T AEONIA Tk,T " c,t AEONIA Tk,T /EONIA A Tk,T. AEONIA Tk,T Tk,T PV swap EONIA discouning Thus: payer swap payer swap PVEURIBOR disc Tk " PVEONIA disc Tk A Tk,T AEONIA Tk,T payer swap payer swap PVEONIA PVEURIBOR disc Tk disc Tk payer swap PVEONIA disc Tk payer swap PVEURIBOR disc Tk payer swap PVEONIA disc Tk payer swap EURIBOR disc PV PV payer swap EURIBOR disc 246 Tk Tk payer swap " PVEONIA disc Tk payer swap " PVEURIBOR disc Tk payer swap PVEONIA disc Tk A Tk,T AEONIA Tk,T AEONIA Tk,T A Tk,T. 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he
If he presen value of he ineres rae swap is negaive, hen he cash collaeral has o be posed and ineres based on EONIA is received. On he assumpion of 3-monh EURIBOR cash funding he overall impac is negaive in comparison o he EURIBOR case (funding and collaeral ineres on 3-monh EURIBOR). Consequenly i is plausible ha he presen value of he ineres rae swap using EONIA discouning is less han for EURIBOR discouning. Therefore he iniial valuaion effec from changing discoun curves can be regarded as he presen value difference of differen ineres pay mens on fuure cash collaerals. Considering he case of jus one ineres period o mauriy he formula above is reduced o: c,t AEONIA Tk,T /EONIA Tk,T PV of swap OIS discouning A Tk,T AEONIA Tk,T " c,t AEONIA Tk,T /EONIA Tk,T B Tk,T B EONIA Tk,T " c,t AEONIA Tk,T /EONIA Tk,T r EONIA Tk,T r Tk,T " c,t AEONIA Tk,T /EONIA Tk,T /EONIA Tk,T r Tk,T r Tk,T r Tk,T EONIA " c,t AEONIA Tk,T PV of swap = collaeral amoun r Tk,T r EONIA Tk,T Ineres period Difference of ineres raes B Tk,T. Discoun facor 22 KPMG AG Wirschafsprüfungsgesellschaf, a subsidiary of KPMG Europe LLP and a member firm of he 247