Implied default probability and Latam local IR swaps

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1 Impled default probablty and Latam local IR swaps Gabrel Gerszten Gustavo Mendonca Samuel Castro hs pece follows the study on Brazl rsk premum and the mpact on the belly/long end of the local IR curve (lnk: Brazl s rsk premum: Call t on the CDS). In ths new study we am to hghlght/quantfy the mpact of the mpled default probablty embedded nto the CDS on the local swap curves of Brazl, Mexco, Chle, and Colomba. If mplemented, the approach would let us construct dfferent scenaros for nterest rates gong forward and recommend payng/recevng strateges anytme the dfference between model and market value were substantal. Brazl 5y DI has the hghest adherence to the mpled default probablty, whereas Chle 5y CLPxCAM has the lowest. he mpact s hgher n Colomba IBR than n Mexco IIE. Background and approach As emprcal evdence suggests, an ncrease n rsk premum/default probablty (IDP) should mpact the long-end of the local curves n Latn Amerca (wthout excepton). We propose the followng approach n order to examne ths emprcal evdence and shed lght on: (a) the mpact of IDP on local IR curves; (b) ts explanatory power; and (c) whether 5y tenor s cheap or rch to CDS: 5y local IR swap t = α + δ (IDP t ) + θ (5y US swap t ) + ε [1] where: IDP s the cumulatve mpled default probablty of a 5y CDS assumng a recovery value of 4%; for further detals, see the Annex at the end of the pece. he data used n our model are at a monthly frequency. We used the IDP and the US swaps as the explanatory factors. In all cases, polcy rates have showed consderably low statstcal sgnfcance (ths s n lne wth our hypothess that longer tenors n Latn Amerca are mostly a functon of dosyncratc rsk and US rates). Mexco As expected, the effect of changes n the mpled default probablty s not nl, yet much lower than n the cases of Colomba and Brazl. Charts 2-3 depct the values and error bands resultng from equaton [1]; chart 1 shows the IDP and 5y IIE. he red lne n chart 3 represents the theoretcal value of the 5y IIE should 5y CDS adjust 5bp to the upsde. In the case of Mexco, the prncpal explanatory varable s the US swap, whch s n agreement wth other BNP Parbas Latam strategy studes showng the strong co-movement between the US and Mexcan fxed ncome markets. As there s no substantal dfference between market and model values for 5y IIE, we wll reman on the sde-lnes. Current model value s 5.24% (or 4bp below market prce). Charts 1-3; IDP and 5y IIE, and market and model levels 17% Default Probablty: Unted Mexcan States 5yr 5y Swap IIE (rhs) y IIE x Model Y IIE x Model 6. 14% 1% 7% 3% 4.4 Assumng 5y CDS 5bp above current level Source: Bloomberg LLP, BNP Parbas; Macrobond; updated as of 3 March March 216

2 Brazl As expected, the effect of changes n the mpled default probablty s substantal: whle most of the explanatory power of the rsk premum/idp over the DI curve has taken place n , the adherence of the perod s sgnfcant and makes the IDP the prncpal component of the long end of the DI curve. Same as n Mexco, charts 2-3 depct the values and error bands resultng from equaton [1]; chart 1 shows the IDP and 5y DI. he red lne n chart 3 represents the theoretcal value of the 5y DI should 5y CDS trade at 325bp. he last chart s ntutve n a sense that only a scenaro of CDS at ~325bp (concdently, the far value resultng from our propretary CDS approach) makes market and model values equal. he results shed lght on our thess that 5y Brazl CDS stll has margn to adjust to the downsde and also open the door for a potental RV trade (e.g. sell 5y CDS and pay DI Jan-21). Impact: f CDS vares 1bp, we should expect that a tenor equvalent to 5y DI moves 13bp. Charts 4-6; IDP and 5y DI, and market and model levels 37% Default Probablty: Federatve Republc of Braz 5yr 5y Swap DI (rhs) % % 1 22% % % 1. 7% y DI x Model Y DI x Model Assumng 5y CDS at 325bp Source: Bloomberg LLP, BNP Parbas; Macrobond; updated as of 3 March 216 Chle As expected, the effect of changes n the mpled default probablty s much lower (notceably low) n Chle than n the rest of the regon (mostly explaned by techncal ssues such as soveregn credt ratng, low level of external/hard currency debt, and relatvely small foregn partcpaton n the government deb. Charts 2-3 depct the values and error bands resultng from equaton [1]; chart 1 shows the IDP and 5y CLPxCAM. he red lne n chart 3 represents the theoretcal value of the 5y CLPxCAM should 5y CDS adjust 5bp to the upsde. he last chart s acute n a sense that only a scenaro of CDS 5bp hgher makes market and model values equal. he result straghtens out the hgher rsk premum that market players are lookng for Chlean assets at the present tme. It also open the door for a potental RV trade (eg. buy 5y CDS and receve 5y CLPxCAM or do the latter outrgh. Charts 7-9; IDP and 5y CLPxCAM, and market and model levels 12% Default Probablty: Republc of Chle 5yr 5y Swap CLPxCAM (rhs) 1% 8% 6% 4% y CLPx CAM x Model Y CLPxCAM x Model 3.6 Assumng 5y CDS 5bp above current level Source: Bloomberg LLP, BNP Parbas; Macrobond; updated as of 3 March March 216

3 Colomba he effect of changes n the mpled default probablty s consderable (makng the IBR and the DI curves the most exposed to default probablty changes). Same as Chle, the last chart shows that only a scenaro of CDS 5bp hgher makes market and model values equal. he results delneate the hgher rsk premum that market players have been expectng for Colomban assets after the collapse of ol prces. he concluson also bodes well for a potental RV trade (e.g. buy 5y CDS and receve 5y IBR or do the latter outrgh. Charts 1-12; IDP and 5y IBR, and market and model levels Default Probablty: Republc of Colomba 5yr 23% 5y Swap IBR (rhs) 2% 16% 13% 9% 6% 2% y IBR x Model Y IBR x Model 4.4 Assumng 5y CDS 5bp above current level Source: Bloomberg LLP, BNP Parbas; Macrobond; updated as of 3 March 216 Annex; IDP calculaton o derve ther model we must frst defne the followng: h(: rsk-neutral default ntensty densty at tme t (condtonal) : survval probablty at tme t : rsk-neutral default probablty densty at tme t (uncondtonal) A(: accrued nterest at tme R: rsk-neutral recovery rate Usng ths model, the frst step n prcng a plan vanlla CDS nvolves fndng the rsk-neutral default probablty densty functon. We start wth the survval probablty. he uncondtonal probablty of default s: ( t, t + d = t d P uncon default + he condtonal probablty of default s: t + d ( t, t + d = = h( t P con default ) Rearrangng yelds: 1 d h( = Integratng leads to: = e h( ) d hs s the survval probablty as a functon of the hazard rate. he rsk-neutral probablty densty s then smply the product of the hazard rate and the survval probablty: = h( = h( e h ( ) d 3 March 216

4 he probablty that a credt event wll occur by tme can be defned as: Lkewse, the probablty that no credt event wll occur s: π = 1 In the event that a default does occur, the protecton buyer wll receve a payment equal to: 1 [1 + A( ] Rˆ Integratng ths over the default densty functon and dscountng to the present yelds: V floatng = {1 [1 + A( ] Rˆ} DF( hs s the value of the contngent leg of the swap. o value the fxed leg, one must dscount the condtonal fxed payments back to the present. hus, the value of the fxed leg s: V fxed = C = 1 t ) DF( t ) he spread that equates the value of these two legs s thus the prce of the contract: C {1 [1 + A( ] Rˆ} DF( = = 1 t ) DF( t ) 3 March 216

5 Emergng s Strategy Contacts hs publcaton s classfed as non-objectve research Wke Groenenberg Global Head of London wke.groenenberg@uk.bnpparbas.com Potr Chwejczak FX & IR CEEMEA Strategst London potr.chwejczak@uk.bnpparbas.com Erkn Isk, CFA FX & IR CEEMEA Strategst Istanbul 9 (216) erkn.sk@teb.com.tr Muhammet Sevm CEEMEA Graduate London muhammet.sevm@uk.bnpparbas.com Stoyan Dogandzhysk CEEMEA Graduate London stoyan.dogandzhysk@uk.bnpparbas.com Mahesh Bhmalngam Head of European and CEEMEA Credt Strategy London mahesh.bhmalngam@uk.bnpparbas.com Andrew MacFarlane, CFA Credt CEEMEA Strategst London andrew.j.macfarlane@uk.bnpparbas.com Clara Leonard Credt CEEMEA Graduate London clara.leonard@uk.bnpparbas.com Mrza Bag Head of FX & IR Asa Strategy Sngapore mrza.s.bag@asa.bnpparbas.com Jasmne Poh FX & IR Asa Strategy Sngapore jasmne.j.poh@asa.bnpparbas.com Jennfer Kusuma FX & IR Asa Strategy Sngapore jennfer.kusuma@asa.bnpparbas.com Altaz Dagha AU/NZ IR Strategst Sngapore altaz.dagha@asa.bnpparbas.com Gabrel Gerszten Head FX & IR Latam Strategy Sao Paulo gabrel.gerszten@br.bnpparbas.com Samuel Castro FX & IR Latam Strategst Sao Paulo samuel.castro@br.bnpparbas.com Gustavo Mendonca FX & IR Latam Strategst Sao Paulo gustavo.mendonca@br.bnpparbas.com Producton and Dstrbuton Barbara Consuelo, London. el: , Emal: barbara.consuelo@uk.bnpparbas.com RESEARCH DISCLAIMERS hs document has been wrtten by our strategy teams. 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