Final Report. Public Consultation No. 14/036 on. Guidelines on the treatment of market. and counterparty risk exposures in the.

Transcription

1 EIOPA-BoS-14/ November 2014 Fnal Repor on Publc Consulaon No. 14/036 on Gudelnes on he reamen of marke and counerpary rsk exposures n he sandard formula EIOPA Weshafen Tower, Weshafenplaz Frankfur Germany - Tel ; Fax ; emal: nfo@eopa.europa.eu se: hps://eopa.europa.eu/

2 Table of Conens 1. Execuve summary Feedback saemen... 5 Annex: Gudelnes /18

3 1. Execuve summary Inroducon Accordng o Arcle 16 of Regulaon EU No 1094/2010 EIOPA Regulaon EIOPA may ssue gudelnes addressed o Naonal Compeen Auhores NCAs or fnancal nsuons. Accordng o Arcle 16 of he EIOPA Regulaon, EIOPA shall, where approprae, conduc open publc consulaons and analyse he poenal coss and benefs. In addon, EIOPA shall reques he opnon of he Insurance and Rensurance Sakeholder Group IRSG referred o n Arcle 37 of he EIOPA Regulaon. Accordng o Arcles 104 1, and 6 of Drecve 2009/138/EC 1 Solvency II Drecve and subsecons 5 and 6 of chaper 5 of he Implemenng Measures 2 underakngs have o cover marke and counerpary rsk when calculang her Solvency Capal Requremen wh he sandard formula. EIOPA decded o draf Gudelnes o faclae convergence of pracces across Member Saes and suppor underakngs n applyng he marke and counerpary defaul rsk modules of he sandard formula. As a resul of he above, on 2 June 2014 EIOPA launched a Publc Consulaon on he draf Gudelnes on he reamen of marke and counerpary rsk exposures n he sandard formula. The Consulaon Paper s also publshed on EIOPA s webse 3. These Gudelnes were ssued o underakngs and Naonal Compeen Auhores o: Esablsh conssen, effcen and effecve supervsory pracces; Ensure he common, unform and conssen applcaon of Unon law on he calculaon of he capal requremen for marke and counerpary defaul rsk. Conen Ths Fnal Repor ncludes he feedback saemen o he consulaon paper EIOPA- CP-14/036 and he Gudelnes. The Impac Assessmen and cos and benef analyss, and he Resoluon of commens are publshed on EIOPA s webse 4. 1 OJ L 335, , p As publshed by he European Commsson on 10 Ocober 2014: hp://ec.europa.eu/nernal_marke/nsurance/docs/solvency/solvency2/delegaed/ delegaed-ac-solvency-2_en.pdf 3 4 hps://eopa.europa.eu/consulaons/consulaon-papers/2014-closed-consulaons/june- 2014/publc-consulaon-on-he-se-1-of-he-solvency--gudelnes/ndex.hml 3/18

4 Nex seps In accordance wh Arcle 16 of he EIOPA Regulaon, whn 2 monhs of he ssuance of hese gudelnes, each compeen auhory shall confrm f comples or nends o comply wh hese gudelnes. In he even ha a compeen auhory does no comply or does no nend o comply, shall nform EIOPA, sang he reasons for non-complance. EIOPA wll publsh he fac ha a compeen auhory does no comply or does no nend o comply wh hese gudelnes. The reasons for non-complance may also be decded on a case-by-case bass o be publshed by EIOPA. The compeen auhory wll receve advanced noce of such publcaon. EIOPA wll, n s annual repor, nform he European Parlamen, he Councl and he European Commsson of he gudelnes ssued, sang whch compeen auhory has no compled wh hem, and oulnng how EIOPA nends o ensure ha concerned compeen auhores follow s gudelnes n he fuure. 4/18

5 2. Feedback saemen Inroducon EIOPA would lke o hank he Insurance and Rensurance Sakeholder Group IRSG and all he parcpans o he Publc Consulaon for her commens on he draf gudelnes. The responses receved have provded mporan gudance o EIOPA n preparng a fnal verson of hese gudelnes. All of he commens made were gven careful consderaon by EIOPA. A summary of he man commens receved and EIOPA s response o hem can be found n he secons below. The full ls of all he commens provded and EIOPA s responses o hem s publshed on EIOPA s webse. General commens 1. Employee benefs a A number of commens dsagreeng wh hs Gudelne were receved. The man argumens were: 1. Holdng capal agans employee benefs would pu nsurers a a dsadvanage compared o oher ndusry secors. 2. Employee benefs are ousde of he scope of Drecve 2009/138/EC. 3. Ths gudelne conradcs Arcle 336 of he Implemenng Measures, whch requres ha he capal requremens for nsuons of occupaonal reremen provson whn he meanng of Drecve 2003/41/EC calculaed accordng o he relevan secoral rules are added o he SCR calculaed based on he consoldaed daa referred o n Arcle 335 1a, b and c of he Implemenng Measures. b For a and b, EIOPA consders ha he requremens o hold capal o cover he marke and counerpary rsk resulng from employee benefs lables provded ha he underakng s fully or parally lable for losses are based on Arcle 1055 of Drecve 2009/138/EC and rsks canno be excluded from he Solvency Capal Requremens based on poenal compeve dsadvanages n labour markes. A he same me he requremen o hold capal o cover he lfe underwrng rsk s accordng o Arcle of Drecve 2009/138/EC lmed o lfe nsurance oblgaons and can herefore no be exended o employee benefs. Regardng pon c, EIOPA has a dfferen readng of he Gudelne and Arcle 336 of he Implemenng Measures. The Gudelne does no nroduce an addonal capal requremen for IORPs on he solo level. On he group level accordng o Arcle 336 of he Implemenng Measures, he proporonal share of he secoral capal requremen for he IORP has o be added o a Solvency Capal Requremen calculaed on he bass of consoldaed daa. The laer fgure has o reflec he rsk of he consoldaed par of he group. If he lables for employee benefs have o be recognsed for he consoldaed par of he group or he nsurer s lable for any losses hen gnorng he assocaed 5/18

6 marke and counerpary rsks could resul n underesmang he Solvency Capal Requremen for he consoldaed par of he group EIOPA s herefore of he opnon ha he Gudelne s n lne wh he Solvency II Drecve and he Implemenng Measures. EIOPA amended he Gudelne o make clearer ha marke and counerpary sresses have o be appled n all cases where lables arsng from employee benefs are recognsed n he balance shee. 2. Smplfcaons a I was suggesed o allow smplfcaons when calculang he duraon of bonds and loans wh call opons. b EIOPA undersand he wsh for smplfcaons, bu Gudelnes canno nroduce smplfcaons n addon o hose defned n he Implemenng Measures. 3. Ineres rae shocks a I was proposed ha he neres rae sresses specfed n Arcles 166 and 167 of he Implemenng Measures should only be appled o he non-exrapolaed par of he curve. The sresses n he exrapolaed par of he curve would hen be smply a resul of he sresses o he non-exrapolaed par. Sakeholders were no clear wha he senence "hs may nvolve a mark o model valuaon for he asses under he sresses" means and suggesed a deleon. Sakeholders also presened wo possbles how neres rae shocks could be appled o bonds valued mark-o-marke. b For he frs pon: EIOPA consders ha he menoned Arcles leave no room for hs nerpreaon. For he second pon: EIOPA clarfed why a mark-o-model valuaon should be appled o bonds whch are marked-o-marke and how o apply he neres rae shock on such bonds. General naure of he parcpans o he Publc Consulaon EIOPA receved commens from he Insurance and Rensurance Sakeholder Group IRSG and egh responses from oher sakeholders o he publc consulaon. All non-confdenal commens receved have been publshed on EIOPA s webse. Respondens can be classfed no hree man caegores: European rade, nsurance, or acuaral assocaons; naonal nsurance or acuaral assocaons; and rensurance groups or underakngs. Below s a summary of he ypes of respondens. 6/18

7 IRSG opnon The IRSG opnon on he draf se 1 of he Solvency II Gudelnes on Pllar 1 and Inernal Models, as well as he parcular commens on he Gudelnes a hand, can be consuled on EIOPA s webse 5. Commens on he Impac Assessmen A separae Consulaon Paper was prepared coverng he Impac Assessmen for he Se 1 of EIOPA Solvency II Gudelnes. Where he need for revewng he Impac Assessmen has arsen followng commens on he gudelnes, he Impac Assessmen Repor has been revsed accordngly. The revsed Impac Assessmen on he Se 1 of EIOPA Solvency II Gudelnes can be consuled on EIOPA s webse. 5 hps://eopa.europa.eu/abou-eopa/organsaon/sakeholder-groups/sgs-opnon-feedback/ndex.hml 7/18

8 Annex: Gudelnes 1. Gudelnes on he reamen of marke and counerpary rsk exposures n he sandard formula Inroducon 1.1. Accordng o Arcle 16 of Regulaon EU No 1094/2010 of he European Parlamen and of he Councl of 24 November 2010 esablshng a European Supervsory Auhory herenafer EIOPA Regulaon 6, EIOPA s ssung Gudelnes on he reamen of marke and counerpary rsk exposure n he sandard formula 1.2. These Gudelnes relae o Arcle 104 and 105 of Drecve 2009/138/EU of he European Parlamen and of he Councl of 25 November 2009 on he akng up and pursu of he busness of Insurance and Rensurance herenafer Solvency II 7 and o 164 o Arcle 202 of he Implemenng Measures These Gudelnes are addressed o supervsory auhores under Solvency II These Gudelnes am a faclang convergence of pracces across Member Saes and supporng underakngs n applyng he marke and counerpary defaul rsk modules of he sandard formula For he purpose of hese Gudelnes, he followng defnon has been developed: - shor equy poson means a shor poson relang o equy resulng from a shor sale whn he meanng of paragraph 1b of Arcle 2 of Regulaon EU 236/ If no defned n hese Gudelnes he erms have he meanng defned n he legal acs referred o n he nroducon These Gudelnes shall apply from 1 Aprl Gudelne 1 Employee benefs 1.8. Where lables for employee benefs are recognsed n accordance wh Chaper II of he Implemenng Measures, underakngs should ake hem no accoun n he calculaon of he capal requremens for counerpary defaul rsk and marke rsk modules. For hs purpose, underakngs should ake no accoun he naure of he benefs and where relevan, he naure of all conracual arrangemens wh an nsuon for occupaonal reremen provson as defned by Drecve 2003/41/EC or anoher nsurance or rensurance underakng for he provson of hese benefs. 6 OJ L 331, , p OJ L 335, , p /18

9 1.9. If he managemen of he asses represenng he lables for employee benefs has been ousourced, underakngs acng as a sponsor should ake hem no accoun n he calculaon of he capal requremen for marke rsk and counerpary defaul rsk modules provded, hey are lable for any loss n value of hese asses. Gudelne 2 - Influence of call opons on duraon When deermnng he duraon of bonds and loans wh call opons underakngs should ake no accoun ha hey may no be called by he borrower n he even ha s credworhness deeroraes, cred spreads wden or neres raes ncrease. Gudelne 3 Average duraon for he duraon-based equy sub-module Underakngs should nerpre he average duraon referred o n Arcle b of Solvency II as he duraon of he aggregaed cash-flows of he lables. Gudelne 4 Ineres rae rsk sub-module Underakngs should nclude all neres rae sensve asses and lables n he calculaon of he capal requremen for he neres rae rsk sub-module The echncal provson should be recalculaed under he scenaros usng he rsk free neres rae erm srucure afer he shock, whch s deermned by sressng he basc rsk free neres rae erm srucure and addng back machng adjusmen, volaly adjusmen or ransonal measure on he rsk free rae under Arcle 308 c of he Solvency II Drecve, f applcable The asses value should be recalculaed under he scenaros by sressng only he basc rsk free neres rae erm srucure and any spreads over he basc rsk free neres rae erm srucure should reman unchanged. Ths may nvolve usng a mark o model valuaon for deermnng he value of he asses under he sresses Insurance and rensurance underakngs should ensure ha he values of asses before he sresses obaned by usng a mark-o-model valuaon are conssen wh he quoed marke prces of relevan asses n acve markes. Gudelne 5 - Invesmens wh equy and deb nsrumen characerscs Where asses exhb deb and equy nsrumen characerscs, underakngs should ake no accoun boh of hese feaures when deermnng whch sandard formula rsk sub-modules should apply When deermnng whch sandard formula rsk sub-modules apply underakngs should consder he economc subsance of he asse. 9/18

10 1.18. Where he asse can be consdered as he compose of dscree componens, underakngs should where approprae apply he relevan sresses o each of hese componens separaely Where s no possble o consder he asse as he compose of separae componens underakngs should base he deermnaon of whch of he sandard formula rsk sub-modules apply on wheher he deb or equy characerscs predomnae n an economc sense. Gudelne 6 - Shor equy posons Where underakngs hold shor equy posons, hey should only be used o offse long equy posons n he calculaon of he capal requremen for equy rsk f he requremens se ou n Arcles 208 o 215 of he Implemenng Measures are me Underakngs should gnore any oher shor equy poson resdual shor equy posons n he calculaon of he capal requremen for equy rsk The resdual shor equy posons should no be consdered o ncrease n value from applyng he sresses o eques. Gudelne 7 Marke rsk concenraon sub-module Whou prejudce o Arcle second par of he Implemenng Measures, underakngs should no assgn a rsk facor of 0 % o nvesmens n enes whch are owned by enes ncluded n he ls se ou n Arcle of he Implemenng Measures. Gudelne 8 Secures lendng ransacons and smlar agreemens When deermnng he capal requremens for secures lendng or borrowng ransacons and repurchase or reverse repurchase agreemens ncludng lqudy swaps, underakngs should follow he recognon of he exchanged ems n he Solvency II balance shee. They should also ake no accoun conracual erms and rsks semmng from he ransacon or agreemen If he len asse remans on he balance shee and he receved asse s no recognsed, underakngs should: a b apply he relevan marke rsk sub-modules o he len asse; nclude he len asse n he calculaon of he capal requremen for counerpary defaul rsk on ype 1 exposures, akng no accoun he rsk-mgaon ha he receved asse provdes f s recognsed as collaeral n accordance wh he requremens se ou n Arcle 214 of he Implemenng Measures If he receved asse s recognsed and he len asse does no reman on he balance shee, underakngs should: a apply he relevan marke rsk sub-modules o he receved asse; 10/18

11 b ake no accoun he len asse n he calculaon of he capal requremen for counerpary defaul rsk on ype 1 exposures based on he balance shee value of he len asse a he me of he exchange, f he conracual erms and he legal provsons n he case of an nsolvency of he borrower gve rse o a rsk ha he len asse s no reurned alhough he receved asse has been handed back If he len asse and he receved asse are recognsed n he Solvency II balance shee, underakngs should: a b c apply he relevan marke rsk sub-modules o he len asse and he borrowed asse; nclude he len asse n he calculaon of he capal requremen for counerpary defaul rsk on ype 1 exposures, akng no accoun he rsk-mgaon ha he receved asse provdes f s recognsed as collaeral n accordance wh he requremens se ou n Arcle 214 of he Implemenng Measures; consder lables on s balance shee whch resul from he lendng arrangemen n he calculaon of he capal requremen for he neres rae rsk sub-module. Gudelne 9 Commmens whch may creae paymen oblgaons As provded for n Arcle e of he Implemenng Measures he capal requremen for ype 1 exposures n he counerpary defaul rsk module should be appled o legally bndng commmens whch an underakng has provded or arranged When no nomnal value s explcly menoned n he commmen arrangemen, underakngs should deermne he correspondng loss gven defaul, as referred o n Arcle of he Implemenng Measures on he bass of an esmaed nomnal amoun The esmaed nomnal value s he maxmum amoun ha s expeced o be pad n case of a cred even of he counerpary. Complance and Reporng Rules Ths documen conans Gudelnes ssued under Arcle 16 of he EIOPA Regulaon. In accordance wh Arcle 16 3 of he EIOPA Regulaon, naonal compeen auhores shall make every effor o comply wh gudelnes and recommendaons Compeen auhores ha comply or nend o comply wh hese Gudelnes should ncorporae hem no her regulaory or supervsory framework n an approprae manner Compeen auhores shall confrm o EIOPA wheher hey comply or nend o comply wh hese Gudelnes, wh reasons for non-complance, whn wo monhs afer he ssuance of he ranslaed versons. 11/18

12 1.34. In he absence of a response by hs deadlne, compeen auhores wll be consdered as non-complan o he reporng and repored as such. Fnal Provson on Revews The presen Gudelnes shall be subjec o a revew by EIOPA. 12/18

13 2. Explanaory ex Gudelne 1 Employee benefs Where lables for employee benefs are recognsed n accordance wh Chaper II of he Implemenng Measures, underakngs should ake hem no accoun n he calculaon of he capal requremens for counerpary defaul rsk and marke rsk modules. For hs purpose, underakngs should ake no accoun he naure of he benefs and where relevan, he naure of all conracual arrangemens wh an nsuon for occupaonal reremen provson as defned by Drecve 2003/41/EC or anoher nsurance or rensurance underakng for he provson of hese benefs. If he managemen of he asses represenng he lables for employee benefs has been ousourced, underakngs acng as a sponsor should ake hem no accoun n he calculaon of he capal requremen for marke rsk and counerpary defaul rsk modules provded, hey are lable for any loss n value of hese asses The followng examples llusrae wha he Gudelne means for parcular cases: Case 1: No ousourcng, all he employee benefs are on he balance shee of he nsurance underakng. The marke rsk and counerpary defaul rsk modules are appled n he same way as for nsurance lables. Case 2: Defned Benef penson promse, compleely ousourced n a sponsor underwren IORP, wh unlmed sponsor suppor. The asses and lables of he IORP have o be aken no accoun n he calculaon of he Solvency Capal Requremen and he shocks have o be appled as f he nsurance underakng were drecly holdng he asses of he IORP. Case 3: Defned Benef penson promse, compleely ousourced n an own fund-iorp or anoher nsurer, wh no sponsor suppor he exernal IORP or nsurer bears he marke rsks No need o nclude he employee benefs n he calculaon of he capal requremen for marke rsk and counerpary defaul rsk. Case 4: Pure Defned Conrbuon penson promse wh no guaranees No need o nclude he employee benefs n he calculaon of he capal requremen for marke rsk and counerpary defaul rsk. Gudelne 2 - Influence of call opons on duraon When deermnng he duraon of bonds and loans wh call opons underakngs should ake no accoun ha hey may no be called by he borrower n he even ha s credworhness deeroraes, cred spreads wden or neres raes ncrease. 13/18

14 1.2. In he case of subordnaed bonds wh call opons, he opons may no be exercsed n a wder range of crcumsances. Ths uncerany needs o be refleced when calculang he duraon of such asses. Gudelne 5 - Invesmens wh equy and deb nsrumen characerscs Where asses exhb deb and equy nsrumen characerscs, underakngs should ake no accoun boh of hese feaures when deermnng whch sandard formula rsk sub-modules should apply. When deermnng whch sandard formula rsk sub-modules apply underakngs should consder he economc subsance of he asse. Where he asse can be consdered as he compose of dscree componens, underakngs should where approprae apply he relevan sresses o each of hese componens separaely. Where s no possble o consder he asse as he compose of separae componens underakngs should base he deermnaon of whch of he sandard formula rsk sub-modules apply on wheher he deb or equy characerscs predomnae n an economc sense Consder as an example bonds wh a fxed erm o maury where he holder can conver hem no a specfed number of shares of he common sock n he ssung company a parcular nervals or durng he erm of he bond. One way of applyng he sandard formula s o consder hem as bond wh a call opon on equy. The bond componen has o be subjec o he spread rsk, neres rae rsk and any oher relevan rsk sub-modules as approprae. The call opon has o be subjec o he equy rsk, neres rae rsk and any oher relevan rsk sub-modules as approprae Wh hs approach he spread rsk charge s no appled o he full marke value of he converble bond bu only o he par whch can be consdered as he fxed ncome bond. Gudelne 7 Marke rsk concenraon sub-module Whou prejudce o Arcle second par of he Implemenng Measures, underakngs should no assgn a rsk facor of 0 % o nvesmens n enes whch are owned by enes ncluded n he ls se ou n Arcle 1873 of he Implemenng Measures As an example consder wo recapalsed banks A and B. A has a cred qualy equvalen o sep 1 and B has a cred qualy equvalen o sep 2. Boh banks are owned by a holdng eny C, whch n urn s owned by he naonal governmen of a Member Sae. The banks A and B are no fully, uncondonally and rrevocably guaraneed by he naonal governmen of a Member Sae An nsurer holds bonds of 50 n bank A and of 100 n bank B. These nvesmens do no arac a rsk facor of 0 % for he calculaon n he marke 14/18

15 rsk concenraon sub-module. Insead he weghed average cred qualy sep of he exposure o A and B has o be used. In hs case he weghed average s 1*50 / * 100 / 150 = 5 / 3. The rounded-up whole number s 2, so he nsurer has o use a cred qualy sep of 2 for hs sngle name exposure Deb nsrumens ssued by he naonal governmen arac a rsk facor of 0 % n accordance wh Arcle of he Implemenng Measures There mgh be suaons where underakngs have exposures o a number of companes owned by enes lsed n Arcle of he Implemenng Measures. Consder an underakng ha has exposures of 10 o A, B and C each. A s lsed n Arcle of he Implemenng Measures. B and C are owned by A and he 0% marke rsk concenraon charge does no apply because hey are no fully, uncondonally and rrevocably guaraneed by he naonal governmen of a Member Sae. As B and C are owned by he same eny hey are consdered o belong o he same sngle name exposure. In accordance wh Arcle of he Implemenng Measures, he exposure o A s excluded from he exposure a defaul for hs sngle name exposure whch has a value of Exposures o counerpares ha are par of he same corporae group as he nsurance underakng, whch do no mee he requremens of Arcle 1842 of he Implemenng Measures for excluson from marke rsk concenraon, have o be assgned o he same sngle name exposure. For example, consder an underakng whch has exposures o he counerpares A, B, C and D of 10 each. The counerpares A, B, C and D are par of he same corporae group as he underakng self. The exposure o A s excluded from he calculaon base of he marke concenraon rsk because s fully, uncondonally and rrevocably guaraneed by an eny lsed n Arcle of he Implemenng Measures. B s excluded from he calculaon base of he marke concenraon rsk because mees he requremens of Arcle of he Implemenng Measures. C and D are ncluded n he calculaon base e.g. because hey are no esablshed n he Unon and herefore do no comply wh pon v of Arcle of he Implemenng Measures. C and D are consdered as a sngle name exposure wh a value of /18

16 Gudelne 9 Commmens whch may creae paymen oblgaons As provded for n Arcle e of he Implemenng Measures he capal requremen for ype 1 exposures n he counerpary defaul rsk module should be appled o legally bndng commmens whch an underakng has provded or arranged. When no nomnal value s explcly menoned n he commmen arrangemen, underakngs should deermne he correspondng loss gven defaul, as referred o n Arcle of he Implemenng Measures on he bass of an esmaed nomnal amoun. The esmaed nomnal value s he maxmum amoun ha s expeced o be pad n case of a cred even of he counerpary The scope of Arcle e of he Implemenng Measures covers a commmen o provde suppor o anoher underakng relaed or oherwse and s also applcable regardless of wheher he em consues an approved Ancllary Own Fund em for a recpen underakng whn he scope of Solvency II. 16/18

17 17/18 Appendx Duraon of cash flows A fuure cash flow s deermned by paymens c a mes, = 1, 2, 3... When dscounng he cash flow one uses n he case of connuously pad neres a curve for he neres rae nensy or for he rae of neres r as a funcon of me. The me s measured n years. The relaon beween hese s gven by 1 1 r e The oal dscouned value of he cash flow s r c e c V 1 The duraon D Macaulay duraon of he dscouned cash flow s he weghed me average of he paymens, defned by V e c D Background The duraon D can be nerpreed as he relave sensvy of he value V o a parallel shf of he neres rae curve. Ths can be shown as follows. Le Vh be he value of he dscouned cash flow a neres rae +h,.e. h e c h V ] [ The dervave of Vh wh respec o h s h e c dh h dv ] [ and herefore V dh h dv D h / 0

18 If he paymens occur a mes = /k, = 1, 2, 3..., where k = 1 for annual paymens, k = 12 for monhly paymens ec., and f he annual rae of neres s consan equal o r, he dscouned value of he cash flow s V c 1 r / k The duraon s D / k c 1 r / k V Background The sensvy of he value V = Vr o a change of he neres rae r can be measured by he dervave of Vr wh respec o r dv r dr / k c 1 r / k 1 The relave sensvy of he value s herefore dv r D / V r dr 1 r / k The quany D/1 + r/ k s called he modfed duraon. The dfference beween hese wo conceps s ofen mmaeral. If he neres curve s no consan, he modfed duraon D mod of a cash flow wh maury T s defned as D mod D 1 r T / k For a cash flow whch s sochasc, fuure paymens are replaced by her expeced values. As an example, for an annuy, where paymen of an amoun B a me wll occur wh probably p, we have c = p B. Duraon can also be deermned for he undscouned cash flow,.e. wh r = 0. 18/18