The con­fer­ence is go­ing to take place at Eötvös Loránd Uni­ver­sity, Bu­dapest, Hun­gary Pázmány Péter Sétány 1/​A, Gömb Aula.

If you need free park­ing place for the time of the con­fer­ence, please send your li­cense plate num­ber to riskconf@math.elte.hu.

Keynote speaker:

• Dami­ano Brigo (Im­pe­r­ial Col­lege)

Con­firmed in­vited speak­ers:

• Wolf­gang Wim­mer (Er­ste Group, Vi­enna)
• Stephane Crepey (Uni­ver­sity of Évry Val)
• Nor­bert Hári (Mor­gan Stan­ley)

Pro­gram:

Dami­ano Brigo (Im­pe­r­ial Col­lege Lon­don):

The sci­ence & art of val­u­a­tion ad­just­ments: Non­lin­ear val­u­a­tion un­der mar­gins, fund­ing costs, gap de­fault close­out, mul­ti­ple curves & cap­i­tal.

The mar­ket for fi­nan­cial prod­ucts and de­riv­a­tives reached an out­stand­ing no­tional size of 708 USD Tril­lions in 2011, amount­ing to ten times the planet gross do­mes­tic prod­uct. Even dis­count­ing dou­ble count­ing, de­riv­a­tives ap­pear to be an im­por­tant part of the world econ­omy and have played a key role in the on­set of the fi­nan­cial cri­sis in 2007. We de­scribe the changes trig­gered by post 2007 events on the the­ory of val­u­a­tion. We re-dis­cuss the val­u­a­tion the­ory as­sump­tions and in­tro­duce con­sis­tent val­u­a­tion un­der coun­ter­party credit risk, col­lat­eral post­ing, ini­tial and vari­a­tion mar­gins, fund­ing costs and cap­i­tal costs. We ex­plain model de­pen­dence in­duced by credit ef­fects, hy­brid fea­tures, con­ta­gion, pay­out un­cer­tainty, and non­lin­ear ef­fects due to re­place­ment close­out at de­fault and pos­si­bly asym­met­ric bor­row­ing and lend­ing rates in the mar­gin in­ter­est and in the fund­ing strat­egy for the hedge of the rel­e­vant port­fo­lio. Non­lin­ear­ity man­i­fests it­self in the val­u­a­tion equa­tions tak­ing the form of semi-lin­ear PDEs or Back­ward SDEs. We pre­sent an in­vari­ance the­o­rem show­ing that the fi­nal val­u­a­tion equa­tions do not de­pend on un­ob­serv­able risk free rates, that be­come purely in­stru­men­tal vari­ables. Val­u­a­tion is thus based only on real mar­ket rates and processes. We also pre­sent a high level analy­sis of the con­se­quences of non­lin­ear­i­ties, both from the point of view of method­ol­ogy and from an op­er­a­tional an­gle, in­clud­ing deal/​en­tity/​ag­gre­ga­tion de­pen­dent val­u­a­tion prob­a­bil­ity mea­sures and the role of banks trea­suries. We briefly dis­cuss con­di­tions un­der which ad­just­ments can be dis­en­tan­gled. Fi­nally, we hint at how one may con­nect these de­vel­op­ments to in­ter­est rate the­ory un­der mul­ti­ple dis­count curves and to val­u­a­tions for CCP cleared trades, thus build­ing a con­sis­tent val­u­a­tion frame­work en­com­pass­ing most post-2007 ef­fects.

In­vited talks

Wolf­gang Wim­mer (Er­ste Group, Vi­enna):

Mon­i­tor­ing of Coun­ter­party Credit Risk / Reg­u­la­tory Chal­lenges

Wolf­gang Wim­mer from Er­ste Group will give an overview about the cur­rent chal­lenges in the coun­ter­party credit risk area. The pre­sen­ta­tion will show how dif­fer­ent risk mea­sures for OTC de­riv­a­tives are used in the daily mon­i­tor­ing process and it will ex­plain how the aris­ing credit risk can be mit­i­gated. Fur­ther­more the course will con­clude with an out­look on reg­u­la­tory changes re­lated to coun­ter­party credit risk (SA-CCR and CVA).

Stéphane Crépey (Uni­ver­sity of Évry Val):

Cap­i­tal Val­u­a­tion Ad­just­ment and Fund­ing Val­u­a­tion Ad­just­ment (joint work with Clau­dio Al­banese and Si­mone Cae­nazzo)

In the af­ter­math of the fi­nan­cial cri­sis, reg­u­la­tors launched in a ma­jor ef­fort of bank­ing re­form aimed at se­cur­ing the fi­nan­cial sys­tem by rais­ing col­lat­er­al­i­sa­tion and cap­i­tal re­quire­ments. Notwith­stand­ing fi­nance the­o­ries ac­cord­ing to which costs of cap­i­tal and of fund­ing for col­lat­eral are ir­rel­e­vant to de­ci­sions, banks have in­tro­duced an ar­ray of XVA met­rics to pre­cisely quan­tify them. In par­tic­u­lar, KVA (cap­i­tal val­u­a­tion ad­just­ment) and FVA (fund­ing val­u­a­tion ad­just­ment) are emerg­ing as met­rics of key rel­e­vance.

We in­tro­duce a cap­i­tal struc­ture model ac­knowl­edg­ing the im­pos­si­bil­ity for a bank to hedge jump-to-de­fault re­lated cash flows. Be­cause of this coun­ter­party credit risk in­com­plete­ness, deals trig­ger wealth trans­fers from bank share­hold­ers to bank cred­i­tors and share­hold­ers need to set cap­i­tal at risk. On this ba­sis we ob­tain a the­ory of XVAs where so-called con­tra-li­a­bil­i­ties and cost of cap­i­tal are sourced from bank clients at trade in­cep­tions, on top of the fair val­u­a­tion of coun­ter­party credit risk, in or­der to com­pen­sate share­hold­ers for wealth trans­fers and risk on cap­i­tal.

We in­tro­duce a frame­work for as­sess­ing KVA, re­flect it into en­try prices and dis­trib­ute it grad­u­ally to the bank share­hold­ers through a div­i­dend pol­icy that would be sus­tain­able even in the limit case of a port­fo­lio held on a run-off ba­sis, with no new trades ever en­tered in the fu­ture. Our FVA is de­fined asym­met­ri­cally since there is no ben­e­fit in hold­ing ex­cess cap­i­tal in the fu­ture. We no­tice that cap­i­tal is fun­gi­ble as a source of fund­ing for vari­a­tion mar­gin (but not for ini­tial mar­gin), caus­ing a ma­te­r­ial re­duc­tion in the FVA num­bers.

Nor­bert Hári (Mor­gan Stan­ley):

Smile and de­fault: The role of sto­chas­tic volatil­ity and in­ter­est rates in coun­ter­party credit risk

In this re­search, we in­ves­ti­gate the im­pact of sto­chas­tic volatil­ity and in­ter­est rates on coun­ter­party credit risk (CCR) for FX de­riv­a­tives. To achieve this we analyse two real-life cases in which the mar­ket con­di­tions are dif­fer­ent, namely dur­ing the 2008 credit cri­sis where risks are high and a pe­riod af­ter the cri­sis in 2014, where volatil­ity lev­els are low. The He­s­ton model is ex­tended by adding two Hull–White com­po­nents which are cal­i­brated to fit the EU­RUSD volatil­ity sur­faces. We then pre­sent fu­ture ex­po­sure pro­files and credit value ad­just­ments (CVAs) for plain vanilla cross-cur­rency swaps (CCYS), bar­rier and Amer­i­can op­tions and com­pare the dif­fer­ent re­sults when He­s­ton–Hull–White or Black–Sc­holes dy­nam­ics are as­sumed. It is ob­served that the sto­chas­tic volatil­ity has a sig­nif­i­cant im­pact on all the de­riv­a­tives. For CCYS, some of the im­pact can be re­duced by al­low­ing for time-de­pen­dent vari­ance. We fur­ther con­firmed that Bar­rier op­tions ex­po­sure and CVA is highly sen­si­tive to volatil­ity dy­nam­ics and that Amer­i­can op­tions’ risk dy­nam­ics are sig­nif­i­cantly af­fected by the un­cer­tainty in the in­ter­est rates.

Con­tributed talks

Lás­zló An­tal – Gá­bor Sala­mon (Mor­gan Stan­ley):

Longstaff–Schwartz for Ex­pected Ex­po­sures in XVA

The Longstaff–Schwartz method (LSM) is an in­dus­try stan­dard for valu­ing Amer­i­can/​Bermu­dan-style op­tions. In this talk we briefly sum­ma­rize the the­o­ret­i­cal back­ground and show how the LSM ap­proach can be used for ex­pected ex­po­sure cal­cu­la­tions with a fo­cus on the prac­ti­cal im­ple­men­ta­tion in the XVA frame­work.

Leonardo Ferro (Mor­ganStan­ley):

Ef­fi­cient ex­po­sure com­pu­ta­tion by risk fac­tor de­com­po­si­tion

The fo­cus of this re­search is the ef­fi­cient com­pu­ta­tion of coun­ter­party credit risk ex­po­sure on port­fo­lio level. Here, the large num­ber of risk fac­tors rules out tra­di­tional PDE-based tech­niques and al­lows only a rel­a­tively small num­ber of paths for nested Monte Carlo sim­u­la­tions, re­sult­ing in large vari­ances of es­ti­ma­tors in prac­tice. We pro­pose a novel ap­proach based on Kol­mogorov for­ward and back­ward PDEs, where we counter the high di­men­sion­al­ity by a gen­er­al­i­sa­tion of an­chored-ANOVA de­com­po­si­tions. By com­put­ing only the most sig­nif­i­cant term in the de­com­po­si­tion, the di­men­sion­al­ity is re­duced ef­fec­tively, such that a sig­nif­i­cant com­pu­ta­tional speed-up arises from the high ac­cu­racy of PDE schemes in low di­men­sions com­pared to Monte Carlo es­ti­ma­tion. More­over, we show how this trun­cated de­com­po­si­tion can be used as con­trol vari­ate for the full high-di­men­sional model, such that any ap­prox­i­ma­tion er­rors can be cor­rected while a sub­stan­tial vari­ance re­duc­tion is achieved com­pared to the stan­dard sim­u­la­tion ap­proach. We in­ves­ti­gate the ac­cu­racy for a re­al­is­tic port­fo­lio of ex­change op­tions, in­ter­est rate and cross-cur­rency swaps un­der a fully cal­i­brated seven-fac­tor model.

Balázs Kozma – Vik­tor Nagy (Citibank):

How to value fu­ture cash flows in the pres­ence of fund­ing costs, credit risk, and col­lat­eral agree­ments?

CVA, FVA, DVA (credit val­u­a­tion ad­just­ment, fund­ing val­u­a­tion ad­just­ment, debit val­u­a­tion ad­just­ment; they are also re­ferred to as ‘XVA’) are hot top­ics in con­tem­po­rary fi­nance and de­riv­a­tives pric­ing. We will give a short overview of the topic and pre­sent a frame­work to take all these costs and risks into con­sid­er­a­tion.

We will dis­cuss a tech­nique called the ‘fund­ing in­vari­ance prin­ci­ple’ to show that, in­ter­est­ingly, as long as fund­ing cash-flows are in­cluded in the val­u­a­tion of a fi­nan­cial con­tract, the choice of the dis­count­ing rate is ir­rel­e­vant.

Sven Sandow

Coun­ter­party Risk and Bank Cap­i­tal

The work­shop is free for reg­is­tered par­tic­i­pants. You can reg­is­ter be­fore Oc­to­ber 14, 2016. If you want to can­cel your reg­is­tra­tion con­tact the or­ga­niz­ers at riskconf@math.elte.hu.

Pro­gram com­mit­tee:

• L. Márkus (chair),
• N.M. Arató,
• J. Gáll,
• Gy. Michalet­zky,
• G. Mol­nár-Sáska,
• V. Prokaj,
• M. Rá­sonyi

Lo­cal or­gan­is­ers:

• A. Zem­pléni (chair),
• Á. Back­hausz,
• V. Csiszár

email: riskconf@math.elte.hu

The main spon­sor is

The work­shop is also sup­ported by the Pal­las Athéné Do­mus Sci­en­tiae Foun­da­tion.