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Stochastic Filtering and Corporate and Sovereign Credit Risk

Pro­ject Staff:

Leader: Rüdi­ger Frey
Prin­cipal In­vestig­at­ors: Kurt Hornik, Stefan Pichler
Scien­ti­fic Staff: Ca­milla Damian, Rainer Hirk, Ric­cardo Ras­telli
Co­oper­at­ing Part­ner: Mi­chaela Szölgy­enyi, Zehra Ek­si-Altay, Ka­tia Colaneri


Short De­scrip­tion:

The fin­an­cial crisis and the fol­low­ing sov­er­eign debt crisis showed that the ex­ist­ing the­or­et­ical frame­work for the mod­el­ling of credit and sov­er­eign debt risk is not suf­fi­cient to provide em­pir­ic­ally sound guidelines for fin­an­cial de­cision mak­ing: some of the ex­ist­ing mod­els are quite sat­is­fact­ory from a the­or­et­ical per­spect­ive, but can­not be dir­ectly im­ple­men­ted be­cause of the non-ob­serv­ab­il­ity of the un­derly­ing eco­nomic vari­ables. Other mod­els such as the pop­ular credit rat­ing or scor­ing mod­els are eas­ily ap­plic­able, but lack a sound meth­od­o­logy for model val­id­a­tion and em­pir­ical test­ing, es­sen­tially be­cause the `true' cred­it­wor­thi­ness of a firm is not ob­serv­able. In this pro­ject we will ad­dress these is­sues by a sys­tem­atic use of stochastic fil­ter­ing tech­niques. Stochastic fil­ter­ing is a mathem­at­ical dis­cip­line that deals with sig­nal de­tec­tion and para­meter es­tim­a­tion in par­tially ob­served sys­tems and is thus a nat­ural tool for the ana­lysis of credit risk. We want to study ap­plic­a­tions of stochastic fil­ter­ing to three re­lated areas: ana­lysis of sov­er­eign credit spreads; stat­ist­ical meth­od­o­logy for credit rat­ing sys­tems; pri­cing and hedging of fin­an­cial as­sets in struc­tural mod­els. We will con­sider the entire mathem­at­ical "pro­duc­tion-­chain", ranging from mathem­at­ical model devel­op­ment and the ex­ten­sion of fil­ter­ing tech­niques to the im­ple­ment­a­tion and test­ing of mod­els on real data. A par­tic­u­lar em­phasis will be put on stat­ist­ical in­fer­ence.

>> De­tailed Sum­mary

  • Leo­bacher, Gun­ther, Szölgy­enyi, Mi­chaela. 2018. Con­ver­gence of the Euler­-­Maruyama method for mul­ti­di­men­sional SDEs with dis­con­tinu­ous drift and de­gen­er­ate dif­fu­sion coef­fi­cient. Nu­merische Mathem­atik 138 (1), 219–239.

  • Damian, Ca­milla, Eksi, Zehra, Frey, Rüdi­ger. 2017. EM Al­gorithm for Markov Chains Ob­served via Gaus­sian Noise and Point Pro­cess In­form­a­tion: The­ory and Case Stud­ies. Stat­ist­ics & Risk Mod­el­ing 35 (1-2), 51–72,

  • Frey, Rüdi­ger, Rösler, Lars, Lu, Dan. 2017. Cor­por­ate se­cur­ity prices in struc­tural credit risk mod­els with in­com­plete in­form­a­tion. Mathem­at­ical Fin­ance. 2017;00:1–33. arXiv:1701.04780

  • Leo­bacher, Gun­ther, Szölgy­enyi, Mi­chaela. 2017. Nu­mer­ical meth­ods for SDEs with drift dis­con­tinu­ous on a set of pos­it­ive reach. In­ter­na­tionale Mathem­at­ische Na­chrichten 235, 1-16. arXiv:1708.06188

  • Eichler, Andreas, Leo­bacher, Gun­ther, Szölgy­enyi, Mi­chaela. 2017. Util­ity indif­fer­ence pri­cing of in­sur­ance cata­strophe de­riv­at­ives. European Ac­tu­ar­ial Journal 7 (2), 515–534.

  • Leo­bacher, Gun­ther, Szölgy­enyi, Mi­chaela. A strong order 1/2 method for mul­ti­di­men­sional SDEs with dis­con­tinu­ous drift. An­nals of Ap­plied Prob­ab­il­ity 27 (4), 2383-2418.

  • Shardin, An­ton A., Szölgy­enyi, Mi­chaela. 2016. Op­timal con­trol of an en­ergy stor­age fa­cil­ity un­der a chan­ging eco­nomic en­vir­on­ment and par­tial in­form­a­tion. In­ter­na­tional Journal of The­or­et­ical and Ap­plied Fin­ance 19 (4): S. 1-27.

  • Szölgy­enyi, Mi­chaela. 2016. Di­vidend max­im­iz­a­tion in a hid­den Markov switch­ing model. Stat­ist­ics & Risk Mod­el­ing 32 (3-4), 143-158. arXiv:1602.04656

  • Neuen­kirch, Andreas, Szölgy­enyi, Mi­chaela, Sz­pruch, Lukasz: An ad­apt­ive Euler­-­Maruyama scheme for stochastic dif­fer­en­tial equa­tions with dis­con­tinu­ous drift and its con­ver­gence ana­lysis. arXiv: 1802.04521

  • Kritzer, Peter, Leo­bacher, Gun­ther, Szölgy­enyi, Mi­chaela, Thon­hauser, Stefan: Ap­prox­im­a­tion meth­ods for piece­wise de­termin­istic Markov pro­cesses and their costs. arXiv:1712.09201

  • Colaneri, Ka­tia, Eksi, Zehra, Frey, Rüdi­ger, Szölgy­enyi, Mi­chaela: Shall I Sell or Shall I Wait? Op­timal Li­quid­a­tion un­der Par­tial In­form­a­tion with Price Im­pact. arXiv:1606.05079

Third Mis­sion:

Young Science Pro­ject: www.young­

Fun­ded by:

WWTF Wiener Wis­senschafts-, Forschungs- und Tech­no­lo­giefonds
(Vi­enna Science and Tech­no­logy Fund)

WWTF pro­ject num­ber: MA14-031
01.04.2015 - 31.03.2019