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An Arbitrage-Free Large Market Model for Forward Spread Curves
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0001-9303-1196
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0835-7536
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0139-0747
2019 (English)In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with Demographics Workshop / [ed] Christos H. Skiadas, 2019Conference paper, Published paper (Refereed)
Abstract [en]

Before the financial crisis started in 2007, the forward rate agreement contracts could be perfectly replicated by overnight indexed swap zero coupon bonds. After the crisis, the simply compounded risk-free overnight indexed swap forward rate became less than the forward rate agreement rate. Using an approach proposed by Cuchiero, Klein, and Teichmann, we construct an arbitrage-free market model, where the forward spread curves for a given finite tenor structure are described as a mild solution to a boundary value problem for a system of infinite-dimensional stochastic differential equations. The constructed financial market is large: it contains infinitely many overnight indexed swap zero coupon bonds and forward rate agreement contracts with all possible maturities. We also investigate the necessary assumptions and conditions which guarantee existence, uniqueness and non-negativity of solutions to the obtained boundary value problem.

Place, publisher, year, edition, pages
2019.
Keywords [en]
Forward Rate Agreement, Overnight Index Swap, Large Market, Mild Solution, Wiener Space, Fundamental Theorem of Asset Pricing for Large Market, Existence, Uniqueness, Non-Negativity
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-47132OAI: oai:DiVA.org:mdh-47132DiVA, id: diva2:1395101
Conference
ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference, Florence, Italy, 11 – 14 June, 2019
Available from: 2020-02-20 Created: 2020-02-20 Last updated: 2021-12-15Bibliographically approved

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Nohrouzian, HosseinNi, YingMalyarenko, Anatoliy

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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Language
  • de-DE
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