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Parsimonious HJM Modelling for Multiple Yield-Curve Dynamics

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  • Nicola Moreni
  • Andrea Pallavicini

Abstract

For a long time interest-rate models were built on a single yield curve used both for discounting and forwarding. However, the crisis that has affected financial markets in the last years led market players to revise this assumption and accommodate basis-swap spreads, whose remarkable widening can no longer be neglected. In recent literature we find many proposals of multi-curve interest-rate models, whose calibration would typically require market quotes for all yield curves. At present this is not possible since most of the quotes are missing or extremely illiquid. Thanks to a suitable extension of the HJM framework, we propose a parsimonious model based on observed rates that deduces yield-curve dynamics from a single family of Markov processes. Furthermore, we detail a specification of the model reporting numerical examples of calibration to quoted market data.

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File URL: http://arxiv.org/pdf/1011.0828
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Paper provided by arXiv.org in its series Papers with number 1011.0828.

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Date of creation: Nov 2010
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Handle: RePEc:arx:papers:1011.0828

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  1. Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
  2. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Fries, Christian P., 2010. "Discounting Revisited. Valuations under Funding Costs, Counterparty Risk and Collateralization," MPRA Paper 23082, University Library of Munich, Germany, revised 30 May 2010.
  4. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
  5. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
  6. Eisenschmidt, Jens & Tapking, Jens, 2009. "Liquidity risk premia in unsecured interbank money markets," Working Paper Series 1025, European Central Bank.
  7. Andrea Pallavicini & Marco Tarenghi, 2010. "Interest-Rate Modeling with Multiple Yield Curves," Papers 1006.4767, arXiv.org.
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Cited by:
  1. Damiano Brigo & Andrea Pallavicini, 2013. "CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?," Papers 1312.0128, arXiv.org, revised Dec 2013.
  2. Marco, Bianchetti & Mattia, Carlicchi, 2012. "Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR," MPRA Paper 42248, University Library of Munich, Germany.
  3. Andrea Pallavicini & Damiano Brigo, 2013. "Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs," Papers 1304.1397, arXiv.org.
  4. Damiano Brigo & Andrea Pallavicini, 2014. "CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins under credit, funding and wrong-way risks: A Unified Valuation Approach," Papers 1401.3994, arXiv.org.

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