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Quantitative Finance Volume 3, 2003 - Issue 6
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Original Articles

A displaced-diffusion stochastic volatility LIBOR market model: motivation, definition and implementation

Mark S Joshi QUARC, Royal Bank of Scotland Group, Level 5, 280 Bishopsgate, London, EC2M 3RB, UK
&
Riccardo Rebonato QUARC, Royal Bank of Scotland Group, Level 5, 280 Bishopsgate, London, EC2M 3RB, UK; OCIAM, Mathematical Institute, 24–29 St Giles, Oxford University, Oxford, OX1 3LB, UK
Pages 458-469 | Received 17 Jan 2003, Published online: 19 Aug 2006

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Robert Matthijs Verschuren. (2020) Stochastic interest rate modelling using a single or multiple curves: an empirical performance analysis of the Lévy forward price model. Quantitative Finance 20:7, pages 1123-1148.
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P. Karlsson, K. F. Pilz & E. Schlögl. (2017) Calibrating a market model with stochastic volatility to commodity and interest rate risk. Quantitative Finance 17:6, pages 907-925.
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Pan Tang, Belal E. Baaquie, Xin Du & Ying Zhang. (2016) Linearized Hamiltonian of the LIBOR market model: analytical and empirical results. Applied Economics 48:10, pages 878-891.
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Eymen Errais. (2015) Chasing market dislocation: The LIBOR shifted model. International Journal of Management Science and Engineering Management 10:4, pages 260-272.
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L. Steinruecke, R. Zagst & A. Swishchuk. (2015) The Markov-switching jump diffusion LIBOR market model. Quantitative Finance 15:3, pages 455-476.
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JoanneE. Kennedy, Subhankar Mitra & Duy Pham. (2012) On the Approximation of the SABR Model: A Probabilistic Approach. Applied Mathematical Finance 19:6, pages 553-586.
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Karl Larsson. (2012) General approximation schemes for option prices in stochastic volatility models. Quantitative Finance 12:6, pages 873-891.
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Ken Nyholm & Riccardo Rebonato. (2008) Long-horizon yield curve projections: comparison of semi-parametric and parametric approaches. Applied Financial Economics 18:20, pages 1597-1611.
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Lixin Wu & Fan Zhang. (2008) Fast swaption pricing under the market model with a square-root volatility process. Quantitative Finance 8:2, pages 163-180.
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Articles from other publishers (52)

Riccardo Rebonato. (2023) The Q -Measure Dynamics of Forward Rates . Annual Review of Financial Economics 15:1, pages 493-522.
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Pierre-Edouard Arrouy, Alexandre Boumezoued, Bernard Lapeyre & Sophian Mehalla. (2022) Jacobi stochastic volatility factor for the LIBOR market model. Finance and Stochastics 26:4, pages 771-823.
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Jaehyuk Choi, Minsuk Kwak, Chyng Wen Tee & Yumeng Wang. (2022) A Black–Scholes user's guide to the Bachelier model. Journal of Futures Markets 42:5, pages 959-980.
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Zhanyu Chen, Kai Zhang & Hongbiao Zhao. (2021) A Skellam market model for loan prime rate options . Journal of Futures Markets 42:3, pages 525-551.
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SASCHA DESMETTRE, SIMON HOCHGERNER, SANELA OMEROVIC & STEFAN THONHAUSER. (2022) A MEAN-FIELD EXTENSION OF THE LIBOR MARKET MODEL. International Journal of Theoretical and Applied Finance 25:01.
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Riccardo Bramante, Gimmi Dallago & Silvia Facchinetti. (2021) Black’s model in a negative interest rate environment, with application to OTC derivatives. Computational Management Science 19:1, pages 25-39.
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Patrice Poncet & Roland PortaitPatrice Poncet & Roland Portait. 2022. Capital Market Finance. Capital Market Finance 719 763 .
Dariusz Gatarek & Juliusz Jabłecki. (2021) Between Scylla and Charybdis: The Bermudan Swaptions Pricing Odyssey. Mathematics 9:2, pages 112.
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JACQUES VAN APPEL & THOMAS A. MCWALTER. (2020) MOMENT APPROXIMATIONS OF DISPLACED FORWARD-LIBOR RATES WITH APPLICATION TO SWAPTIONS. International Journal of Theoretical and Applied Finance 23:07, pages 2050046.
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Jie Xiong, Geng Deng & Xindong Wang. (2020) Extension of SABR Libor Market Model to handle negative interest rates. Quantitative Finance and Economics 4:1, pages 148-171.
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Christian P. Fries, Tobias Nigbur & Norman Seeger. (2017) Displaced relative changes in historical simulation: Application to risk measures of interest rates with phases of negative rates. Journal of Empirical Finance 42, pages 175-198.
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Mark S. Joshi & Dan Zhu. (2016) THE EFFICIENT COMPUTATION AND THE SENSITIVITY ANALYSIS OF FINITE-TIME RUIN PROBABILITIES AND THE ESTIMATION OF RISK-BASED REGULATORY CAPITAL. ASTIN Bulletin 46:2, pages 431-467.
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Anatoliy SwishchukAnatoliy Swishchuk. 2016. Change of Time Methods in Quantitative Finance. Change of Time Methods in Quantitative Finance 107 124 .
. 2015. XVA: Credit, Funding and Capital Valuation Adjustments. XVA: Credit, Funding and Capital Valuation Adjustments 469 488 .
Ana M. Ferreiro, José A. García-Rodríguez, José G. López-Salas & Carlos Vázquez. (2014) SABR/LIBOR market models: Pricing and calibration for some interest rate derivatives. Applied Mathematics and Computation 242, pages 65-89.
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Tao L. Wu & Shengqiang Xu. (2014) A Random Field LIBOR Market Model. Journal of Futures Markets, pages n/a-n/a.
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CHRISTOPHER BEVERIDGE & MARK JOSHI. (2014) THE EFFICIENT COMPUTATION OF PRICES AND GREEKS FOR CALLABLE RANGE ACCRUALS USING THE DISPLACED-DIFFUSION LMM. International Journal of Theoretical and Applied Finance 17:01, pages 1450001.
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Lea Steinrücke, Rudi Zagst & Anatoliy Swishchuk. 2014. Hidden Markov Models in Finance. Hidden Markov Models in Finance 85 116 .
José Da Fonseca, Alessandro Gnoatto & Martino Grasselli. (2013) A flexible matrix Libor model with smiles. Journal of Economic Dynamics and Control 37:4, pages 774-793.
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Matthias Muck. (2012) Spread ladder swaps—an analysis of controversial interest rate derivatives. Financial Markets and Portfolio Management 26:2, pages 269-289.
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Roger Lee & Dan Wang. (2009) Displaced lognormal volatility skews: analysis and applications to stochastic volatility simulations. Annals of Finance 8:2-3, pages 159-181.
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. 2012. The SABR/LIBOR Market Model. The SABR/LIBOR Market Model 271 274 .
Marc Decamps & Ann De Schepper. (2010) Edgeworth expansions of stochastic trading time. Physica A: Statistical Mechanics and its Applications 389:16, pages 3179-3192.
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Marc Henrard. (2010) Swaptions in Libor Market Model with local volatility. Wilmott Journal 2:3, pages 135-154.
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Belal E. Baaquie. (2009) Interest rates in quantum finance: The Wilson expansion and Hamiltonian. Physical Review E 80:4.
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Antonio Díaz, Vicente Meneu & Eliseo Navarro. (2009) International evidence on alternative models of the term structure of volatilities. Journal of Futures Markets 29:7, pages 653-683.
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Dariusz Gatarek, Przemyslaw Bachert & Robert Maksymiuk. 2007. The LIBOR Market Model in Practice. The LIBOR Market Model in Practice 259 265 .
S. Galluccio, J.‐M. Ly, Z. Huang & O. Scaillet. (2006) THEORY AND CALIBRATION OF SWAP MARKET MODELS. Mathematical Finance 17:1, pages 111-141.
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Leif B. G. Andersen & Vladimir V. Piterbarg. (2006) Moment explosions in stochastic volatility models. Finance and Stochastics 11:1, pages 29-50.
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RICCARDO REBONATO. (2011) FORWARD-RATE VOLATILITIES AND THE SWAPTION MATRIX: WHY NEITHER TIME-HOMOGENEITY NOR TIME-DEPENDENCE ARE ENOUGH. International Journal of Theoretical and Applied Finance 09:05, pages 705-746.
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Matthias Muck & Markus Rudolf. 2006. Kapitalmarkt, Unternehmensfinanzierung und rationale Entscheidungen. Kapitalmarkt, Unternehmensfinanzierung und rationale Entscheidungen 453 472 .
Riccardo Rebonato. 2004. Volatility and Correlation. Volatility and Correlation 805 812 .
T. Di Matteo, M. Airoldi & E. Scalas. (2004) On pricing of interest rate derivatives. Physica A: Statistical Mechanics and its Applications 339:1-2, pages 189-196.
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Riccardo Rebonato. (2004) Review Paper. Interest–rate term–structure pricing models: a review. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460:2043, pages 667-728.
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Daniel Alexandre Bloch. (2007) Libor Market Models Within the Affine and Quadratic Models. SSRN Electronic Journal.
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Eymen Errais & Fabio Mercurio. (2005) Yes, Libor Models can Capture Interest Rate Derivatives Skew: A Simple Modelling Approach. SSRN Electronic Journal.
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Marc Decamps, Marc Goovaerts & Wim Schoutens. (2005) Self Exciting Threshold Interest Rates Models. SSRN Electronic Journal.
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Leif B. G. Andersen & Vladimir Piterbarg. (2005) Moment Explosions in Stochastic Volatility Models. SSRN Electronic Journal.
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Stefano Galluccio, O. Scaillet, Zhijiang Huang & Jean-Michel Ly. (2005) Theory and Calibration of Swap Market Models. SSRN Electronic Journal.
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Jaehyuk Choi, Minsuk Kwak, Chyng Wen Tee & Yumeng Wang. (2021) A Black-Scholes User's Guide to the Bachelier Model. SSRN Electronic Journal.
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Zhanyu Chen, Kai Zhang & Hongbiao Zhao. (2020) Loan Prime Rate Options. SSRN Electronic Journal.
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Poh Ling Neo & Chyng Wen Tee. (2019) Swaption Portfolio Risk Management: Optimal Model Selection in Different Interest Rate Regimes. SSRN Electronic Journal.
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Jaehyuk Choi, Chenru Liu & Jay Woo. (2018) An Efficient Approach for Removing Look-Ahead Bias in the Least Square Monte Carlo Algorithm: Leave-One-Out. SSRN Electronic Journal.
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Robert Verschuren. (2018) Stochastic Interest Rate Modeling: An Empirical Performance Analysis of the L vy Forward Price Model. SSRN Electronic Journal.
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Wolfram Boenkost & Wolfgang M. Schmidt. (2014) A Functional Libor Market Model: Implementation and Application to Exposure Measurement. SSRN Electronic Journal.
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Giorgio Mori. (2013) Study and Calibration of a LIBOR Forward Swap Model with Stochastic Volatility. SSRN Electronic Journal.
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Alessandro Gnoatto, Martino Grasselli & José Da Fonseca. (2012) A Flexible Matrix Libor Model with Smiles. SSRN Electronic Journal.
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Karl Larsson. (2010) Dynamic Extensions and Probabilistic Expansions of the SABR Model. SSRN Electronic Journal.
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Sanjay K. Nawalkha. (2009) The LIBOR/SABR Market Models: A Critical Review. SSRN Electronic Journal.
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Marc Decamps & Ann De Schepper. (2009) Edgeworth Expansions of Stochastic Trading Time. SSRN Electronic Journal.
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Sanjay K. Nawalkha. (2009) The LIBOR Market Model: A Critical Review. SSRN Electronic Journal.
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Marc P. A. Henrard. (2007) Swaptions in Libor Market Model with Local Volatility. SSRN Electronic Journal.
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