Citation: Jie Xiong, Geng Deng, Xindong Wang. Extension of SABR Libor Market Model to handle negative interest rates[J]. Quantitative Finance and Economics, 2020, 4(1): 148-171. doi: 10.3934/QFE.2020007
[1] | Anderson L, Andreason J (2000) Volatility skews and extensions of the libor market model. Appl Math Financ 7: 1-32. doi: 10.1080/135048600450275 |
[2] | Antonov A, Konikov M, Spector M (2015) The free boundary SABR: Natural extension to negative rates. Risk. |
[3] | Balland P, Tran Q (2013) SABR goes normal. Risk, 76-81. |
[4] | Brace A (1997) The market model of interest rate dynamics. Math Financ 7: 127-147. doi: 10.1111/1467-9965.00028 |
[5] | Brigo D, Mercurio F (2006) Interest Rate Models-Theory and Practice, Springer, New York. |
[6] | Chesney M, Yor M, Jeanblanc M (2009) Mathematical Methods for Financial Markets, Springer, United Kingdom. |
[7] | Ferreiro A, García-Rodríguez J, López-Salas J, et al. (2014) SABR/LIBOR market models: Pricing and calibration for some interest rate derivatives. Appl Math Comput 242: 65-89. doi: 10.1016/j.amc.2014.05.017 |
[8] | Hagan P, Kumar D, Lesniewski A, et al. (2002) Managing smile risk. Wilmott Mag, 84-108. |
[9] | Henry-Labordere P (2007) Unifying the BGM and SABR models: A short ride in hyperbolic geometry. SSRN. Available from: https://ssrn.com/abstract=877762 or http://dx.doi.org/10.2139/ssrn.877762. |
[10] | Honda Y, Inoue J (2019) The effectiveness of the negative interest rate policy in Japan: An early assessment. J Japanese Int Econ 52: 142-153. doi: 10.1016/j.jjie.2019.01.001 |
[11] | Joshi M, Rebonato R (2003) A stochastic-volatility displaced-diffusion extension of the LIBOR market model. Quant Financ 3: 458-469. doi: 10.1088/1469-7688/3/6/305 |
[12] | Kienitz J (2015) Approximate and PDE solution to the boundary free SABR model-application to pricing and calibration. Working Paper. |
[13] | LeFloch F, Kennedy G (2013) Finite difference techniques for arbitrage free SABR. Working Paper. |
[14] | López-Salas J, Vázquez C (2018) PDE formulation of some SABR/LIBOR market models and its numerical solution with a sparse grid combination technique. Comput Math Applications 75: 1616-1634. doi: 10.1016/j.camwa.2017.11.024 |
[15] | Morini M, Mercurio F (2007) No-arbitrage dynamics for a tractable SABR term structure LIBOR model. Bloomberg Portfolio Res Pap. |
[16] | Pedersen H, Swanson N (2019) A survey of dynamic Nelson-Siegel models, diffusion indexes, and big data methods for predicting interest rates. Quant Financ Econ 3: 22-45. doi: 10.3934/QFE.2019.1.22 |
[17] | Piterbarg V (2003) A stochastic volatility forward LIBOR model with a term structure of volatility smiles. Appl Math Financ 12: 147-185. doi: 10.1080/1350486042000297225 |
[18] | Rebonato R (2002) Modern pricing of interest-rate derivatives, Princeton University Press. |
[19] | Rebonato R (2007) A time-homogeneous, SABR-consistent extension of the LMM: calibration and numerical results. Risk. |
[20] | Rebonato R, McKay K, White R (2009) The SABR/LIBOR Market Mode: Pricing, Calibration and Hedging for Complex Interest-Rate Derivertives, Wiley, United Kingdom. |
[21] | Schoenmakers J, Coeffey B (2000) Stable implied calibration of a multi-factor LIBOR model via a semi-parametric correlation structure. WIAS Working Paper. |
[22] | Wu L, Zhang F (2006) LIBOR market model with stochastic volatility. J Ind Manage Optim 2: 199-227. |
[23] | Zhu J (2007) An extended LIBOR market model with nested stochastic volatility dynamics. Available at SSRN 955352. |