Journal of Finance and Accounting
Volume 4, Issue 2, March 2016, Pages: 25-32
Received: Mar. 6, 2016;
Published: Mar. 6, 2016
Views 4857 Downloads 277
Fangfang Zhao, School of Information, Renmin University of China, Beijing, China
Zuoliang Xu, School of Information, Renmin University of China, Beijing, China
Changjing Li, School of Mathematical Sciences, Shandong Normal University, Jinan, China
This paper concerns a problem of calibrating implied volatility in generalized Hull-White model from the market prices of zero-coupon bonds. By using the regularization method, we establish the existence and stability of the optimal solution, and give the necessary condition that the solution satisfies. Finally numerical results show that the method is stable and effective.
Calibration of Implied Volatility in Generalized Hull-White Model, Journal of Finance and Accounting.
Vol. 4, No. 2,
2016, pp. 25-32.
O. Vasicek, An equilibriurm characterization of the term structure, Jounal of Financial Economics, 1977, 5(2): 177-188.
J. C. Cox, J. E. Ingersoll, S. A. Ross, A Theory of the Term Structure of Interest Rates, Econometrica, 1985, 53(2): 385-407.
J. Hull, A. White, Pricing Interest-Rate-Derivative Securitites, The Review of Financial Studies, 1990, 3(4): 573-392.
K. R. Chan, G. A. Karolyi, F. Longstaff, A. B. Sanders, An Empirical Comparison of Alternative Models of the Short-Term Interest Rate, Journal of Finance, 1992, 47(3): 1209-1228.
J. Hull, A. White, Numerical Procedures for Implementing Term Structure Models I: Single-Factor Models, Journal of Derivatives, 1994, 2(1): 7-16.
J. Hull, A. White, The general Hull-White model and super calibration, Finance Analysts Journal, 2001, 57(6): 34-43.
I. Bouchouev, V. Isakov, N. Valdivia, Recovery of volatility coefficient by linearization, Quantitive Finance, 2002, 2: 257-263.
I. Bouchouev, V. Isakov, Uniqueness, stability and numerical methods for the inverse problem that arises in fnancial markets, Inverse Problems, 1999, 15(3): 95-116.
H. Egger, T. Hein, B. Hofmann, On decoupling of volatility smile and term structure in inverse option pricing, Inverse Problem, 2006, 22(4): 1247-1259.
R. Kramer, M. Richter, Ill-posedness versus ill-conditioning -an example from inverse option pricing, Applicable Analysis, 2008, 87(4): 465-477.
J. Hull, A. White, A generalized procedure for building trees for the short rate and its application to determining market implied volatility functions, Quantitative Finance, 2015, 15(3): 443-454.
A. M. Ferreiro, J. A. García-Rodríguez, J. G. López-Salas, C. Vázquez, SABR/LIBOR market models: Pricing and calibration for some interest rate derivatives, Applied Mathematics and Computation, 2014, 242: 65-89.
Y. F. Wang, Computational Methods for Inverse Problems and Their Applications, Higher Education Press, Beijing, 2007. (In chinese)
H. Egger, H. W. Engl, Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates, Inverse Problems, 2005, 21(3): 1027-1045.
S. Doi, Y. Ota, An application of microlocal analysis to an inverse problem arising from financial markets, arXiv: 1404. 7018, 2014.
C. Y. Tang, S. X. Chen, Parameter estimation and bias Correction for diffusion processes, Journal of Econometrics, 2009, 149(1): 65-81.
M. Rainer, Calibration of stochastic models for interest rate derivatives, Optimization, 2009, 58(3): 373-388.
M. Rodrigo, R. Mamon, An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions, Quantitative Finance, 2014, 14(11): 1961-1970.
D. Duffie, R. A. Kan, Yield-factor model of interest rates, Mathematical Finance, 1996, 6(4): 379-406.