Bond Pricing and the Term Structure of Spot and Forward Interest Rates: A Multi-factor Vasicek and Cir Model Approach

[1] Y. Ait-Sahalia, Testing continuous-time models of the spot interest rate, Review of Financial Studies, 9(2)(1996), 385-426. http://www.jstor.org/stable/2962210
[2] S.H. Babbs, B. Nowman, Kalman Filtering of Generalized Vasicek Term Structure Models, Journal of Financial and Quantitative Analysis, 34(1999), 115-130. http://www.jstor.org/stable/2676248
[3] F. Black, P. Karasinski, Bond and Option Pricing When Short Rates Are Lognormal, Financial Analysts Journal, 48(4)(1991), 52-59. http://www.jstor.org/stable/4479456
[4] D.J. Bolder, Affine Term-Structure Models: Theory and Implementation, Bank of Canada, Working Paper 2001-15, Financial Markets Department, 2001. https://www.bankofcanada.ca/wp-content/uploads/2010/02/wp01-15a.pdf
[5] M. Brennan, E. Schwartz, An equilibrium model of bond pricing and a test of market efficiency, Journal of Financial and Quantitative Analysis, 17(1982), 301-329. http://www.jstor.org/stable/2330832
[6] M. Brennan, E. Schwartz, Analyzing Convertible Bonds, Journal of Financial and Quantitative Analysis, 15(1980), 907-929. http://www.jstor.org/stable/2330567
[7] M. Brennan, E. Schwartz, The pricing of equity-linked life insurance policies with an asset value guarantee, Journal of Financial Economics, 3(1976), 195-213. https://www.sciencedirect.com/science/article/pii/0304405X76900039
[8] J.Y. Campbell, A defence of tradditional hyphoteses about the term structure of interest rates., Journal of Finance, 441(1986), 183-193. http://www.jstor.org/stable/2328351
[9] E. Canabarro, Where do One-Factor Interest Rate Models Fail?, Journal of Fixed Income, 5(2)(1995), 31-52. doi: 10.3905/jfi.1995.408145
[10] G. Chaplin, K. Sharp, Analytic solutions for bonds and bond options under n correlated stochastic processes., Research Report 93-16, University of Waterloo, (1995).
[11] R.R. Chen, L. Scott, Interest Rate Options in Multifactor Cox-Ingersoll-Ross Models of the Term Structure, Journal of Fixed Income, 5(1)(1995), 14–31.
[12] R.R. Chen, Interest Rate Dynamics, Derivatives Pricing, and Risk Management, Springer, 1996. Zbl 0862.90015
[13] R.R. Chen, L. Scott, Multi-Factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model, The Journal of Real Estate Finance and Economics, 27(2)(2003), 143-172. https://link.springer.com/article/10.1023/A:1024736903090
[14] G. Courtadon, The Pricing of Options on Default-Free Bonds, Journal of Financial and Quantitative Analysis, 17(1)(1982), 75-100. http://www.jstor.org/stable/2330930
[15] J.C. Cox, J.E. Jr. Ingersoll, S.A. Ross, An Analysis of Variable Rate Loan Contracts, Journal of Finance, 35(2)(1980), 389-403. doi:10.1111/j.1540-6261.1980.tb02169.x
[16] J.C. Cox, J.E. Jr. Ingersoll, S.A. Ross, A Theory of the Term Structure of Interest Rates, Econometrica, 53(2)(1985), 385-407. http://www.jstor.org/stable/1911242
[17] Q. Dai and K. J. Singleton, Specification analysis of affine term structure models, Journal of Finance, 55(5)(2000), 1943–1978.
[18] L.U. Dothan, On the term structure of interest rates, Journal of Financial Economics, 6(1)(1978), 59-69. https://ideas.repec.org/a/eee/jfinec/v6y1978i1p59-69.html
[19] J.C. Duan, J.G. Simonato, Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter, Review of Quantitative Finance and Accounting, 13(1999), 111-135. doi:10.1023/A:1008304625054
[20] D. Duffie and R. Kan, A yield-factor model of interest rates, Mathematical Finance, 6(4)(1996), 379–406.
[21] Y. Esmaeelzade Aghdam, A. Neisy, A. Adl, Simulating and Pricing CAT Bonds Using the Spectral Method Based on Chebyshev Basis, Computational Economics, 63(2024), 423–435. doi: 10.1007/s10614-023-10423-7
[22] R.M. Galisteo, Dinamica de la estructura temporal de tipos de interes: modelo de tres factores, Universitat de Barcelona. Departament d’Econometria, Estad´ıstica i Economia Espanyola, 2000. https://www.tdx.cat/handle/10803/1463#page=1
[23] L. G´omez del Valle, J. Mart´ınez Rodr´ıguez, Pricing zero-coupon bonds with differenct market prices of risk, 2nd Italian-Spanish Conference of Financial Mathematics, Napoli, Italia, (1999).
[24] T.S.Y. Ho, S.B. Lee, Term Structure Movements and Pricing Interest Rate Contingent Claims, The Journal of Finance, 41(5)(1986), 1011-1029. doi: 10.1111/j.1540-6261.1986.tb02528.x
[25] J. Hull, A. White, Pricing Interest-Rate-Derivative Securities, The Review of Financial Studies, 3(4)(1990), 573-592. Zbl 1386.91152
[26] J. Hull, A. White, A, Numerical Procedures for Implementing Term Structure Models I: Single-Factor Models, The Journal of Derivatives, 2(1)(1994), 7-16. doi:10.3905/jod.1994.407902
[27] F.A. Longstaff, E.S. Schwartz, Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model, Journal of Finance, 47(4)(1992), 1259-1282. doi:10.1111/j.1540-6261.1992.tb04657.x
[28] J. Lund, Econometric analysis of continuous-time arbitrage-free models of the term structure of interest rates, Working paper, The Aarthus School of Business, 1995. https://www.econbiz.de/Record/working-paper/10011913908#tabnav
[29] F. Mercurio, J.M. Morelada, An Analytically Tractable Interest Rate Model with Humped Volatility, European Journal of Operational Research, 120 (1)(2000), 205-214. Zbl 1028.91589
[30] H. Mesgarani, A. Adl, Y. Esmaeelzade Aghdam, The Convergence Investigation of a Numerical Scheme for the Tempered Fractional Black–Scholes Model Arising European Double Barrier Option, Computational Methods for Differential Equations, 11(2)(2023), 385–398. doi: 10.22034/cmde.2022.53942.2219
[31] H. Mesgarani, A. Adl, Y. Esmaeelzade Aghdam, Approximate Price of the Option Under Discretization by Applying Fractional Quadratic Interpolation, Computational Methods for Differential Equations, 10(4)(2022), 1075–1085. doi: 10.22034/cmde.2021.45656.1918
[32] M. Moreno, Asset pricing under a two-factor model of the term structure of interest rates, Mathematica de las Operaciones Financieras, IV Congreso MOF, Barcelona, (1997), 609-658.
[33] S.F. Richard, An arbitrage model of the term structure of interest rates, Journal of Financial Economics, 6(1)(1978), 33-57. doi: 10.1016/0304-405X(78)90019-3
[34] S.M. Schaefer, E.S. Schwartz, A Two-Factor Model of the Term Structure: An Approximate Analytical Solution, Journal of Financial and Quantitative Analysis, 19(4)(1984), 413-424. doi:10.2307/2330783
[35] O. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics, 5(2)(1977), 177-188. Zbl 1372.91113
[36] A. White, A.D. Hull, One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities,Journal of Financial and Quantative Anaysis, 28 (2)(1993), 235-254. doi:10.2307/2331288
[37] S. Zeytun, A. Gupta, A Comparative Study of the Vasicek and the CIR Model of the Short Rate, Institut Techno- und Wirtschaftsmathematik, 2007. https://kluedo.ub.rptu.de/frontdoor/index/index/docId/1979