Abstract
In the Black-Scholes model, it was assumed that the interest rate is a constant or a deterministic function. For short-dated options on stock-like assets, it is an acceptable approximation. However, for pricing interest rate derivatives or interest rate risk management, it is an unreasonable assumption. Therefore, one of the major topics in finance theory is the modeling of random interest rates and the pricing of interest rate derivatives.
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Ait-Sahalia, Y.: Testing continuous-time models of the spot interest rates. Rev. Financ. Stud. 9, 385–426 (1996)
Baxter, M.: General interest-rate models and the universality of HJM. In: Dempster, A.H., Pliska, S.R. (eds.) Mathematics of Derivative Securities. Publications of the Newton Institute, pp. 315–335. Cambridge University Press, Cambridge (1997)
Björk, T.: Interest rate theory. In: Runggaldier, W. (ed.) Financial Mathematics, pp. 53–122. Springer, Berlin (1997)
Björk, T.: Abitrage Theory in Continous Time. Oxford University Press, Oxford (1998)
Black, F., Karasinski, P.: Bond and option pricing when short rates are lognormal. Financ. Anal. J. 47, 52–59 (1991)
Black, F., Derman, E., Toy, W.: A one factor model of interest rates and its application to treasury bond options. Financ. Anal. J. 46, 33–39 (1990)
Brace, A., Gatarek, D., Musiela, M.: The market model of interest rate dynamics. Math. Financ. 7, 127–154 (1997)
Brown, R.G., Schaefer, S.M.: Interest rate volatility and the shape of the term structure. Philos. Trans. R. Soc. Lond. A 347, 563–576 (1994)
Chen, L.: Interest Rate Dynamics, Derivatives Pricing and Risk Management. Lecture Notes in Economics and Mathematical Systems, vol. 435, Springer, Berlin (1996)
Constantinides, G.M., Ingersoll, J.E.: Optimal bond trading with personal taxes. J. Financ. Econ. 13, 299–335 (1984)
Cox, J.C., Ingersoll, J.E., Ross, S.A.: A theory of term structure of interest rates. Econometrica 53, 385–407 (1985)
Dothan U.: On the term structure of interest rates. J. Financ. Econ. 6, 59–69 (1978)
Duffie, D.: Dynamic Asset Pricing Theory, 2nd edn. Princeton University Press, Princeton (1996)
Duffie, D., Kan, R.: A yield-factor model of interest rates. Math. Financ. 6, 379–406 (1996)
Filipović, D.: A general characterization of one factor affine term structure models. Finance Stoch. 5, 389–412 (2001)
Flesaker, B., Hughston, L.: Positive interest. Risk Mag. 9(1), 46–49 (1996)
Fong, H.G., Vasicek, O.A.: Fixed income volatility management. J. Portf. Manag. Summer 17, 41–46 (1991)
Heath, D., Jarrow, A., Morton, A.: Bond pricing and the term structure of interest rates. preprint (1987)
Heath, D., Jarrow, A., Morton, A.: Bond pricing and the term structure of the interest rates; a new methodology. Econometrica 60(1), 77–105 (1992)
Ho, T.S, Lee, S.B.: Term structure movements and pricing interest rate contingent claims. J. Financ. 41, 1011–1029 (1986)
Hull, J., White, A.: Pricing interest rate derivatives securities. Rev. Financ. Stud. 3, 573–592 (1990)
Hull, J., White, A.: Bond option pricing on a model for the evolution of bond prices. Adv. Futur. Opt. Res. 6, 1–13 (1993a)
Hull, J., White, A.: One-factor interest rate models and the valuation of interest rate derivative securities. J. Financ. Quant. Anal. 28, 235–254 (1993b)
Hull, J., White, A.: Numerical procedures for implementing term structure models II: two factor models. J. Deriv. 2, 37–47 (1994)
Hull, J., White, A.: Hull-White on Derivatives. Risk Publications, London (1996)
Jamshidian, F.: Libor and swap market model and measures. Financ. Stoch. 1, 293–330 (1997)
Longstaff, F., Schwartz, E.: Interest rate volatility and the term structure: a two-factor general equilibrium model. J. Financ. 47, 1259–1282 (1992a)
Maghsoodi, Y.: Solution to the extended CIR term structure and bond option valuation. Math. Financ 6, 89–109 (1996)
Marsh, T., Rosenfeld, E.R.: Stochastic processes for interest rates and equilibrium bond prices. J. Financ. 38, 635–646 (1983)
Merton, R.C.: An intertemporal capital asset pricing model. Econometrica 41, 867–887 (1973a)
Miltersen, K., Sandmann, K., Sondermann, D.: Closed form solutions for term structure derivatives with log-normal interest rates. J. Financ. 52, 409–430 (1997)
Pearson, N.D., Sun, T.-S.: Exploiting the conditional density in estimating the term structure: an application to the Cox, Ingersoll, and Ross model. J. Financ. 49, 1279–1304 (1994)
Protter, P.: Stochastic Integration and Differential Equations, 2nd edn. Springer, Berlin (2004)
Rogers, L.C.G.: Which model for the term-structure of interest rates should one use? In: Davis, M.H.A., et al. (eds.) Mathematical Finance, IMA vol. 65, pp. 93–116. Springer, New York (1995)
Rutkowski, M.: A note on the Flesaker-Hughston model of the term structure of interest rates. Appl. Math. Financ. 4, 151–163 (1997)
Schmidt, W.M.: On a general class of one-factor models for the term structure of interest rates. Finance Stoch. 1, 3–24 (1997)
Vasicek, O.A.: An equilibrium characterization of the term structure. J. Financ. Econ. 5, 177–188 (1997)
Yan, J.A.: Semimartingale theory and stochastic calculus. In: Kannan, D., Lakshmikantham, V. (eds.) Handbook of Stochastic Analysis and Applications. Marcel Dekker, Inc., New York, pp. 47–106 (2002b)
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Yan, JA. (2018). Term Structure Models for Interest Rates. In: Introduction to Stochastic Finance. Universitext. Springer, Singapore. https://doi.org/10.1007/978-981-13-1657-9_8
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