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Cox–Ingersoll–Ross two factors model; rapidly oscillating volatility; singular limit of solution; asymptotic expansion
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll–Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution to the two factors generalized CIR model and we show that the first two terms in the expansion are independent of the variable representing stochastic volatility.
[1] D. Brigo and F. Mercurio: Interest Rate Models – Theory and Practice. With smile, inflation and credit. Springer–Verlag, Berlin 2006. MR 2255741
[2] J. C. Cox, J. E. Ingersoll, and S. A. Ross: A theory of the term structure of interest rates. Econometrica 53 (1985), 385–408. MR 0785475
[3] K. C. Chan, G. A. Karolyi, F. A. Longstaff, and A. B. Sanders: An empirical comparison of alternative models of the short-term interest rate. J. Finance 47 (1992), 1209–1227.
[4] J.-P. Fouque, G. Papanicolaou, and K. R. Sircar: Derivatives in Markets with Stochastic Volatility. Cambridge University Press, Cambridge 2000. MR 1768877
[5] K. S. Moon, A. Szepessy, R. Tempone, G. Zouraris, and J. Goodman: Stochastic Differential Equations: Models and Numerics. Royal Institute of Technology, Stockholm.$^{\sim }$szepessy/sdepde.pdf
[6] J. Hull and A. White: Pricing interest rate derivative securities. Rev. Financial Studies 3 (1990), 573–592.
[7] Y. K. Kwok: Mathematical Models of Financial Derivatives. Springer–Verlag, Berlin 1998. MR 1645143 | Zbl 1146.91002
[8] B. Stehlíková: Modeling volatility clusters with application to two-factor interest rate models. J. Electr. Engrg. 56 (2005), 12/s, 90–93.
[9] O. A. Vašíček: An equilibrium characterization of the term structure. J. Financial Economics 5 (1977), 177–188.
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