On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility

Beáta Stehlíková; Daniel Ševčovič

Kybernetika (2009)

  • Volume: 45, Issue: 4, page 670-680
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Stehlíková, Beáta, and Ševčovič, Daniel. "On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility." Kybernetika 45.4 (2009): 670-680. <http://eudml.org/doc/37715>.

@article{Stehlíková2009,
abstract = {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.},
author = {Stehlíková, Beáta, Ševčovič, Daniel},
journal = {Kybernetika},
keywords = {Cox–Ingersoll–Ross two factors model; rapidly oscillating volatility; singular limit of solution; asymptotic expansion; Cox-Ingersoll-Ross two factor model; rapidly oscillating volatility; singular limit of solution; asymptotic expansion},
language = {eng},
number = {4},
pages = {670-680},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility},
url = {http://eudml.org/doc/37715},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Stehlíková, Beáta
AU - Ševčovič, Daniel
TI - On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 670
EP - 680
AB - 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.
LA - eng
KW - Cox–Ingersoll–Ross two factors model; rapidly oscillating volatility; singular limit of solution; asymptotic expansion; Cox-Ingersoll-Ross two factor model; rapidly oscillating volatility; singular limit of solution; asymptotic expansion
UR - http://eudml.org/doc/37715
ER -

References

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  1. Interest Rate Models – Theory and Practice, With smile, inflation and credit. Springer–Verlag, Berlin 2006. MR2255741
  2. A theory of the term structure of interest rates, Econometrica 53 (1985), 385–408. MR0785475
  3. An empirical comparison of alternative models of the short-term interest rate, J. Finance 47 (1992), 1209–1227. 
  4. Derivatives in Markets with Stochastic Volatility, Cambridge University Press, Cambridge 2000. MR1768877
  5. Stochastic Differential Equations: Models and Numerics, Royal Institute of Technology, Stockholm. www.math.kth.se/szepessy/sdepde.pdf 
  6. Pricing interest rate derivative securities, Rev. Financial Studies 3 (1990), 573–592. 
  7. Mathematical Models of Financial Derivatives, Springer–Verlag, Berlin 1998. Zbl1146.91002MR1645143
  8. Modeling volatility clusters with application to two-factor interest rate models, J. Electr. Engrg. 56 (2005), 12/s, 90–93. 
  9. An equilibrium characterization of the term structure, J. Financial Economics 5 (1977), 177–188. 

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