Previous |  Up |  Next


convergence model of interest rate; approximate analytic solution; order of accuracy
This paper deals with convergence model of interest rates, which explains the evolution of interest rate in connection with the adoption of Euro currency. Its dynamics is described by two stochastic differential equations – the domestic and the European short rate. Bond prices are then solutions to partial differential equations. For the special case with constant volatilities closed form solutions for bond prices are known. Substituting its constant volatilities by instantaneous volatilities we obtain an approximation of the solution for a more general model. We compute the order of accuracy for this approximation, propose an algorithm for calibration of the model and we test it on the simulated and real market data.
[1] Brigo, D., Mercurio, F.: Interest Rate Models-Theory and Practice, With Smile, Inflation and Credit. Second edition. Springer Finance, 2006. MR 2255741
[2] Chan, K. C., Karolyi, G. A., Longstaff, F., Sanders, A.: The volatility of short-term interest rates: an empirical comparison of alternative models of the term structures of interest rates. J. Finance 47 (1992), 1209–1227. DOI 10.1111/j.1540-6261.1992.tb04011.x
[3] Choi, Y., Wirjanto, T. S.: An analytic approximation formula for pricing zero-coupon bonds. Finance Res. Lett. 4 (2007), 2, 116–126.
[4] Corzo, T., Schwartz, E. S.: Convergence within the European Union: Evidence from interest rates. Econom. Notes 29 (2000), 243–268. DOI 10.1111/1468-0300.00032
[5] Kwok, Y. K.: Mathematical Models of Financial Derivatives. Second edition. Springer, 2008. MR 2446710
[6] Lacko, V.: Two-Factor Convergence Model Of Cox-Ingersoll-Ross Type. Master's Thesis, 2010.
[7] Lacko, V., Stehlíková, B.: Two-factor convergence model of Cox-Ingersoll-Ross type. In: Proc. 17th Forecasting Financial Markets Conference, Hannover 2010.
[8] Melicherčík, I., Olšárová, L., Úradníček, V.: Kapitoly z finančnej matematiky. Epos, 2005.
[9] Privault, N.: An Elementary Introduction to Stochastic Interest Rate Modeling. Second edition. World Scientific, 2008. MR 2519413
[10] Stehlíková, B.: Approximate formula for the bond price based on the Vasicek model. Preprint.
[11] Stehlíková, B., Ševčovič, D.: Approximate formula for pricing zero-coupon bonds and their asymptotic analysis. Internat. J. Numer. Anal. Modeling 6 (2009), 2, 274–283. MR 2574908
[12] Ševčovič, D., Stehlíková, B., Mikula, K.: Analytické a numerické metódy oceňovania finančných derivátov. Nakladateľstvo STU, 2009.
[13] Ševčovič, D., Urbánová Csajková, A.: On a two-phase minmax method for parameter estimation of the Cox, Ingersoll, and Ross interest rate model. Central Europ. J. Oper. Res. 13 (2005), 169–188. MR 2148753
[14] Zíková, Z.: Konvergenčné modely úrokových mier. Master's Thesis, 2011.
Partner of
EuDML logo