Financial derivatives pricing using differential equations
Members of the research team from the DAMS
prof. RNDr. Daniel Ševčovič, DrSc.
doc. RNDr. Beáta Stehlíková, PhD.
Mgr. Alex Babiš
In the research we focus on the qualitative and numerical analysis of partial differential equations describing the derivative price changes of the underlying assets, such as interest rate derivatives or equities. We pay special attention to asymptotic and perturbation analysis of solutions depending on parameters and model calibrations for real market data. We also examine the problems leading to the solution of complementarity problems and variational inequalities appearing by valuation of American types of derivatives with early exercise.
Chernogorova, T., Stehlíková, B.: A Comparison of Asymptotic Analytical Formulae with Finite-Difference Approximations for Pricing Zero Coupon Bond. Numerical Algorithms 59 (4), 2012, pp. 571-588.
Stehlíková, B., Zíková, Z.: Convergence model of interest rates of CKLS type, Kybernetika, Vol. 48, No. 3, (2012), s. 567-586.
Stehlíková, B., Capriotti, L.: An effective approximation for zero-coupon bonds and Arrow-Debreu prices in the Black-Karasinski model, International Journal of Theoretical and Applied Finance, Vol. 17, No. 6 (2014), Art. No. 1450037, s. 1-16.
D. Ševčovič, B. Stehlíková, K. Mikula: Analytical and numerical methods for pricing financial derivatives. Nova Science Publishers, Inc., Hauppauge, 2011. ISBN: 978-1-61728-780-0 (Hardcover), ISBN: 978-1-61761-350-0 (ebook).
B. Stehlíková and D. Ševčovič: Approximate formulae for pricing zero-coupon bonds and their asymptotic analysis, International Journal of Numerical Analysis and Modeling, 6(2) 2009, 274-283.
M. Grossinho, Y. Kord Faghan, D. Ševčovič: Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility Function, Asia-Pacific Financial Markets, 24(4) 2017, 291-308.
D. Ševčovič, M. Žitňanská: Analysis of the nonlinear option pricing model under variable transaction costs, Asia-Pacific Financial Markets, 23(2) 2016, 153-174.
K. Ďuriš, Shih-Hau Tan, Choi-Hong Lai, D. Ševčovič: Comparison of the analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations, Computational Methods in Applied Mathematics 16(1) 2016, 35-50.
T. Bokes, D. Ševčovič: Early exercise boundary for American type of floating strike Asian option and its numerical approximation, Applied Mathematical Finance, 18(5) 2011, 367-394.
M. Lauko, D. Ševčovič: Comparison of numerical and analytical approximations of the early exercise boundary of American put options, ANZIAM journal 51, 2010, 430-448.