GENERALIZED EXPONENTIAL BASIS FOR EFFICIENT SOLVING OF HOMOGENEOUS DIFFUSION FREE BOUNDARY PROBLEMS: RUSSIAN OPTION PRICING

• DOI: 10.1007/s10958-022-05890-0
• Publication Date: 2022-08-23T05:02:35Z
• Authors: Igor V. Kravchenko; Vladislav V. Krav...; Sergii M. Torba; José Carlos Dias
• Keywords: Mathematics - Analysis of PDEs; FOS: Mathematics; Mathematics - Numerical Analysis; Numerical Analysis (math.NA); 0101 mathematics; 01 natural sciences; 34A25, 34L40, 35A22, 35A35, 35C09, 35K05, 35K10, 35R35, 35Q91, 60H15, 65M70, 65M80, 65N35, 91B25, 91G60; Analysis of PDEs (math.AP)

28 pages, 6 figures, 1 table. Added subsection 4.4 with new Proposition 19 and part of subsection 7.3. Some updates to Section 5 and to Problem 24. Some typos corrected<br/>This paper develops a method for solving free boundary problems for time-homogeneous diffusions. We combine the complete exponential system of solutions for the heat equation, transmutation operators and recently discovered Neumann series of Bessel functions representation for solutions of Sturm-Liouville equations to construct a complete system of solutions for the considered partial differential equations. The conceptual algorithm for the application of the method is presented. The valuation of Russian options with finite horizon is used as a numerical illustration. The solution under different horizons is computed and compared to the results that appear in the literature.<br/>