Modelling of processes on financial markets and prediction of firm default by real options

Principal Investigator:	doc. RNDr. Ing. Ladislav LUKÁŠ, CSc.
Project Number:	GA15-20405S
Grant awarded by:	GA ČR
Term:	2015-2016

CO-INVESTIGATORS:

• Ing. Mgr. Milan SVOBODA, Ph.D.
• Ing. Kateřina MIČUDOVÁ, Ph.D.
• Dr. Ing. Jiří HOFMAN

PROJECT ANNOTATION:

Project is focused on analysis of fin. market processes, and prediction of firm default by real options approach. Pricing of fin. derivatives, Am. options in particular, forms our main issue, since it leads to nonlinear BVP defined within a framework of variational inequalities theory. We implement FEM for num. solving of such problems. The FE with polynomial basis may have curved boundaries and surfaces suitable for solving pricing problems of compound options with time-dependent free boundaries of optimal exercising. This procedure is used for analysis and pricing of real options, which are to characterize firm market value. Estimation and prediction of firm default in framework of real options is approached using barrier stoch. process representing a firm market trajectory. Time of firm default is defined by barrier hitting-time. We concern also development of tech. analysis of stocks based upon Markov chains, and connections of firm default estim. methods proposed with classical ones. Project issues will be publications in impact journals and presentations on int. conferences. Project goals: New method of pricing compound options with free exercise date implementing FEM with curved elements. Prediction of firm default by real options theory and its comparison with classic ones. New methods of tech. analysis of stocks based on MC. Four papers to publish in impact journals.