作者： José Manuel Teixeira Santos Cruz
DOI:
关键词: Differential equation 、 Function (mathematics) 、 Variance gamma process 、 Mathematical economics 、 Put option 、 Applied mathematics 、 Lévy process 、 Mathematics 、 Jump process 、 Exponential function 、 Valuation of options
摘要: This dissertation discusses under which conditions we can express the function that represents option price as solution of a certain partial integro-differential equation (PIDE) in exponential Levy model. The main difference between this case and Black-Scholes is there non-local term equation, makes analysis more complicated. Also, discuss obtain Feynman-Kac formula for pure jump process prices are classical solutions PIDEs. When such not verified, consider concept viscosity only requires representing continuous. Continuity results barrier options presented some types processes. In addition, show same continuity processes finite variation with no diffusion component. present examples discontinuous. Moreover, numerical scheme gives an European put Variance Gamma process. was initially proposed by Cont Voltchkova, to solve numerically associated PIDE.