Module cf_functions::affine_process [−][src]
Functions
From page 8 and 9 of my ops risk paper https://github.com/danielhstahl/OpsRiskPaper/releases/download/0.2.0/main.pdf The expectation is E[e^{lambda*(E[e^uiL]-1)\int v_s ds}] Using the duffie ODE formula, rho0=0, rho1=lambda*(1-E[e^uiL]), k0=a, k1=-akappahat (where kappahat=1+correlation/a and and correlation=deltaE[L]lambda), h0=0, h1=sigmasigma, l0=0, l1=lambda. In previous versions of this code base I had simplified so that rho1=0 by adjusting the cf of the jump to have (u-ideltabeta) instead of just u. I switched to the more generic “cf_jump” and “cf_jump_extended” to accommodate more complicated jump processes such as CGMY See equation 8 in my ops risk paper.
Returns log of moment generating function for Cox Ingersoll Ross process evaluated at complex argument.
Returns log of moment generating function for Cox Ingersoll Ross process evaluated at complex argument and with complex kappa.
Returns moment generating function for Cox Ingersoll Ross process evaluated at complex argument.
Returns moment generating function for Cox Ingersoll Ross process evaluated at complex argument and with complex kappa.
Returns log CF of time-changed diffusion where the time-change is governed by a Cox Ingersoll Ross process
http://web.stanford.edu/~duffie/dps.pdf page 10 https://poseidon01.ssrn.com/delivery.php?ID=737027111000006077113070089110095064016020050037028066000080065074127006086092092026061120060015055036110006010126103066122080108059078076004070004065091125021108014077028121011029092117112080127092065007111098070065099086069122086067104098093017117&EXT=pdf&INDEX=TRUE page 11. l1 is incorporated as part of the characteristic function
Solves Duffie’s MGF when analytical solution (eg CIR) is not available