I need the characteristic function of the Heston model with jumps in price and variance, or in other words, the characteristic function of the Bates model (1996) adding jumps in the variance dynamics. An example of the Bates characteristic function is given in the book of Gilli, Maringer, Schumann:

φBates = e^(A+B+C+D),


A =iωs0+iω(r−q)τ ;

B =θκ/σ^2((κ − ρσiω − d)τ − 2 log((1 − ge^(−dτ))/(1 − g)) ;

C =v0/σ^2((κ − ρσiω − d)(1 − e^(−dτ))/(1 − ge^(−dτ)) ;

D =−λμJiωτ+λτ((1 + μJ)^(iω)e^((1/2)σj^2iω(iω−1))−1 ;

d =squareroot((ρσiω − κ)^2+σ^2(iω + ω2)) ;

g =(κ−ρσiω−d)/(κ−ρσiω+d)

I need something like this. A characteristic function in this terms.


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