I am not quite familiar with Mathematica. I am attempting to use below codes to simulate a Jump Diffusion process where the deterministic component is: miu-[Lambda]*k. For some reason I am getting several errors listed below.
Besides this, I would like to change the Jump Diffusion to be evaluated given a Binomial Distribution and jump size of -0.3, constant volatility of the jump.
The whole problem can be defined as:
dSt = (\[Micro] - \[Lambda]k) Stdt + \[Sigma]StdZt + Stdqt, where dq is jump following binomial distribution and jump size is -0.3
I am including the codes and errors hereby:
JumpD = TransformedProcess[(miu - \[Lambda]*k) t + \[Sigma] w[t] - j[t], {w \[Distributed] WienerProcess[r, \[Sigma]], j \[Distributed] CompoundPoissonProcess[\[Lambda], NormalDistribution[k, \[Delta]]]}, t]; data = RandomFunction[ JumpD /. {\[Sigma] -> 0.2, \[Lambda] -> 0.5, \[Delta] -> 0, r -> 0, k -> 0.3, miu -> 0.3}, {0, 1, 0.003}, 20] ListLinePlot[data]
Errors hereby: RandomFunction::pintprm: Parameter 20.`16. at position 3 in RandomFunction[TransformedProcess[0.15 \[FormalT]+0.2 \[FormalP]1[\[FormalT]]-1.000000000000000 \[FormalP]2[\[FormalT]],{\[FormalP]1\[Distributed]WienerProcess[0,0.2],\[FormalP]2\[Distributed]CompoundPoissonProcess[0.5,NormalDistribution[0.3,0]]},\[FormalT]],{0,1.000000000000000,0.003},20.00000000000000] is expected to be a positive integer. RandomFunction::pintprm: Parameter 20.` at position 3 in RandomFunction[TransformedProcess[0.15 \[FormalT]+0.2 \[FormalP]1[\[FormalT]]-1. \[FormalP]2[\[FormalT]],{\[FormalP]1\[Distributed]WienerProcess[0.,0.2],\[FormalP]2\[Distributed]CompoundPoissonProcess[0.5,NormalDistribution[0.3,0.]]},\[FormalT]],{0.,1.,0.003},20.] is expected to be a positive integer. ListLinePlot::lpn: RandomFunction[TransformedProcess[0.15 \[FormalT]+0.2 \[FormalP]1[\[FormalT]]-1. \[FormalP]2[\[FormalT]],{\[FormalP]1\[Distributed]WienerProcess[0.,0.2],\[FormalP]2\[Distributed]CompoundPoissonProcess[0.5,NormalDistribution[0.3,0.]]},\[FormalT]],{0.,1.,0.003},20.] is not a list of numbers or pairs of numbers.
****Output of ListLinePlot hereby as well:
ListLinePlot[ RandomFunction[ TransformedProcess[ 0.15 \[FormalT] + 0.2 \[FormalP]1[\[FormalT]] - \[FormalP]2[\[FormalT]], \ {\[FormalP]1 \[Distributed] WienerProcess[0, 0.2], \[FormalP]2 \[Distributed] CompoundPoissonProcess[0.5, NormalDistribution[0.3, 0]]}, \[FormalT]], {0, 1, 0.003}, 20]]