2 votes

Does discretizing a diffusion model make it look like a jump diffusion model?

This not possible. The compensated Poisson process $N_t-\lambda t$ converges in the limit of large intensity $\lambda$ to a Brownian motion with variance rate $\lambda\,.$ Therefore, the pure jump ...
Kurt G.'s user avatar
  • 2,013
1 vote

Kou model — solving PIDE for European and American options in Python

The issue I described in my initial question is linked to the integral term. In the paper, this term is multiply by $ \theta \Delta \text{t} $ but this is only the "implicit" part of the ...
pierrot's user avatar
  • 86
1 vote
Accepted

Pure jump process in Duffie, Pan and Singleton's paper

Essentially yes - $Z_t$ is a compound Poisson process, except that the underlying counting process $N_t$ has intensity $\lambda(X_t)$. I.e $$ N_t - N_s \sim Pois\bigg( \int_s^t \lambda(X_u) \mathrm{d}...
Achrbot's user avatar
  • 178
1 vote

Does discretizing a diffusion model make it look like a jump diffusion model?

The principle is to assume some mathematical models (for example: the sample is generated from a log-normal process, or log-normal process with jumps, or CIR process, ...) and then estimate the ...
NN2's user avatar
  • 1,008

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