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Currently applying the Merton's jump diffusion to test how Option price change as parameters change. However, I am struggling to specify the poisson rate $\lambda$. We know that:

$P(\text{There is a jump})= \lambda dt $ and $P(\text{There is not a jump})= 1-\lambda dt $

I am using the code provided by the following link:

https://www.mathworks.com/matlabcentral/fileexchange/41939-merton-jump-diffusion-option-price-matrixwise

I am confused with the term poisson rate. Do we refer in the jump rate as as percent of the total steps $T/N$, which is the cardinality of the partition (e.g $5\%$= "5 jumps per 100 steps", which is $\lambda dt$) or the arrival rate in the whole interval (e.g 120 jumps in total, which is $\lambda$)?

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$\lambda$ is the intensity of the number of jumps per unit of time.

If you call $N_t$ the number of jumps up to time $t$ then $E[dN_t]=\lambda dt$ is the expected number of jumps in the interval $(t,t+dt)$

For more details you can check the wiki page

https://en.m.wikipedia.org/wiki/Poisson_point_process

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  • $\begingroup$ So if if $la$ is the percentage jump rate, then as input in the code above should I set $l=la/dt$? $\endgroup$ – alexbougias Dec 31 '18 at 14:17
  • $\begingroup$ I have no idea what the function you are calling actually does so i cannnot comment on that specifically. $\endgroup$ – Ezy Dec 31 '18 at 14:57
  • $\begingroup$ Would be pleased if you ( or someone else) specify which of the 2 should be used. $\endgroup$ – alexbougias Jan 1 at 12:24
  • $\begingroup$ @Coxswaiiiin i would suggest you test both on a simple case of european vanilla and you will see based on jump size and intensity which value matches your expectation of total variance since total variance = diffusion variance + jump variance $\endgroup$ – Ezy Jan 1 at 12:43

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