Right now I am not very sure, how to implement Merton's Jump Diffusion Model. This is my first try, working out, but after reading that, even "in the special case of complete ruin the option on a stock that has a positive propability is more valuable than an option on a stock that does not" (Merton p.321) I have the suspicion my price can't be right, because it is lower tha a Blackn Scholes Price.
Also: I want to "n" to act randomly and to be independent from the past... and the SUM Formula to get to work for evolving a Price and finally my implied volatility. If anybody has a hint for me how to go further and implement it the right way, it would help me a lot for my homework /paper I need to do for university.
In the attachements you can find my intent of programming the merton model.
Thanks for your interest.
Best regards, Pantelis
Thanks for your support to both of you.
Right now I am already working on your hints!
Have a nice day guys!
Jump-diffusions are best implemented numerically. Why? Because the solution through the PDE is more involved and in the end results in the semi-analytical solution anyway.
Below is my document where I touched upon the jump-diffusion processes in Mathematica.
Hope this helps.
Jump-diffusions with Mathematica
you might want to have a look at this presentation:
You can jump (no pun intended) to 6:20 in the video.