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I have simulated 10000 price paths from the SVCJ model under $\mathbb{Q}$ from $S_{t0}$ until $S_{tm}$ and have computed one discounted option price $C_t$.

  1. I want to compute the numerical simulated value of my call at $C_{t1}, \dots, C_{t(m-1)}$. How should I proceed ?

  2. I want to compute the value of a call that starts $S_{t1}$ until $S_{tm}$. I assume that I have to simulate an additional path.

Should I take the average of $S_{ti}, i = 1, \dots 10000$ ?

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    $\begingroup$ you should google pricing american options using monte carlo. there are pretty well-established methods for this. $\endgroup$ – Chris Apr 30 at 21:48

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