# Multiple layer Monte Carlo Option pricing

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 $$S_{ti}, i = 1, \dots 10000$$ ?

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