# Pricing Asian option at discrete times

I hope you can help me again regarding pricing an arithmetic Asian option.

Asumme we have a time grid $(0=t_0,t_1,t_2=T)$ and we buy an Asian option at time 0 and the maturity is at T. Now we would like to price the option at each time with a Monte-Carlo simulation. Now assume the risk-free rate and the strike $K=0$ and we just do one simulation (a simplification for this example) .

At $t=t_0$: Clear. First of all simulate the future price at $t_1$ and $t_2$. Then $Asian =max(0,(S(t_0)+S(t_1)+S(t_2))/3$).

At $t=t_1$: Here is now my problem. We still have the information at time $t_0$. I think just simulate a new price at $t_2$ and hence $Asian =max(0,(S(t_0)+S(t_1)+S_{new}(t_2))/3$). $S(t_0),S(t_1)$ are from $t_0$.

Is that correct? Thank you very much!!!!

• You can use $\LaTeX$ in your question to make the maths easier to read. – will Feb 26 '17 at 1:15
• Done, thank you :) – Mathestudent Feb 26 '17 at 9:44
• You are correct that when you have fixings in the past, you don't need to simulate them. How you achieve this is an implementation detail. Further more, with the example you've given, if the underlying can't go negative, there's no convexity and so you can just price based on the fwd curve and don't need mc. – will Feb 26 '17 at 10:12