How to price the American style Asian option with recent N day average
, for example, we exercise at t
day, then the payment is
$$\Psi(t) = \dfrac{1}{N}\sum\limits^t_{i=t - N+1}S_i$$
Since the early exercise
and path dependence
, we can not use the Monte Carlo simulation
and tree method
. And since the average is not from the begin day to today, we are not allowed to use the addition variable:
$$I_j = \sum\limits^j_{i=j - N+1}S_i$$
namely, we can't use the PDE
method. This is because, we don't know $I_{j+1}$ just from $I_j$ and $S_{j+1}.$
I only know above three methods to price the option. Is there any reference or advanced method to price such option?
Asian option
usingPDE approach
, the differential $d\ I_t$ can be represented by $I_t$ and $S_t.$ But in this case, we can't, it is the reason for the failure of PDE approach I think. $\endgroup$ – A.Oreo Apr 5 '17 at 8:07