Recently because of some personal reason, I tried to price Snowball Autocall using MC and PDE, assuming single underlying.
12 months Snowball, Monthly autocall observations, Daily Put Down & In.
if Autocall, then 100% principal + autocall coupon
if Knock in and No Autocall, then client lose because of short put
if No autocall and No Knock in, ...
The building blocks of this BRC are (assuming the most common specification, there is always variations but it's impossible to tell the details without any termsheet provided):
long a zero-coupon bond
short a down-and-in rainbow put on the min (worst-of), with barrier below strike usually, and either European or American exercise style
The discount of the ...