I'm currently studying the pricing of autocallable options, especially snowball (accumalated coupon) and phoenix (accumlated coupon, but the coupon may also be autocalled if the underlying price touches the lower barrier) type with down-and-in put option embedded (The underlying asset could be single asset or a basket of assets), but I cannot find any materials talking about this topic.
I'm confused about the following questions:
What are we pricing in this product in reality? The option premium given the coupon rate or the coupon rate that set the option premium to be zero?
How to price the option? If Monte Carlo simulation is the only way for pricing, or we can find PDE and solve it numerically, or there are some other better ways?
How is the coupon much higher than the other fixed-income products? And how to implement the hedging strategy for this kind of products?