I'm trying to build a convertible bond pricer. In my case a convertible bond is a complex derivative with call, put and conversion price reset clauses, and all of the clauses are triggered in a path-dependent fashion. For example, the call clause might be:
In 30 consecutive trading days, if the closing stock price is bigger than 130% of conversion price in 15 trading days, then the issuer has the option to redeem the bond.
At the present stage I'm still looking for the right model. Considering the path-dependencies, I see Monte Carlo as somewhat the only way to go. And considering the call/put/reset-ability which are American in nature, LSMC (Least Square Monte Carlo) seems to be the only choice.
However, being non-deterministic and quite fiddly, LSMC should be a last resort. If possible, I would prefer easier methods such as finite difference methods and tree methods, but none of them seems able to deal with the path-dependencies entailed in the call/put/reset clauses.
Is there any way to somehow accommodate such path-dependencies in tree models/finite difference models instead of LSMC? Thanks!