Hello, Does anyone have any references or insights on how to price a structured product that has a payoff as follows:A) $0.2 quarterly +B) the compound monthly return on a stock where the return has a floor of -10% and a cap of 5%. The monthlyreturn is calculated as of the 20th of every month for the next 5 years.I know I can price it by Monte Carlo but I was wondering if there was anyway I could use the PDE approach.My intuition tells me that the ending payoff is path dependant so I can't use the PDE approach but if that is notthe case, how would I go about it?The reason I'm asking is because I would like to say something about how the structured product could be hedgedand I don't think that Monte Carlo will give me any insight to this end. It's for a school project.Many thanks,r

The quarterly coupon is just an annuity, so just take that out.Depends what you mean by "compound monthly return". I usually see these things simply summing the capped and floored returns, in which case it is merely a cliquet that you can price with the formula in Haug's book and a calibrated forward vol surface.The PDE approach actually handles path dependant exotics very well if the underlying process is markovian and 1-2 dimensional. In a nutshell, the approach is to define a state variable that contains the return up to that point in time, then defining your end and boundary conditions on that variable. Check out the book by Tavella & Randall.Monte Carlo can give you hedging parameters if your answers are accurate enough (try Sobol sequences or other variance-reducing methods), by simply nudging your inputs and rerunning. Of course, if you use the analytic formula for a cliquet, you know what to do...

Exotiq, Thanks for the reply. What I meant by compound return is as follows:For each month, you get a maximum return of 5% and a minimum return of -10% on the capitalappreciation of a stock. The window where that return is measured is reset every month so basically it's like taking for P&L every month on the following strategy:Long the stockWrite a Call with Strike price that's 5% higher than the price at the end of the last periodBuy a put with Strike price that's 10% lower than the price at the end of the last periodHold the position until the end of the next period and liquidaterepeat this process every month for about five years.I didn't think that I could use the PDE approach because the strike prices on the options I needare going to move over time. Does anyone have any references or insights for pricing this type of securityThanks,r