When pricing an autocall, there are 3 parts:
- Strip of coupon,
- Zero coupon bond,
- Put down and in.
Probabilities of a call is given from the trigger level on call dates. However, let's say my autocall is 1Y max and is callable on months 6 and 12, should I price 2 put D&I and multiply the price by the autocall probabilities ? Or should I just compute the 1Y Put D&I ?
The reason is: When pricing a down and in put with Heston model I'm in line with what's expected. However, when moving to autocall products, my coupons are below what are priced by bank's pricers
About my computation: Given Monte Carlo paths and trigger level, I compute probabilities of touching the trigger. This gives me a set of probabilities for each call dates. I compute then discount factors * ZC bond value and this gives me my expected ZC bond value given my probabilities. In the end, I sum up the price of the put and (1 - ZC Present value). Finally I divide the result by the ZC bond expected value. Is it correct ?
Edit: what i am looking for if given the put price, my probabilities, my discount factors, i want to get the guaranteed coupons. So this is not exactly the same as getting the payoff and computing the value of the product.. I'm solving the equation Present Value of contingent coupon (probabilized) + PV of probabilized zero coupon - Put = 0. Some help would be appreciated, thanks