Hi

How should the expected value of the Spot prices be taken as a martingale?

I'm using the same risk neutral probabilities as for the payoffs and the Spots are converging to another value other than that used to build the final time layer.

eg. If I use a Spot of 100 to build the final time layer, and then take the expected present values of the Spots all the way back to time 0, I get an initial Spot of say, 71 (which is not equal to 100).

This also results in the American options having the same price as the European options.

Many thanks