I was talking about pricing an exponential in general, not an answer to the original question. If you build a tree you have to build steps over time and over level. If you just approximate the payoff with european calls you can price those with closed form so you only need to calculate over level. It’s not really an important point.

Allright, thx.

worow is correct - piecewise linear.use a call-strip (infinite) to over/under estimate the payout.forget all this tree stuff, does no-one trade equity? you have to price the skew!!initial=100final=100over estimator:payout=call(k=100)+2call(k=101)+2call(k=102)+2call(k=103).......payout>(x)^2underestimator:payout=2call(k=101)+2call(k=102)+2call(k=103)........payout< (x)^2any shape european payout function can be reduced to a distribution of options

I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.

ppauper,i think the math up is screwed up a little for his homework question ...The price for the crazy option is 1156,100695 by discounting the discreteexpectVal(payOff) = sum( payOff(i)*probability(i), i=1..4) = 1806,25.With delta = 25 resp 100 for the last year for stock at 10 resp 40 i agree.The prices are 170,0074039 resp 2720,118462 in 1 y and 136,0118465 resp2176,189544 for today. Now today i buy d stocks and sell the option and in1 y i will switch everything to the above known options (selling the stockand buying the option back in a very liquid market for a fair price hehehe)and its known hedge - ok? For this one needs d to be s.th. the cash flows are equal, ie - d*20 + 1156,100695 + d*40 - 2720,118462=- d*20 + 1156,100695 + d*10 - 170,0074039So my current delta is ~ 85 for the crazy stock & and that crazy option.Pls let me know whether i screwed math up even more or misunderstood you.

I think you are over pricing this option, see my post below