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Unformatted text preview: Introduction to derivatives, Fall 2011 BUSI 588, Case 5 solutions Solutions to Iniesta and risk-neutral pricing 1. (*) The quick way around this problem was to find the risk-neutral probabilities, given the information we have on the stock and the bond. Using the notation in my notes, we have that u = 1 . 5 (Barcelona FC can go up by 50%), and d = 0 . 6 (it can go do by 40%), and that r = 1 . 1. Using the formulae in the notes or the book, one immediately can get the risk-neutral proba- bilities for this problem. ˆ p u = 1 . 1- . 6 1 . 5- . 6 = 5 9 ; ˆ p d = 1 . 5- 1 . 1 1 . 5- . 6 = 4 9 . The only price consistent with no-arbitrage for the HalaMadrid security is P HM = (4 / 9)100 1 . 1 = 40 . 40 . 2. (**) The prices that Ronaldo is setting are too high. We would like to sell high and buy low. It is intuitive that the thing we need to sell is the HM securities Ronaldo is willing to trade at too high a price. In order to see what we need to buy, we shall look for a “synthetic HalaMadrid” security. In particular, let’s try to replicate the payoffs from the HalaMadridHalaMadrid” security....
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