174%202011%20Summer%20Quiz_2

174%202011%20Summer%20Quiz_2 - 174 Quiz 2 Solution Gabe...

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Unformatted text preview: 174 Quiz 2 Solution Gabe Merton August 19, 2011 The first thing to realize is the underlying asset is a futures contract and not a stock. The first step is to create a binomial tree for this asset. Recall that we model the value of a futures contract via the formula F = S e ( r- ) t where t is the time to expiration of the contract. Furthermore, for futures contracts we set u = e h and d = e- h . This is equivalent to modeling a stock where r = . With these parameters, we also have p * = 1- d u- d . Thus, F = 50 e (0 . 08- . 04) 52 . 0405 u = e . 3 . 25 1 . 1618 d = e- . 3 . 25 . 8607 p * = 1- . 8607 1 . 1618- . 8607 . 46257 From here on Ill just use = when I should use . One constructs the tree for the futures contract by multiplying F by combinations of u and d as usual. The tree is below. 1 52.0405 44.7917 60.4625 38.5526 52.0405 70.2474 33.18 44.7917 60.4625 81 . 6158 For example, the calculation of the up, up, down node is: (52 . 0405)...
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174%202011%20Summer%20Quiz_2 - 174 Quiz 2 Solution Gabe...

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