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174%202011%20Summer%20Quiz%201

# 174%202011%20Summer%20Quiz%201 - p p = e r-δ h-d u-d = e(0...

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Quiz 1 Solutions Gabe Merton August 10, 2011 1 Part A I’ll use the notation S u , S ud etc. to indicate the stock price and C ud , C dd etc. to indicate the option payout. Start by calculating u and d using the ﬁrst period of the tree: u = 126 . 4443 / 100 = 1 . 264443 d = 82 . 7263 / 100 = 0 . 82763 Now we can calculate the values of the question marks. S uu = (126 . 4443)(1 . 264443) = 159 . 8816 S ud = S du = (126 . 4443)(0 . 827263) = 104 . 6027 The option payouts are, C uu = 159 . 8816 - 102 = 57 . 8816 C ud = 104 . 6027 - 102 = 2 . 6027 C dd = 0 The last ingredient we need is

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Unformatted text preview: p * . p * = e ( r-δ ) h-d u-d = e (0 . 07-. 025)(0 . 5)-. 82763 1 . 264443-. 827263 = 0 . 44716 1 The call premium is then, C = e-2 rh ( p * 2 C uu + 2 p * (1-p * ) C ud + (1-p * 2 ) C dd ) ) = e-. 07 ( (0 . 44716) 2 (57 . 8816) + 2(0 . 44716)(0 . 55284)(2 . 6027) ) = 11 . 9929 2 Part B p = c + Ke-rT-S e-δT = 11 . 9929 + 102 e-. 07-100 e-. 025 = 9 . 5661 2...
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174%202011%20Summer%20Quiz%201 - p p = e r-δ h-d u-d = e(0...

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