Tree Parameters for a

Tree Parameters for a - K = 50 r =10 σ = 40 T = 5 months =...

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Tree Parameters for a Nondividend Paying Stock We will assume that u = 1/ d . When t is small we can estimate the option value using: 1 t r t t e a d u d a p e d e u σ - σ = - - = = =

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Stock Prices on the Tree S 0 u 2 S 0 u 4 S 0 d 2 S 0 d 4 S 0 S 0 u S 0 d S 0 S 0 S 0 u 2 S 0 d 2 S 0 u 3 S 0 u S 0 d S 0 d 3 2
Backwards Induction We know the value of the option at the final nodes. We work back through the tree using risk-neutral valuation to calculate the value of the option at each node, testing for early exercise when appropriate. 3

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Example: Put Option S 0 = 50;
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Unformatted text preview: K = 50; r =10%; σ = 40%; T = 5 months = 0.4167; ∆ t = 1 month = 0.0833 The parameters imply u = 1.1224; d = 0.8909; a = 1.0084; p = 0.5073 4 Example (continued) 89.07 0.00 79.35 0.00 70.70 70.70 0.00 0.00 62.99 62.99 0.64 0.00 56.12 56.12 56.12 2.16 1.30 0.00 50.00 50.00 50.00 4.49 3.77 2.66 44.55 44.55 44.55 6.96 6.38 5.45 39.69 39.69 10.36 10.31 35.36 35.36 14.64 14.64 31.50 18.50 28.07 21.93 5...
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This note was uploaded on 01/19/2012 for the course FIN 4520 taught by Professor Lucyackert during the Spring '12 term at Kennesaw.

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Tree Parameters for a - K = 50 r =10 σ = 40 T = 5 months =...

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