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A stock index is currently 990, the risk free rate is 5%, and the dividend yield...

A stock index is currently 990, the risk free rate is 5%, and the dividend yield on the index is 2%. Use a three step to value and 18-month American put option with a strike price of 1000 when the volatility is 20% per annum.

What position in the stock is initially necessary to hedge the risk of the put option?

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Answer #1

The value of the option is 87.51. It is optimal to exercise at the lowest node at time one year. If early exercise were not possible the value at this node would be 236.63. The gain made at the one year point is therefore 253.90 – 236.63 =17.27

1513.18 0.00 1313.63 0.00 1140.39 31.07 1140.39 0.00 990.00 87.51 990.00 66.08 859.44 152.75 859.44 140.56 746.10 253.90 647.

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