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A stock index currently stands at 300 and has a volatility of 20%. The risk-free interest...

A stock index currently stands at 300 and has a volatility of 20%. The risk-free interest rate is 8% and the dividend yield on the index is 3%. Use a three-step binomial tree to evaluate a six-month put option on the index with a strike price of 300 if it is (a) European and (b) American?

Solutions

Expert Solution

Standard Options Period 1 2 3
European or American E Option Price 14.3917 300 325.5227 353.2167 383.2668
Call or Put P uptick factor 1.085076 276.4784 300 325.5227
Current Asset Price S(0) 300 downtick factor 0.921595 254.8011 276.4784
Strike Price X 300 Upside probability 0.530786 234.8233
Time to Maturity T 0.5 Downside probability 0.469214 Price
Volatility 0.2 14.3917 5.042274 0 0
Risk-Free Interest Rate r 0.08 25.37969 10.89046 0
Dividend Yield q 0.03 42.4963 23.52157
No of Steps n 3 65.17666
Standard Options Period 1 2 3
European or American A Option Price 14.97105 300 325.5227 353.2167 383.2668
Call or Put P uptick factor 1.085076 276.4784 300 325.5227
Current Asset Price S(0) 300 downtick factor 0.921595 254.8011 276.4784
Strike Price X 300 Upside probability 0.530786 234.8233
Time to Maturity T 0.5 Downside probability 0.469214 Price
Volatility zigma 0.2 14.97105 5.042274 0 0
Risk-Free Interest Rate r 0.08 26.631 10.89046 0
Dividend Yield q 0.03 45.19892 23.52157
No of Steps n 3 65.17666

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