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Chapter 19b

# Chapter 19b - UN-11I A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15...

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UN-11I FIVE DATE AMERICAN BINOMIAL CALL OPTION PRICING Up-down--including dividends State prices Note: The period T = 1 is divided into 4 Up 1.4191 0.3324 <-- =((1-E14)*B9-B5)/(B4-B5) subperiods. "Up" for each period is defined Down 0.7788 0.6528 <-- =(B4-(1-E14)*B9)/(B4-B5) Initial stock price 50 Mean 20% mean = 20% and sigma = 60%. The annual Exercise price 30 Sigma 60% interest rate of 6% is discretized as 1.0151 r 6% exp[6%/4] -1 for each subperiod. T 1 The dividend rate of 8% is paid out Dividend rate quarterly. Annual 8% 2.00% <-- =E13/4 Stock price including dividends (same as if div. yld. = 0%) 202.7600 142.8826 100.6876 111.2770 70.9534 78.4156 50.0000 55.2585 61.0701 38.9400 43.0354 30.3265 33.5160 23.6183 18.3940 Stock price after dividend payout 198.7048 140.0249 98.6739 109.0515 69.5343 76.8473 49.0000 54.1534 59.8487 38.1612 42.1747 29.7200 32.8457 23.1460 18.0261 t=0 t=0.25 t=0.5 t=0.75 t=1 Dividends: Difference between two preceding trees 4.0552 2.8577 2.0138 2.2255 1.4191 1.5683 1.0000 1.1052 1.2214 0.7788 0.8607 0.6065 0.6703 0.4724 0.3679 168.7048 American call price 110.0249 68.6739 79.0515 39.5343 46.8473 20.3665 24.1534 29.8487 11.0717 12.1747 4.6636 2.8457 0.9458 0.0000 European call price on after-dividend stock 168.7048 107.6710 65.6530 79.0515 36.7652 45.7570 19.1171 22.8955 29.8487 10.5675 11.7778 4.5318 2.8457 0.9458 0.0000 Early exercise points Early Early Early Early No Early No Early No No Value of call option if kept alive (not used anywhere) 168.7048 107.6710 65.6530 79.0515 36.7652 45.7570 19.1171 22.8955 29.8487 10.5675 11.7778 4.5318 2.8457 0.9458 0.0000

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