American put

# American put - American put 1 Stock 40 72 48 32 r= 1.05...

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American put 1 Page 1 Stock price r = 1.05 50 60 72 40 48 32 Risk-neutral p 0.6250 0.6250 0.6250 Return from wait action Return from exercising the option 5.1361 1.4286 0 2 0 0 9.5238 4 12 4 20 20 Put value = 5.1361

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American put 2 Page 2 S_0 = 9 r = 0.06 K = 10 Sigma = 0.3 T = 3 M = dt = 0.150 u = 1.1257 d = 0.8923 e^(-r*dt) = 0.9910 Homogeneous tree of risk-neutral stock prices 29.42 26.13 23.32 23.21 20.71 18.48 20.62 18.4 16.42 14.65 18.318 16.35 14.58 13.01 11.61 16.272 14.519 12.96 11.56 10.32 9.2 14.454 12.898 11.509 10.27 9.16 8.18 7.3 12.8397 11.457 10.223 9.122 8.14 7.26 6.48 5.78 11.4056 10.1773 9.081 8.103 7.231 6.45 5.76 5.14 4.58 10.1316 9.0406 8.0670 7.198 6.423 5.731 5.11 4.56 4.07 3.63 9 8.0308 7.1660 6.3943 5.706 5.091 4.543 4.05 3.62 3.23 2.88 Table of American put values denotes cells where put is exercised 0 0 0.01 0.02 0.03 0.05 0.05 0.08 0.13 0.22 0.112 0.18 0.28 0.43 0.65 0.222 0.336 0.5 0.73 1.05 1.47 0.391 0.567 0.808 1.13 1.55 2.08 2.72 0.6287 0.878 1.204 1.622 2.14 2.77
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American put - American put 1 Stock 40 72 48 32 r= 1.05...

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