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fm3_chapter23.3barrier - A 1 2 3 4 5 6 7 8 9 10 11 12 13 14...

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PRICING A KNOCKOUT BARR Initial stock price 30 Up 1.40 Down 0.80 Interest 1.08 Option exercise price 30 Barrier 50.00 0.4321 ### 0.4938 ### Risk-neutral probability, up 0.4667 ### Risk-neutral probability, down 0.5333 ### STO Paths Period 1 Period 2 Period 3 Period 4 Period 0 Period 1 All up (1 path) up up up up 30.00 42.00 One down (4 paths) down up up up 30.00 24.00 up down up up 30.00 42.00 up up down up 30.00 42.00 up up up down 30.00 42.00 Two down (6 paths) down down up up 30.00 24.00 down up down up 30.00 24.00 down up up down 30.00 24.00 up down down up 30.00 42.00 up up down down 30.00 42.00 up down up down 30.00 42.00 Three down (4 paths) up down down down 30.00 42.00 down up down down 30.00 24.00 down down up down 30.00 24.00 down down down up 30.00 24.00 Four down (1 path) down down down down 30.00 24.00 q U q D A B C D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
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30 A B C D E F G H 44 45 46 47
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RIER OPTION #MACRO? OCK PRICE Period 2 Period 3 Period 4 58.80 82.32 115.25 0.00 0.0474 0.00 33.60 47.04 65.86 0.00 0.0542 0.00 33.60 47.04 65.86 0.00 0.0542 0.00 58.80 47.04 65.86 0.00 0.0542 0.00 58.80 82.32 65.86 0.00 0.0542 0.00 19.20 26.88 37.63 1.00 0.0619 7.63 33.60 26.88 37.63 1.00 0.0619 7.63 33.60 47.04 37.63 1.00 0.0619 7.63 33.60 26.88 37.63 1.00 0.0619 7.63 58.80 47.04 37.63 0.00 0.0619 0.00 33.60 47.04 37.63 1.00 0.0619 7.63 33.60 26.88 21.50 1.00 0.0708 0.00 33.60 26.88 21.50 1.00 0.0708 0.00 19.20 26.88 21.50 1.00 0.0708 0.00 19.20 15.36 21.50 1.00 0.0708 0.00 19.20 15.36 12.29 1.00 0.0809 0.00 Knockout value 1.7375 #MACRO? #MACRO? Max(S t )< Barrier? Path risk-neutral probability Knockout option payoff I J K L M N O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
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I J K L M N O 44 45 46 47
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PRICING A KNOCKIN BARR Initial stock price 30 Up 1.40 Down 0.80 Interest 1.08 Option exercise price 30 Barrier 50.00 0.4321 ### 0.4938 ### Risk-neutral probability, up 0.4667 ### Risk-neutral probability, down 0.5333 ### STO Paths Period 1 Period 2 Period 3 Period 4 Period 0 Period 1 All up (1 path) up up up up 30.00 42.00 One down (4 paths) down up up up 30.00 24.00 up down up up 30.00 42.00 up up down up 30.00 42.00 up up up down 30.00 42.00 Two down (6 paths) down down up up 30.00 24.00 down up down up 30.00 24.00 down up up down 30.00 24.00 up down down up 30.00 42.00 up up down down 30.00 42.00 up down up down 30.00 42.00 Three down (4 paths) up down down down 30.00 42.00 down up
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