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Unformatted text preview: 12 = 49 7 7 7 54 Example 6.5. Knockout options. In these options when the price falls below a certain level the option is worthless no matter what the value of the stock is at the end. To illustrate consider the binomial model from Example 6.4: u = 3/2, d = 2/3, and r = 1/6. This time we suppose S0 24 and consider a call (S3 28)+ with a knockout barrier at 20, that is if the stock price drops below 20 the option becomes worthless. As we have computed the risk neutral probability is p⇤ = 0.6 and the value recursion is Vn (a) = 6 [.6Vn (aH ) + .4Vn (aT )], 7 with the extra boundary condition that if the price is 20 the value is 0. 81 53 54 H 30 HH H 36 HH36 HH 8 16.839 HH 24 H 24 HH H HH H 8.660 4.114 HH H H 16 H 16 H H 0 0 To check the answer note that the knockout feature eliminates one of the paths to 36 so V0 = (6/7)3 [(.6)3 · 53 + 2(.6)2 (.4) · 8] = 8.660 From this we see that the knockout barrier reduced the value of the option by (6/7)3 (0.6)2 (0.4) · 8 = 0.7255. 6.4 Capital A...
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