18.6 The Complete Tree (Figure 18.2) Sod Options, Futures, and Other Derivatives, 5th edition C 2002 by John C Hull
18.6 Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull The Complete Tree (Figure 18.2) S0 S0u S0d S0 S0 S0u 2 S0d 2 S0u 2 S0u 3 S0u 4 S0d 2 S0u S0d S0d 4 S0d 3
18.7 Backwards induction We know the value of the option at the final nodes We work back through the tree using risk-neutral valuation to calculate the value of the option at each node, testing for early exercise when appropriate Options, Futures, and Other Derivatives, 5th edition C 2002 by John C Hull
18.7 Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull Backwards Induction • We know the value of the option at the final nodes • We work back through the tree using risk-neutral valuation to calculate the value of the option at each node, testing for early exercise when appropriate
188 Example: Put Option S0=50;X=50;r=10%;σ=40%; T=5 months =04167 δt=1 month=00833 The parameters imply ll=1.1224:d=0.8909 a=1.0084;p=0.5076 Options, Futures, and Other Derivatives, 5th edition C 2002 by John C Hull
18.8 Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull Example: Put Option S0 = 50; X = 50; r =10%; s = 40%; T = 5 months = 0.4167; dt = 1 month = 0.0833 The parameters imply u = 1.1224; d = 0.8909; a = 1.0084; p = 0.5076
18.9 Example(continued) igure 18.3 8907 9.35 70.70 70.70 0.00 0.00 064 56.1 56.1 56.1 2.16 1.30 0.00 50.00 50.00 50.00 449 3.77 266 44.55 44.55 44.55 6.96 6.38 5.45 3969 39.69 10.36 10.31 35.36 35.36 14.64 14.64 3150 1850 28.07 21.93 Options, Futures, and Other Derivatives, 5th edition C 2002 by John C Hull
18.9 Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull Example (continued) Figure 18.3 89.07 0.00 79.35 0.00 70.70 70.70 0.00 0.00 62.99 62.99 0.64 0.00 56.12 56.12 56.12 2.16 1.30 0.00 50.00 50.00 50.00 4.49 3.77 2.66 44.55 44.55 44.55 6.96 6.38 5.45 39.69 39.69 10.36 10.31 35.36 35.36 14.64 14.64 31.50 18.50 28.07 21.93
18.10 Calculation of delta Delta is calculated from the nodes at time st 2.16-6.96 △ 0.41 56.12-44.55 Options, Futures, and Other Derivatives, 5th edition C 2002 by John C Hull
18.10 Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull Calculation of Delta Delta is calculated from the nodes at time dt 0.41 56.12 44.55 2.16 6.96 = − − − =