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Lecture 8 (part 2)

17intheexampleifr8 optionpricing optionpricing

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Unformatted text preview: example: Stock u = 1.25 Option (X = \$35) \$50 \$40 C d = 0.75 \$30 H = 0.75 Cu = Su – X = \$50 ­ \$35 = \$15 Cd = 0 not exercised) Option Pricing Option Pricing ­ Binomial Option Pricing Model Qn: Then what is the price of the call (C)? Basic principle: The return on a Hedged portfolio = Riskless rate (r) At the end of 1 period, initial investment will become: = (HS – C) (1 + r) Option Pricing Option Pricing ­ Binomial Option Pricing Model Since payoffs are the same regardless of price. (HS – C) (1 + r) = uHS – Cu or dHS ­ Cd Substituting for H: C = [(1+r­d)/(u­d)][Cu/(1+r)] + [(u­1­r)/(u­d)][Cd/(1+r)] = \$9.17 (in the example if r = 8%) Option Pricing Option Pricing ­ Binomial Option Pricing Model 2 Period Model Stock Option (X = \$35) Cuu = \$50 ­ \$35 \$50 Cu \$44.72 \$38.73 \$40 \$34.64 Cud = Cdu = \$38.73 ­ \$35 = \$3.73 C \$30 u = 1.118, d = 0.866 = \$15 Cd Cdd = 0 Option Pricing Option Pricing ­ Binomial Option Pricing Model Cu = [(1+r­d)/(u­d)][Cuu/(1+r)] + [(u­1­r)/(u­d)][Cud/(1+r)] = \$11.04 Cd = [(1+r­d)/(u­d)][Cdu/(1+r)] + [(u­1­r)/(u­...
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