Note that by the arbitrage-free principle, it is easy to show that when a stock pays...
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Note that by the arbitrage-free principle, it is easy to show that when a stock pays a dividend D₁ at t₁, the stock's value is immediately reduced by the amount of the dividend. In other words, liment, St - D1 = limtut St. ملا کر است 3.4 م 3.E 37 3.6 3.5 3.3 3.2 3.1 ا ا 10 12 Figure 1.2: t1 = 5, ta = 10, D = 0.4, D2 = 0.4. Assume that a dividend D, is paid at time tj, where 0<t₁ < t₂<< tn ≤ T. Let D denote the present value of the dividend stream: D=er₁ D₁ + e ₂-rt₂ D₂ +· (1.34) Consider an European call option and an European put option, each with strike price K, maturity T, and underlying one share of S, assumed to be dividend-paying. We want to prove (1.35) Co + Ke-rT The idea is to consider two portfolios at t = 0: P₁ = c + Ke $₂ = p + S. e + D = Po + So. -rT -rtn Dn. + D₂ It means that ₁ consists of a call option, a zero-coupon bond with face value (par value) K and maturity T, and n zero-coupon bonds with face values Dk and maturity times tk, k = 1, 2, · · ·‚n. Þ2 consists of a put option and the stock which will pay dividend D, at tj. Now, you are asked to prove Vr(Þ1) = Vr(Þ₂). Then we can conclude Vo(P₁) = Vo(Þ₂) which is precisely (1.35) by Corollary 1.1. Note that by the arbitrage-free principle, it is easy to show that when a stock pays a dividend D₁ at t₁, the stock's value is immediately reduced by the amount of the dividend. In other words, liment, St - D1 = limtut St. ملا کر است 3.4 م 3.E 37 3.6 3.5 3.3 3.2 3.1 ا ا 10 12 Figure 1.2: t1 = 5, ta = 10, D = 0.4, D2 = 0.4. Assume that a dividend D, is paid at time tj, where 0<t₁ < t₂<< tn ≤ T. Let D denote the present value of the dividend stream: D=er₁ D₁ + e ₂-rt₂ D₂ +· (1.34) Consider an European call option and an European put option, each with strike price K, maturity T, and underlying one share of S, assumed to be dividend-paying. We want to prove (1.35) Co + Ke-rT The idea is to consider two portfolios at t = 0: P₁ = c + Ke $₂ = p + S. e + D = Po + So. -rT -rtn Dn. + D₂ It means that ₁ consists of a call option, a zero-coupon bond with face value (par value) K and maturity T, and n zero-coupon bonds with face values Dk and maturity times tk, k = 1, 2, · · ·‚n. Þ2 consists of a put option and the stock which will pay dividend D, at tj. Now, you are asked to prove Vr(Þ1) = Vr(Þ₂). Then we can conclude Vo(P₁) = Vo(Þ₂) which is precisely (1.35) by Corollary 1.1.
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Managing Business Ethics Making Ethical Decisions
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