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含离散分红的 1 年远期定价

Price a 1 year forward

专题
Finance / 金融
难度
L4

题目详情

Price a 1 year forward, risk free rate =5%= 5\%, spot =(1= \\ (1 and a dividend of $$0.10(after 6 months.

解析

离散分红在 Td=0.5T_d=0.5 年支付 d=0.10d=0.10。无套利远期价：

F=S0erT−d er(T−Td).\boxed{F=S_0e^{rT}-d\,e^{r(T-T_d)}}.

代入 S0=1,r=5%,T=1S_0=1,r=5\%,T=1：

F=1⋅e0.05−0.1 e0.05⋅0.5≈1.0513−0.1025≈0.95.F=1\cdot e^{0.05}-0.1\,e^{0.05\cdot 0.5}\approx 1.0513-0.1025\approx 0.95.

即

F≈0.95.\boxed{F\approx 0.95}.