100 天 vs 200 天：call 报价怎么变

day call option 2

专题: Finance / 金融
难度: L4
来源: QuantQuestion

题目详情

A customer calls up and wants a price on a European 100- day call option. You quote $100. He calls back a minute later and wants a quote on the same option but with 200 days to maturity. How does the second price quote compare to the first price quote? Explain carefully.

解析

到期更远的欧式 call 不会更便宜：

\boxed{C_{200d}\ge C_{100d}}.

若近似在 $r\approx 0$ 且 ATM 的情形，可用

C\approx \frac{\sigma S\sqrt{T}}{\sqrt{2\pi}},

因此期限从 100 天到 200 天，价格大致按 $\sqrt{T}$ 缩放：

\boxed{C_{200d}\approx \sqrt{2}\,C_{100d}\approx 1.41\,C_{100d}}.

若深 OTM，延长到期带来的相对增幅可能更大；深 ITM 则增幅更小。