四年期 vs 一年期：时间单位改变时的 σ

Consider two European call options on the same underlying stock. The options have the same strike price. Assume constant interest rates. One option matures in one year; the other option matures in four years. Suppose that you put $\sigma = 15\%$ into the Black- Scholes formula to value the one- year option. What value of $\sigma$ do you put into the Black- Scholes formula to value the four- year option? Assume that you set $T - t = 1$ in the Black- Scholes formula in both cases (i.e., one unit of time equals four years in the second case but only one year in the first case).

Story: Some recent questions include "What do you think an investment banker does?" Not only that, but "Do you understand the hours investment bankers work and why?" Some of these folks look like Hell when you meet them. Are you sure about this career choice?