−(T−t)=-0.5是怎么来的呢

NO.PZ2023040401000079

问题如下：

A European put option with six months remaining to maturity has an exercise price (X) of USD 48. Suppose the underlying stock has no additional cash flows, the risk-free rate is 2%, the current underlying price (St) is USD 54. If the current put option price is USD 4.6, Which of the following calculations of the exercise value and the time value is correct?

选项：

The exercise value of the put option is 0;The time value of the put option is USD 4.6.

The exercise value of the put option is 4.6; The time value of the put option is USD 0.

The exercise value of the put option is 0；The time value of the put option cannot be calculated.

解释：

Put option exercise value = Max (0, X(1 + r)^−(T−t) − S_t) = Max (0, 48(1 + 2%)^−0.5 − 54) = 0

Put option time value = p_t – Max (0, X(1 + r)^−(T−t) − S_t) = 4.6-0 = USD 4.6.

−(T−t)=-0.5是怎么来的呢

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1 个答案

李坏_品职助教 · 2025年05月28日

嗨，爱思考的PZer你好：

T-t指的是这个合约的期限，T是到期日，t是现在的时刻。

题目说“A European put option with six months remaining to maturity”，意思是这个期权合约还剩下六个月到期，六个月就是0.5年。所以T-t = 0.5.

所以−(T−t)=-0.5

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NO.PZ2023040401000079 问题如下 A Europeput option with six months remaining to maturity hexercise pri(X) of US48. Suppose the unrlying stohno aitioncash flows, the risk-free rate is 2%, the current unrlying pri(St) is US54. If the current put option priis US4.6, Whiof the following calculations of the exercise value anthe time value is correct? A.The exercise value of the put option is 0;The time value of the put option is US4.6. B.The exercise value of the put option is 4.6; The time value of the put option is US0. C.The exercise value of the put option is 0；The time value of the put option cannot calculate Put option exercise value = M(0, X(1 + r)−(T−t) − St)= M(0, 48(1 + 2%)−0.5 − 54) = 0Put option time value = pt – M(0, X(1 + r)−(T−t)− St) = 4.6-0 = US4.6. 可以把现在的期权费54（1+2%）^0.5 与X=48比较吗？

2024-04-18 17:27 2 · 回答

NO.PZ2023040401000079 问题如下 A Europeput option with six months remaining to maturity hexercise pri(X) of US48. Suppose the unrlying stohno aitioncash flows, the risk-free rate is 2%, the current unrlying pri(St) is US54. If the current put option priis US4.6, Whiof the following calculations of the exercise value anthe time value is correct? A.The exercise value of the put option is 0;The time value of the put option is US4.6. B.The exercise value of the put option is 4.6; The time value of the put option is US0. C.The exercise value of the put option is 0；The time value of the put option cannot calculate Put option exercise value = M(0, X(1 + r)−(T−t) − St)= M(0, 48(1 + 2%)−0.5 − 54) = 0Put option time value = pt – M(0, X(1 + r)−(T−t)− St) = 4.6-0 = US4.6. time value为什么等于期权费啊，value的计算不算期权费，profit or loss是在value的基础上算上期权费。

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