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期权到期价值

Optionality

专题
Finance / 金融
难度
L2

题目详情

请完成下列句子：

A 部分：如果 ABC 到期时的收盘价为 $20，则执行价为 $19.50 的看涨期权价值为 $_____

B 部分：如果 ABV 到期时的收盘价为 $20，则执行价为 $22.50 的看涨期权价值为 $_____

C 部分：如果 ABX 到期时的收盘价为 $25，则执行价为 $23.25 的看跌期权价值为 $_____

D 部分：如果 ABY 到期时的收盘价为 $22，则执行价为 $23.25 的看跌期权价值为 $_____

Please complete the following sentences:

Part A: If the close price of ABC at expiration is $20, a $19.50 strike call is worth $_____

Part B: If the close price of ABV at expiration is $20, a $22.50 strike call is worth $_____

Part C: If the close price of ABX at expiration is $25, a $23.25 strike put is worth $_____

Part D: If the close price of ABY at expiration is $22, a $23.25 strike put is worth $_____

解析

到期时，期权价值等于内在价值：

  • 看涨：max⁡(S−K,0)\max(S-K,0)
  • 看跌：max⁡(K−S,0)\max(K-S,0)

A 部分：max⁡(20−19.5,0)=0.5\max(20-19.5,0)=\boxed{0.5} 美元。

B 部分：max⁡(20−22.5,0)=0\max(20-22.5,0)=\boxed{0} 美元。

C 部分：max⁡(23.25−25,0)=0\max(23.25-25,0)=\boxed{0} 美元。

D 部分：max⁡(23.25−22,0)=1.25\max(23.25-22,0)=\boxed{1.25} 美元。

Original Explanation

Part A: A $19.50 strike call would give the option holder the right to buy stock ABC at $19.50 on or before the date when the contract expires. Since the close price of the stock at expiration is $20 the value of the option is 0.5\boxed{0.5} dollars.

Part B: Since the close price of ABV at expiration is $20 and the call option was purchased at a strike price of $22.5, the option has no intrinsic value and expires worthless for 0\boxed{0} dollars.

Part C: A $23.25 strike put would give the option holder the right to sell stock ABX at $23.25 on or before the date when the contract expires. Since the close price of ABX at expiration is $25, the right to sell at $23.25 is worthless since you can sell on the open market for $25. Thus, the value of the option is 0\boxed{0} dollars.

Part D: Since the close price of ABY at expiration is $22, the value of a $23.25 strike put option does have some inherent value, and can be found as:

Value of Option at Expiration=Value of strike put−Close price of ABY=23.25−22=1.25\textrm{Value of Option at Expiration} = \textrm{Value of strike put} - \textrm{Close price of ABY} = 23.25 - 22 = \boxed{1.25} dollars.