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Timedbean · 2024年10月20日

Exp(-q*t)

  1. FRM I
  2. Financial Markets And Products

NO.PZ2023091802000209

问题如下：

An options trader is applying the Black-Scholes-Merton option pricing model to estimate the delta of a long 1-year European put option on a dividend-paying stock. Relevant data is provided below:

· Annual continuously compounded risk-free rate of interest: 2.0%

· Annual dividend yield on the stock: 3.5%

· N(d1): 0.5411

· N(d2): 0.4287

What is the delta of the put option?

选项：

A.

−0.5517

B.

−0.5411

C.

−0.4589

D.

−0.4431

解释：

D is correct. The delta of a put option on a stock paying a dividend at rate q is given by exp(−q * t) * [N(d1 ) – 1]. Given that N(d1) = 0.5411,

delta = exp(−0.035 * 1) * (0.5411 – 1)

= exp(−0.035 * 1) * − 0.4589 = −0.4431.

A is incorrect. −0.5517 is the result if N(d2) is used instead of N(d1) in the formula above.

B is incorrect. −0.5411 is −N(d1).

C is incorrect. −0.4589 is N(d1) – 1, which would be the delta of the option if the stock were dividend-free.

请问为什么答案还需要乘以 EXP (-q*t）呢？

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1 个答案

pzqa39 · 2024年10月21日

嗨，努力学习的PZer你好：


Delta=exp（-q * T）*[ N(d1)-1]

这个公式表达的是欧式看跌期权的Delta，Delta用于衡量期权价格对标的资产价格变化的敏感性。

公式解读如下：

  • Delta：是期权价格对标的资产价格变化的敏感性。对于看跌期权，Delta通常为负，表示标的资产价格上升时期权价格下降。
  • exp(-q * T)：这是表示连续股息率的折现因子，其中：
  • q 是标的资产的连续股息率。
  • T 是期权的到期期限。
  • N(d1)：这是标准正态分布的累积分布函数，表示标的资产价格相对于行权价的概率，d1 是Black-Scholes公式中的计算参数。


这个公式中，N(d1) 是正态累积分布函数值，减去1后得到负值，表示看跌期权的Delta是负的，反映了标的资产价格上升时看跌期权价值的下降。

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NO.PZ2023091802000209 问题如下 options trar is applying the Black-Scholes-Merton option pricing mol to estimate the lta of a long 1-yeEuropeput option on a vinpaying stock. Relevant ta is provibelow:· Annucontinuously compounrisk-free rate of interest: 2.0%· Annuvinyielon the stock: 3.5%· N(): 0.5411· N(): 0.4287Whis the lta of the put option? A.−0.5517 B.−0.5411 C.−0.4589 −0.4431 is correct. The lta of a put option on a stopaying a vinrate q is given exp(−q * t) * [N( ) – 1]. Given thN() = 0.5411,lta = exp(−0.035 * 1) * (0.5411 – 1)= exp(−0.035 * 1) * − 0.4589 = −0.4431.A is incorrect. −0.5517 is the result if N() is useinsteof N() in the formula above.B is incorrect. −0.5411 is −N().C is incorrect. −0.4589 is N() – 1, whiwoulthe lta of the option if the stowere vinfree.

2024-05-10 20:38 2 · 回答