Question text 2Marks A European call option has 8 months to expiry and a strike price of $32.The underlying stock has a current price of $30 and volatility (σ) of 0.50 per annum.The riskfree rate of interest is 5% per annum continuously compounded. Calculate N(d1) as required for the Black-Scholes model Answer 1[input] Enter your answer to 4 decimal places.Notes Report question issue Question 7 Notes多项填空题
登录即可查看完整答案
我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

Question

Question text 2Marks A European call option has 8 months to expiry and a strike price of $32.The underlying stock has a current price of $30 and volatility (σ) of 0.50 per annum.The riskfree rate of interest is 5% per annum continuously compounded. Calculate N(d1) as required for the Black-Scholes model Answer 1[input] Enter your answer to 4 decimal places.Notes Report question issue Question 7 Notes多项填空题

登录即可查看完整答案

我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

BlackTom AI · Accepted Answer

Compute d1 = [ln(S/K) + (r + 0.5σ^2)T] / (σ√T).

1. Relevant knowledge points and concepts
- Black–Scholes requires d1 and d2, where d1 = (ln(S/K) + (r + 0.5σ^2)T)/(σ√T).
- N(d1) is the cumulative standard normal distribution evaluated at d1.

2. Complete reasoning process step by step
- Given: S = 30, K = 32, σ = 0.50, r = 0.05 (continuous), T = 8 months = 8/12 = 2/3 year ≈ 0.6666667.
- Compute ln(S/K), σ^2, (r + 0.5σ^2)T, σ√T, then d1, and finally N(d1).

3. Calculations with intermediate steps
- ln(S/K) = ln(30/32) = ln(0.9375) = -0.064538521.
- σ^2 = 0.50^2 = 0.25. 0.5σ^2 = 0.125.
- r + 0.5σ^2 = 0.05 + 0.125 = 0.175.
- (r + 0.5σ^2)T = 0.175 × (2/3) = 0.175 × 0.6666667 = 0.116666667.
- Numerator = ln(S/K) + (r + 0.5σ^2)T = -0.064538521 + 0.116666667 = 0.052128146.
- √T = √(2/3) ≈ 0.816496581. σ√T = 0.50 × 0.816496581 = 0.408248290.
- d1 = 0.052128146 / 0.408248290 = 0.127658 (approximately).

- Now N(d1): for z = 0.12766, standard normal CDF yields N(0.12766) ≈ 0.5508 (interpolating between N(0.12)=0.5478 and N(0.13)=0.5517).

4. Why the correct answer is correct
- The computed d1 ≈ 0.12766 plugged into the standard normal CDF gives N(d1) ≈ 0.5508. All intermediate calculations follow directly from the Black–Scholes d1 formula and standard normal tables/interpolation.

5. Other options
- Not applicable (this was a numeric fill-in). Any other numeric values would be inconsistent with the algebraic steps and the standard normal CDF evaluation shown above.

6. Conclusion
- Therefore N(d1) = 0.5508, which matches the provided answer.

类似问题

When the non-dividend paying stock price is $40, the strike price is $42, the risk-free rate is 3% p.a. (continuously compounded), the volatility is 25% and the time to maturity is 6 months, which of the following is the price of a European call option on the stock?[Fill in the blank]

What is the upper bound of an American put option with 7 months to expiry and a strike price of $ 6. The underlying stock is currently trading at $ 1.5, and the risk-free rate is 2.6%. Do not enter the dollar sign "$".

An option has strike price of $8 and 2 months to expiry.The current price of the underlying share is $26 and its volatility (sigma) is 22%.The riskfree rate of interest is 6% per annum. Calculate d1 for this option. [your answer should have at least 2 decimal places]

You could answer this question using your intuition for option pricing. You are comparing the value of options which only differ in terms of their strike price (all other key inputs are identical). Which of the following is true?

What is the lower bound of a European call option with 9 months to expiry and a strike price of $7.9. The underlying stock is currently trading at $14.5, and the risk-free rate is 1.8%. Do not enter the dollar sign "$".

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单