A single branch on a Binomial tree is represented by the following diagram. Calculate how many shares of the underlying asset (delta) are required to delta hedge.Enter your answer to two decimal places. If your answer is negative, then enter the negative sign.数值题
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

A single branch on a Binomial tree is represented by the following diagram. Calculate how many shares of the underlying asset (delta) are required to delta hedge.Enter your answer to two decimal places. If your answer is negative, then enter the negative sign.数值题

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

Delta in a one-step binomial model is the slope of the option payoff with respect to the underlying: delta = (V_up − V_down) / (S_up − S_down).

1) Knowledge points and concepts
- Delta for a replicating portfolio in a one-step binomial tree is found by taking the difference in option values between the up and down states divided by the difference in stock prices between those states.
- For a put option, the option value falls when the stock price rises, so delta is negative.

2) Step-by-step reasoning and intermediate calculations
- From the diagram: S0 = $12, S_up = $13.80, S_down = $10.44. Put option values: P_up = $0, P_down = $2.56.
- Compute differences:
  - V_up − V_down = 0 − 2.56 = −2.56
  - S_up − S_down = 13.80 − 10.44 = 3.36
- Delta = (V_up − V_down) / (S_up − S_down) = −2.56 / 3.36.

3) Arithmetic shown
- −2.56 / 3.36 = −256/336. Reduce fraction: divide numerator and denominator by 16 → −16/21 ≈ −0.76190476.
- Round to two decimal places → −0.76.

4) Why this is correct
- This delta is the number of shares of the underlying to hold (short or long) to replicate the option’s payoff for the one-step tree. The negative sign indicates a short position in the underlying is required to hedge a long put (put value falls when stock rises).

5) Why other approaches are incorrect
- Using current stock price S0 or mixing up numerator sign (e.g., V_down − V_up) would give wrong sign or magnitude. Solving the two linear equations for a replicating portfolio yields the same delta: subtracting the equations eliminates the cash account and gives the same slope calculation.

6) Conclusion
- Therefore the required delta (shares) is −0.76, matching the provided answer.

A single branch on a Binomial tree is represented by the following diagram. Calculate how many shares of the underlying asset (delta) are required to delta hedge.Enter your answer to two decimal places. If your answer is negative, then enter the negative sign.数值题

类似问题

What is the basic idea behind the delta-hedging approach to valuing a derivative?[Fill in the blank]

Is the following statement true or false? In the products of methylation-hydrolysis, every -OH group corresponds to the position of a glycosidic bond in the starting polysaccharide.

Which of the follwoing structures represents amylopectin?

Which of the following is true about an aldopentose?I. It is a monosaccharide.II. It contains a CHO groupIII. It is a disaccharide.IV. It is an oligosaccharide.

For stock A, we have 𝛽 𝑖 = 0.70. Suppose the expected market risk premium next year is 9% and the risk-free rate is 3%. What is the expected return of this stock based on the CAPM? (Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

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