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Carolyne · 2024年02月20日

第一句话对吗

  1. CFA II
  2. Derivative

NO.PZ2023020101000021

问题如下：

High Street Investment Management is an investment subadvisory firm partnering with Registered Investment Advisors to provide counsel for options trading strategies. Scott Cummins is High Street’s CEO and chief investment officer. Phyllis Schwartz leads the client relationship team. David Spelding is a recent college graduate, who just joined the firm as an analyst. Cummings and Schwartz are conducting an introductory training session on options pricing, focusing on the binomial option valuation model (i.e., the binomial model).

Cummins begins the session by listing, in Exhibit 1, variables and values for a binomial model to illustrate an outcome.

Exhibit 1: Binomial Model Variables and Values

Schwartz states, “The one-period binomial model is based on the no-arbitrage approach in which an investor does not take any risk or use his own money. Based on the information in Exhibit 1, the probability of an up move is 45%. For an investor, the no-arbitrage approach is similar to both the expectations approach and the discounted cash flow approach. Each approach is based on the investor’s expectation regarding the future course of the underlying stock price.”

Is Schwartz’s statement about the one-period binomial model most likely correct?

选项：

A.

Yes.

B.

No, she is incorrect about the probability of an up move.

C.

No, she is incorrect about expectations of future stock prices.

解释：

Schwartz’s statement is incorrect. The expectations approach is a variation of the no-arbitrage approach to the binomial model. The results of each are identical. Under the no-arbitrage approach and the expectations approach, expected options payoffs are a function of a risk-neutral probability. The investor’s outlook with respect to the future course of the stock price is not a relevant consideration for the no-arbitrage approach or the expectations approach. The investor’s outlook with respect to the future course of the stock price is a relevant consideration for the discounted cash flow approach to securities valuation.

Schwartz’s statement with respect to the probability of an up move is correct. The calculation follows:

π=[ FV( 1 )−d ]/( u−d )=[ 1.02−0.75 ]/( 1.35−0.75 )=0.27/0.60=0.45=45%

请问Schwartz 说的第一句话对吗

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1 个答案

pzqa35 · 2024年02月21日

嗨，努力学习的PZer你好：


第一句话是正确的哈：

本题考察的是一期二叉树下的No-arbitrage Approach和Expectations approach。

问题是Schwartz关于一期二叉树的表述是否正确。对应题干中的表格1和最后一段的信息。

Schwartz的第一句话：一期二叉树基于的是无套利原则，因此投资者既不承担风险也不动用自己的钱。这句话是正确的。

Schwartz的第二句话：根据表1中的信息，向上移动的概率是45%。这句话正确，可以根据公式π=[ FV( 1 )−d ]/( u−d )=[ 1.02−0.75 ]/( 1.35−0.75 )=0.27/0.60=0.45=45%计算得到。

Schwartz的第三句话：对于投资者来说，无套利法和预期法、现金流折现方法类似。都是基于投资者对潜在股价未来走势的预期。这里是错误的。预期法是二项模型中无套利方法的一种变体，因此二者是类似的。但二者与现金流折现法不相似，现金流折现法需要考虑投资者对股票价格未来走势的预期，但无套利法和预期法不需要考虑。

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