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karweillas · 2024年07月26日

如下

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 ]/( ud )=[ 1.02−0.75 ]/( 1.35−0.75 )=0.27/0.60=0.45=45%

怎么理解“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对股票价格未来走势的预期。”?能举个具体例子吗?

1 个答案

李坏_品职助教 · 2024年07月27日

嗨,努力学习的PZer你好:


现金流折现法是用股票未来每一年的分红以及未来预期的卖出价格,作为现金流,然后以股票的必要报酬率(这个是用CAPM模型算出来的收益率)作为折现率进行折现,求和之后作为股票现在的价值。所以需要我们对股票未来的分红、股票的收益率以及预计的卖出价格都有准确的预期。


无套利法和预期法:在理想化的无套利均衡状态下,我们可以通过购买一定量的股票(加上无风险利率的借贷)来完美复制出和期权一样的现金流,这样的话,期权当前时刻理论的价值就等于股票和无风险借贷的价值之和。这里的利率用的是风险中性世界里的rf,与投资人的预期无关。

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