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沐沐的方盒 · 2023年10月23日

请问无套利模型不是基于expectation,那是基于什么呢?

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%

如题

1 个答案
已采纳答案

李坏_品职助教 · 2023年10月23日

嗨,爱思考的PZer你好:


无套利原则: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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