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(๑• . •๑) · 2020年03月24日

问一道题:NO.PZ2016031202000009 [ CFA I ]

问题如下:

Is it true that the expected payoff of the derivative can be discounted at the risk-free rate plus a risk premium?

选项:

A.

No, because a conbination of a derivative and the underlying can produce a risk-free asset.

B.

Yes, because most investors are risk averse, they require a risk premium.

C.

No, because most investors are risk neutrality, they do not need a premium.

解释:

A is correct. The expected payoff of the derivative can be discounted at the risk-free rate, because a derivative can be combined with an asset to produce a risk-free position and the derivative price can be obtained by assuming that the investor is risk neutral.

C is incorrect because most investors are risk averse, however the investor's risk aversion does not affect the derivative price.

老师,我不太能理解这道题的解释,太抽象了,可以举例子吗?比如用mbs作为一个衍生品举例,为什么未来的pay off要用无风险利率来折现?之前不是说需要加一个信用风险溢价spread吗?

1 个答案
已采纳答案

xiaowan_品职助教 · 2020年03月24日

嗨,从没放弃的小努力你好:


同学你好,这里其实想考察的是衍生品定价的原则:无套利定价原则;

这部分的理解可以和现货做一个比对,现货价格的确定如图

对于一个风险厌恶的投资者来说,需要考虑无风险利率,以及风险溢价,而衍生品定价的原则是无套利定价,

无论是远期,期货,期权,互换的定价都是遵循这一规则,所以定价结果与投资者的风险偏好无关。

举个例子来说,long 基础资产 + short 相应份额远期合约 到期后会获得无风险收益,这个确定的payoff。

 


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