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nicole 麦子🌳 · 2025年07月05日

完全不懂逻辑在哪

NO.PZ2024050101000057

问题如下:

Banko, Inc., entered into a $10 million notional, 7-year CDS as a protection buyer three years ago at a spread of 1.85%. The current 4-year CDS spread for the same reference entity is 2.30% based on the PV of expected payoff of 0.0312 per $1 notional. The value of the CDS to Banko, Inc., is closest to:

选项:

A.

−$55,000

B.

−$60,900

C.

+$61,000

D.

+$53,000

解释:

英文解析:

Recognize that the value of the CDS is calculated such that:

Current PV of expected payment = current PV of expected payoff = 0.0312

Using the current spread of 2.30%, the current PV of expected payments = s=0.0312/0.023=1.3565

Applying this value to the initial CDS spread of 1.85% yields:

PV of expected payments = 0.0185*1.3565=0.0251

Value to the protection buyer = PV of expected payoff - PV of expected payments = 0.0312 - 0.0251 = 0.0061 per 1$ notional.

The swap value for the $10 million notional = 0.0061 × 10,000,000 = $61,000. Because the spread has widened, the protection buyer gains.

中文解析:

信用违约互换(CDS)的价值计算方式如下:

预期支付的当前现值 = 预期收益的当前现值 = 0.0312。

使用当前2.30%的利差,预期支付的当前现值 = s = 0.0312 / 0.023 = 1.3565。

将该值应用于初始1.85%的CDS利差可得:预期支付的现值 = 0.0185 × 1.3565 = 0.0251。

对于保护买方而言的价值 = 预期收益的现值 - 预期支付的现值 = 0.0312 - 0.0251 = 每1美元名义金额0.0061。

1000万美元名义金额的互换价值 = 0.0061 × 10,000,000 = 61,000美元。

由于利差扩大,保护买方获利。

已经看了全部之前的学生提问,完全看不懂,老师能用英文专有名词,再加中文语句解释一下这题到底该怎么算吗?

为什么PV expected payment = PV expected payoff?

0.0312/0.023,就是PV expected payoff➗ current spread 这个代表是什么意思,公式在课件第几页能找到?

1 个答案

pzqa27 · 2025年07月07日

嗨,爱思考的PZer你好:


已经看了全部之前的学生提问,完全看不懂,老师能用英文专有名词,再加中文语句解释一下这题到底该怎么算吗?

为什么PV expected payment = PV expected payoff?

这个题是对CDS进行估值,用到的原理是

CDS 的价值等于保护买方预期获得的赔付现值与需支付的保费现值的差额,即:CDS价值=预期赔付现值−预期保费现值,关于这一原理的推导,请参考基础班的这个视频的这个位置,并且这个视频里有个例子,基本上这个题目木就是改编自原版书上的这个例子。何老师在这个视频里有详细地介绍。


0.0312/0.023,就是PV expected payoff➗ current spread 这个代表是什么意思,公式在课件第几页能找到?

我强烈推荐同学先去看下这里的例题,这个题目用的原理是PV expected payment = PV expected payoff

在基础班的例题里,我们在计算PV expected payment的时候,是对保费算一个期望,然后折现,最终得到4.0728s,这里的s是spread,所以PV expected payment实际上可以看作是一个系数X乘上spread,在基础班的例子中,这个系数X是4.0728。

在这个题目里,系数X是未知的,但是我们知道spread是2.3%,根据PV expected payment = PV expected payoff,可以列出X*2.3%=0.0312 ,然后就可以把这个系数X求出来了。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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