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宇宙球求 · 2024年06月18日

“时,它还包含了支付固定利率的30年期掉期合约的权利,如果长期收益率上升,这个掉期合约的价值也会增加。”

NO.PZ2021120102000006

问题如下:

An active fund trader seeks to capitalize on an expected steepening of the current upward-sloping yield curve using option-based fixed-income instruments.

Which of the following portfolio positioning strategies best positions her to gain if her interest rate view is realized?

选项:

A.

Sell a 30-year receiver swaption and a 2-year bond put option.

B.

Purchase a 30-year receiver swaption and a 2-year bond put option.

C.

Purchase a 30-year payer swaption and a 2-year bond call option.

解释:

C is correct.

A steepening of the yield curve involves an increase in the slope, or the difference between long-term and short-term yields-to-maturity. An optimal portfolio positioning strategy is one which combines a short duration exposure to long-term bonds and a long duration exposure to short-term bonds.

Portfolio C involves the right (but not the obligation) to purchase a 2-year bond, which will increase in value as short-term yields fall with the right to pay-fixed on a 30-year swap, which increases in value if long-term yields rise. Portfolio A involves the sale of two options. Although they will expire unexercised in a steeper curve environment, the investor’s return is limited to the two option premia. Portfolio B is the opposite of Portfolio C, positioning the investor for a flattening of the yield curve.

请问这句话的意思是不是因为利率环境是上升的所以,只是支付固定coupon,但是合约升值,因此值得投资;另外,为什么会掉期反倒是升值的,而不是逐渐平值。

1 个答案

发亮_品职助教 · 2024年06月19日

嗨,努力学习的PZer你好:


with the right to pay-fixed on a 30-year swap, which increases in value if long-term yields rise.

是上面这句话的理解吗?


这块是Purchase 30-year payer swaption,买入一个底层资产是30年期的Pay fixed swap,然后外面嵌套了一个进入Swap的权利option。我们最终分析的是option的value改变哈。


所以,当长期30年期利率上升时,我们需要判断利率上升对option价值的影响,而Option的价值取决于底层资产pay 30-year fixed swap,所以需要分析一下长期利率上升时,这个swap的价格改变,进而判断是否行权/权利的价值改变。


当长期利率上升时,pay 30-year fixed swap的价值上升,原因是按照最新的市场利率重新签订一个30-year pay fixed swap的话,重新签订的fixed rate会因长期市场利率上升而上升,也就是新合约要支付更高的fixed rate,而旧合约只需支付较低的fixed rate就可以换取floating rate。这说明我们之前签订的旧合约有价值,其value上升。


所以,底层资产pay 30-year fixed swap的value上升,那我们会行使该option,该option的value会上升,于是该swaption的value上升,我们因为持有该swaption而盈利。


关于利率上升时,Pay 30-year fixed swap的价值上升还有另外一个分析思路。底层资产原来支付的是30-year的fixed rate,现在利率上升,市场上最新的30-year fixed rate肯定上升。


这时候我们就想分析一下对旧swap合约value的影响。所有的衍生品合约在判断value影响时,都可以假设此刻立即签订一个反向合约平掉旧头寸,平仓的盈利就是旧合约带来的,就是旧合约的影响。

所以此刻,我们按照最新的更高的fixed swap,签订反向合约receive 30-year fixed swap,就可以平仓平掉旧合约pay 30-year fixed swap

这样的话,旧合约是支付较低的30-year fixed rate,平仓的新合约是收到较高的30-year fixed rate,两个利率算差值,我们有一个净收入。这说明当利率上升时,旧合约的value是上升的。

既然这份底层合约的value上升,那基于该底层合约的option value也上升。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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