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fangxiao · 2019年12月02日

问一道题:NO.PZ2019103001000041

问题如下:

McLaughlin and Michaela Donaldson, a junior analyst at Delphi, are now discussing how to reposition the portfolio in light of McLaughlin’s expectations about interest rates over the next 12 months. She expects interest rate volatility to be high and the yield curve to experience an increase in the 2s/10s/30s butterfly spread, with the 30-year yield remaining unchanged. Selected yields on the Treasury yield curve, and McLaughlin’s expected changes in yields over the next 12 months, are presented in Exhibit 1.

Donaldson suggests they also consider altering the portfolio’s convexity to enhance expected return given McLaughlin’s interest rate expectations.

Given McLaughlin’s interest rate expectations over the next 12 months, one way that Donaldson and McLaughlin could alter convexity to enhance expected return would be to:

选项:

A.

sell call options on bonds held in the portfolio.

B.

buy call options on long-maturity government bond futures.

C.

sell put options on bonds they would be willing to own in the portfolio.

解释:

B is correct.

McLaughlin expects interest rate volatility to be high and the yield curve to experience an increase in the butterfly spread, with the 30-year yield remaining unchanged. To increase the portfolio’s expected return, Donaldson and McLaughlin should buy call options on long-maturity government bond futures to increase convexity.

为什么buy option能增加Convexity呢?

1 个答案
已采纳答案

发亮_品职助教 · 2019年12月03日

嗨,努力学习的PZer你好:


“为什么buy option能增加Convexity呢?”


债券的Convexity,表现出来的特性就是“涨多跌少”;那如果Option也能表现出这种“涨多跌少”的特性,就说明Option也就有Convexity性质。



以Call option为例,当标的物的价格下跌的时候,Option的价格也下跌;但是Option价格下跌的速度会比标的物下跌的速度更慢,原因是当标的物价格跌破行权价(Strike price)时,Option的内在价值就变为零,不能再下跌了,此时Option止跌;而标的物自己的价格跌破行权价后,还可以继续下跌;

这就表现出来了Option在下跌时的“跌少”。


当标的物的价格上升时,Option的价值上升,且Option价值加速上升。尤其是当标的物价格处在行权价附近时,也就是Option处在At-the-money附近时,Option的Delta为0.5,即标的物价格上涨1元,Option的价值上涨0.5元,也就是Option的价值变动与标的物的价值变动呈现0.5:1的关系;

当标的物的价格继续上升、继续超过行权价一点时,Option的Delta会快速变成1,也就是标的物价格上涨1元,Option的价值上升1元,即Option的价值变动与标的物的价值变动呈现1:1的关系。发现,标的物的价格只是上升一点点,但Option的价值会迅速上升,且呈现出加速上涨的态势,这就是涨多。


所以Option也具有“涨多跌少”的性质,也就是Convexity性质。于是Long option,我们就可以获得Convexity。


-------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!


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