NO.PZ2020011303000069
问题如下:
A portfolio depends on a 3.5-year, risk-free rate interest rate and no other rates or risk factors. It is calculated that the portfolio will increase in value by USD 500 for each one-basis-point increase in the rate. The rates that are modeled are the three month, six-month, one-year, two-year, three-year, five-year, ten-year, and thirty year
解释:
The portfolio has a delta with respect to the 3- and 5-year rates and no other rates. When the 3-year rate changes by one basis point, the 3.5-year rate changes by 0.75 basis points. When the 5-year rate changes by one basis point, the 3.5-year rate changes by 0.25 basis points. The deltas with respect the 3- and 5-year rates are therefore USD 375 and USD 125, respectively.
题目问:投资组合取决于 3.5 年期的无风险利率,没有其他利率或风险因素。 根据计算,利率每增加一个基点,投资组合的价值将增加 500 美元。 建模的利率是三个月、六个月、一年、两年、三年、五年、十年和三十年的利率。 相对于这些利率中的每一个,投资组合的 delta 是多少?
3.5年和3年 比3.5年和5年更加接近,所以肯定是3年对portfolio的影响更大一些。
解答这类题目的思路是用3年和5年去凑一个3.5年,假设3年的影响比重为x,那么5年的影响比重则为1-x,得到
3x+5(1-x)=3.5,得x=0.75
老师好,1、从课程里讲到的内容,3.5年的利率,虽然受邻近的3年和5年影响最大,但是也会辐射到1年,6个月,10年呀。是说frm的题目就只考虑邻近的2个期限的利率吗?
2、离得越近,辐射影像越大,所以3年影响最大?