问题如下图:
coupon rate没有给,答案为什么用0.5算呢?
NO.PZ2020021204000049问题如下Suppose ththe six-month Libor rate is 5%, the forwarLibor rate for the periobetween 0.5 an1.0 yeis 5.6% anthe forwarLibor rate for the periobetween 1.0 an1.5 years is 6.0. The two-yeLibor swrate is 5.7%. All risk-free rates are 4.5%. Whis the forwarLibor rate for the periobetween 1.5 an2.0 years? All rates are expressewith semi-annucompounng.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #443e44}span.s1 {color: #4869}span.s2 {color: #65544b}span.s3 {color: #2f496b}A swwhere 5.7% is paianLibor is receiveis worth zero. Per 100 of principal, first FRA is worth:0.5 X (0.05 − 0.057) X 1001 + 0.045/2\frac{0.5\;X\;(0.05\;-\;0.057)\;X\;100}{1\;+\;0.045/2}1+0.045/20.5X(0.05−0.057)X100= -0.342The seconFRA is worth:0.5 X (0.056 − 0.057) X 100(1 + 0.045/2)2\frac{0.5\;X\;(0.056\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^2}(1+0.045/2)20.5X(0.056−0.057)X100= -0.048The thirFRA is worth:0.5 X (0.060 − 0.057) X 100(1 + 0.045/2)3\frac{0.5\;X\;(0.060\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^3}(1+0.045/2)30.5X(0.060−0.057)X100= 0.14If the requireforwarrate is R then:0.5 X (R − 0.057) X 100(1 + 0.045/2)4\frac{0.5\;X\;(R\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^4}(1+0.045/2)40.5X(R−0.057)X100- 0.342 - 0.048 + 0.140 = 0This csolveto give R = 0.0625. The forwarrate for the periobetween 1.5 an2.0 years is 6.25% (semiannually compoun.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #443f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453f47}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #484047}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #463f46}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453e45}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #3f3945}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4435}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #46434b}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #473f45}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4b4247}p.p11 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4c474e}p.p12 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464247}span.s1 {color: #4b6f}span.s2 {color: #67564span.s3 {color: #635f67}span.s4 {color: #7f7b7b}span.s5 {color: #635251}span.s6 {color: #435263}span.s7 {color: #6f6b69}span.s8 {color: #615456}span.s9 {color: #7f7b7f}span.s10 {color: #6b6b6b}span.s11 {font: 6.0px Helvetica}span.s12 {color: #615454}span.s13 {color: #7f7f7f}span.s14 {color: #5c5b65}span.s15 {font: 9.0px Helvetica}span.s16 {color: #6f6b73}span.s17 {color: #7b7span.s18 {color: #4e5c70}那里有呢,沒有印象呢
NO.PZ2020021204000049问题如下Suppose ththe six-month Libor rate is 5%, the forwarLibor rate for the periobetween 0.5 an1.0 yeis 5.6% anthe forwarLibor rate for the periobetween 1.0 an1.5 years is 6.0. The two-yeLibor swrate is 5.7%. All risk-free rates are 4.5%. Whis the forwarLibor rate for the periobetween 1.5 an2.0 years? All rates are expressewith semi-annucompounng.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #443e44}span.s1 {color: #4869}span.s2 {color: #65544b}span.s3 {color: #2f496b}A swwhere 5.7% is paianLibor is receiveis worth zero. Per 100 of principal, first FRA is worth:0.5 X (0.05 − 0.057) X 1001 + 0.045/2\frac{0.5\;X\;(0.05\;-\;0.057)\;X\;100}{1\;+\;0.045/2}1+0.045/20.5X(0.05−0.057)X100= -0.342The seconFRA is worth:0.5 X (0.056 − 0.057) X 100(1 + 0.045/2)2\frac{0.5\;X\;(0.056\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^2}(1+0.045/2)20.5X(0.056−0.057)X100= -0.048The thirFRA is worth:0.5 X (0.060 − 0.057) X 100(1 + 0.045/2)3\frac{0.5\;X\;(0.060\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^3}(1+0.045/2)30.5X(0.060−0.057)X100= 0.14If the requireforwarrate is R then:0.5 X (R − 0.057) X 100(1 + 0.045/2)4\frac{0.5\;X\;(R\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^4}(1+0.045/2)40.5X(R−0.057)X100- 0.342 - 0.048 + 0.140 = 0This csolveto give R = 0.0625. The forwarrate for the periobetween 1.5 an2.0 years is 6.25% (semiannually compoun.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #443f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453f47}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #484047}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #463f46}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453e45}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #3f3945}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4435}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #46434b}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #473f45}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4b4247}p.p11 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4c474e}p.p12 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464247}span.s1 {color: #4b6f}span.s2 {color: #67564span.s3 {color: #635f67}span.s4 {color: #7f7b7b}span.s5 {color: #635251}span.s6 {color: #435263}span.s7 {color: #6f6b69}span.s8 {color: #615456}span.s9 {color: #7f7b7f}span.s10 {color: #6b6b6b}span.s11 {font: 6.0px Helvetica}span.s12 {color: #615454}span.s13 {color: #7f7f7f}span.s14 {color: #5c5b65}span.s15 {font: 9.0px Helvetica}span.s16 {color: #6f6b73}span.s17 {color: #7b7span.s18 {color: #4e5c70}(1+5%/2)(1+5.6%/2)(1+6%/2)(1+X/2)=(1+5.7%/2) ^4
NO.PZ2020021204000049 问题如下 Suppose ththe six-month Libor rate is 5%, the forwarLibor rate for the periobetween 0.5 an1.0 yeis 5.6% anthe forwarLibor rate for the periobetween 1.0 an1.5 years is 6.0. The two-yeLibor swrate is 5.7%. All risk-free rates are 4.5%. Whis the forwarLibor rate for the periobetween 1.5 an2.0 years? All rates are expressewith semi-annucompounng.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #443e44}span.s1 {color: #4869}span.s2 {color: #65544b}span.s3 {color: #2f496 A swwhere 5.7% is paianLibor is receiveis worth zero. Per 100 of principal, first FRA is worth:0.5 X (0.05 − 0.057) X 1001 + 0.045/2\frac{0.5\;X\;(0.05\;-\;0.057)\;X\;100}{1\;+\;0.045/2}1+0.045/20.5X(0.05−0.057)X100= -0.342The seconFRA is worth:0.5 X (0.056 − 0.057) X 100(1 + 0.045/2)2\frac{0.5\;X\;(0.056\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^2}(1+0.045/2)20.5X(0.056−0.057)X100= -0.048The thirFRA is worth:0.5 X (0.060 − 0.057) X 100(1 + 0.045/2)3\frac{0.5\;X\;(0.060\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^3}(1+0.045/2)30.5X(0.060−0.057)X100= 0.14If the requireforwarrate is R then:0.5 X (R − 0.057) X 100(1 + 0.045/2)4\frac{0.5\;X\;(R\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^4}(1+0.045/2)40.5X(R−0.057)X100- 0.342 - 0.048 + 0.140 = 0This csolveto give R = 0.0625. The forwarrate for the periobetween 1.5 an2.0 years is 6.25% (semiannually compoun.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #443f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453f47}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #484047}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #463f46}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453e45}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #3f3945}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4435}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #46434b}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #473f45}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4b4247}p.p11 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4c474e}p.p12 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464247}span.s1 {color: #4b6f}span.s2 {color: #67564span.s3 {color: #635f67}span.s4 {color: #7f7b7b}span.s5 {color: #635251}span.s6 {color: #435263}span.s7 {color: #6f6b69}span.s8 {color: #615456}span.s9 {color: #7f7b7f}span.s10 {color: #6b6b6b}span.s11 {font: 6.0px Helvetica}span.s12 {color: #615454}span.s13 {color: #7f7f7f}span.s14 {color: #5c5b65}span.s15 {font: 9.0px Helvetica}span.s16 {color: #6f6b73}span.s17 {color: #7b7span.s18 {color: #4e5c70} 分子就是浮动和固定的利率差 * 本金,那0.5是什么呢。
NO.PZ2020021204000049 问题如下 Suppose ththe six-month Libor rate is 5%, the forwarLibor rate for the periobetween 0.5 an1.0 yeis 5.6% anthe forwarLibor rate for the periobetween 1.0 an1.5 years is 6.0. The two-yeLibor swrate is 5.7%. All risk-free rates are 4.5%. Whis the forwarLibor rate for the periobetween 1.5 an2.0 years? All rates are expressewith semi-annucompounng.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #443e44}span.s1 {color: #4869}span.s2 {color: #65544b}span.s3 {color: #2f496 A swwhere 5.7% is paianLibor is receiveis worth zero. Per 100 of principal, first FRA is worth:0.5 X (0.05 − 0.057) X 1001 + 0.045/2\frac{0.5\;X\;(0.05\;-\;0.057)\;X\;100}{1\;+\;0.045/2}1+0.045/20.5X(0.05−0.057)X100= -0.342The seconFRA is worth:0.5 X (0.056 − 0.057) X 100(1 + 0.045/2)2\frac{0.5\;X\;(0.056\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^2}(1+0.045/2)20.5X(0.056−0.057)X100= -0.048The thirFRA is worth:0.5 X (0.060 − 0.057) X 100(1 + 0.045/2)3\frac{0.5\;X\;(0.060\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^3}(1+0.045/2)30.5X(0.060−0.057)X100= 0.14If the requireforwarrate is R then:0.5 X (R − 0.057) X 100(1 + 0.045/2)4\frac{0.5\;X\;(R\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^4}(1+0.045/2)40.5X(R−0.057)X100- 0.342 - 0.048 + 0.140 = 0This csolveto give R = 0.0625. The forwarrate for the periobetween 1.5 an2.0 years is 6.25% (semiannually compoun.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #443f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453f47}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #484047}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #463f46}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453e45}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #3f3945}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4435}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #46434b}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #473f45}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4b4247}p.p11 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4c474e}p.p12 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464247}span.s1 {color: #4b6f}span.s2 {color: #67564span.s3 {color: #635f67}span.s4 {color: #7f7b7b}span.s5 {color: #635251}span.s6 {color: #435263}span.s7 {color: #6f6b69}span.s8 {color: #615456}span.s9 {color: #7f7b7f}span.s10 {color: #6b6b6b}span.s11 {font: 6.0px Helvetica}span.s12 {color: #615454}span.s13 {color: #7f7f7f}span.s14 {color: #5c5b65}span.s15 {font: 9.0px Helvetica}span.s16 {color: #6f6b73}span.s17 {color: #7b7span.s18 {color: #4e5c70} 假设本金100,每期固定coupon 2.85,那么2.85/(1+5%/2)+2.85/(1+5.6%/2) 2 +2.85/(1+6%/2) 3 +102.85/(1+X/2) 4 =100倒算X,为什么不可以?
NO.PZ2020021204000049 问题如下 Suppose ththe six-month Libor rate is 5%, the forwarLibor rate for the periobetween 0.5 an1.0 yeis 5.6% anthe forwarLibor rate for the periobetween 1.0 an1.5 years is 6.0. The two-yeLibor swrate is 5.7%. All risk-free rates are 4.5%. Whis the forwarLibor rate for the periobetween 1.5 an2.0 years? All rates are expressewith semi-annucompounng.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #443e44}span.s1 {color: #4869}span.s2 {color: #65544b}span.s3 {color: #2f496 A swwhere 5.7% is paianLibor is receiveis worth zero. Per 100 of principal, first FRA is worth:0.5 X (0.05 − 0.057) X 1001 + 0.045/2\frac{0.5\;X\;(0.05\;-\;0.057)\;X\;100}{1\;+\;0.045/2}1+0.045/20.5X(0.05−0.057)X100= -0.342The seconFRA is worth:0.5 X (0.056 − 0.057) X 100(1 + 0.045/2)2\frac{0.5\;X\;(0.056\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^2}(1+0.045/2)20.5X(0.056−0.057)X100= -0.048The thirFRA is worth:0.5 X (0.060 − 0.057) X 100(1 + 0.045/2)3\frac{0.5\;X\;(0.060\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^3}(1+0.045/2)30.5X(0.060−0.057)X100= 0.14If the requireforwarrate is R then:0.5 X (R − 0.057) X 100(1 + 0.045/2)4\frac{0.5\;X\;(R\;-\;0.057)\;X\;100}{{(1\;+\;0.045/2)}^4}(1+0.045/2)40.5X(R−0.057)X100- 0.342 - 0.048 + 0.140 = 0This csolveto give R = 0.0625. The forwarrate for the periobetween 1.5 an2.0 years is 6.25% (semiannually compoun.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #443f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453f47}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #484047}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #463f46}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453e45}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #3f3945}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4435}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #46434b}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #473f45}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4b4247}p.p11 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4c474e}p.p12 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464247}span.s1 {color: #4b6f}span.s2 {color: #67564span.s3 {color: #635f67}span.s4 {color: #7f7b7b}span.s5 {color: #635251}span.s6 {color: #435263}span.s7 {color: #6f6b69}span.s8 {color: #615456}span.s9 {color: #7f7b7f}span.s10 {color: #6b6b6b}span.s11 {font: 6.0px Helvetica}span.s12 {color: #615454}span.s13 {color: #7f7f7f}span.s14 {color: #5c5b65}span.s15 {font: 9.0px Helvetica}span.s16 {color: #6f6b73}span.s17 {color: #7b7span.s18 {color: #4e5c70} 1、为什么用无风险利率折现?,固定利率产生的现金流折现不是应该用浮动利率么?2、为什么不能直接这么算:(1+5%/2)(1+5.6%/2)(1+6%/2)(1+X/2)=(1+5.7%/2) 4 这样算出来X=6.2%现金流不就是应该为了各期利率相乘和YTM一致一样的道理么?