## Question

###### 2. (Spot update) Given the (y?aly) spol lale curve s = (50, 5 3,5 6, 5...

2. (Spot update) Given the (y?aly) spol lale curve s = (50, 5 3,5 6, 5 8, 60, 61), find the spot rate curve lol ???1 year

## Answers

Year(i) 1 2 3 4 5 6 Spot Rate (s) 5.00 5.30 5.60 5.80 6.00 6.10 Spot rate (f 1, i) - 5.601 5.901 5.968 6.067 6.027 Using formula= f1,2 = (( 1+s2)^2/(1+s1)) - 1

f1,2 = [(1 + 0.053)^2 / (1 + 0.05)] - 1

= 5.601

Using formula

(1+j2)

^{2}= (1+i1,2)(1+i2,3)(1 + j2)2 = 1.05601 * (1.056)^3 / (1 + 0.053)^2

(1 + j2)2 = 1.12151

j2 = (1.12151)^1/2 - 1

j2 = 5.901 %

(1+j3)3 = (1+i1,2)(1+i2,3) (1 +i3,4) = 1.05601 * 1.05901 * ( 1.058)^4 / (1.056)^3

(1+j3)3 = 1.189923

j3 = (1.189923)^1/3 - 1

j3 = 5.968

(1+j4)4 = 1.05601 * 1.05901 * 1.05968 *( 1.06)^5 / (1.058)^4

(1+j4)4 = 1.2657

j4 = (1.2657)^1/4 - 1

j4 = 6.067

(1+j5)5 = 1.05601 * 1.05901 * 1.05968 * 1.06067 * (1.061)^6 / (1.06)^5

(1+j5)5 = (1.339942)

j5 = (1.339942)^1/5 - 1

j5 = 6.027

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