Answer to Question #204973 in Financial Math for Stefano Balters

Question

1. At time t=0 the following instruments are quoted in an arbitrage-free market

• a ZCB with maturity 2 years, notional 100 and priced 96.2 euros;
• a coupon bond with maturity 2 years, notional 100, paying annual coupons, with coupon rate 2.2% (on the notional) and priced 100.5 euros;
• an immediate postponed annuity paying 3 instalments of 40 euros, priced 116.2 euros Determine i(0, 1), i(0, 2) and i(0, 3).

Answer 1

The simplest way to calculate a bond yield is to divide its coupon payment by the face value of the bond. This is called the coupon rate. If a bond has a face value of 116.2 euros. and made interest or coupon payments of 40 euros per year, then its coupon rate is 10% (116.2eruos)/96.2 erouros= 21℅

Determine 1) (0, 1) which will be per value/ (r +1 years) spot rate

(96.2÷2.2/100+ 1+0)+ (96.2÷2.2/100+1+1)

( 96.2/0.022+1{96.2/0.022+2}) 8748.45454 answer

2) (0,2) (96.2/0.022+0) + (96.2/0.022+2)= 8747.45454ans

3) ( 96.2/0.022)+ (96.2/0.022+ 3)= 8748.45455 answer