4

The prices of 1 year, 2 year, 3 year and 4 year zero coupon bonds that pay $952,381, $898,473, $842,054 and $786,232. Calculate the annualised yields of the corresponding 1 year yield and 1 year forward rates.
Solution
ForwardRate
Bond Price 
Forward Rate 

Year 1 
952,381 

Year 2 
898,473 
6.0% 
Year 3 
842,054 
6.7% 
Year 4 
786,232 
7.1% 

Consider a 3 year bond with coupon rate 4% paid annually. Its yield to maturity is 6% and its face value is $1,000.

Calculate the price of the bond and duration of bond.
Bondprice
Inthis case, the coupon rate is 4 percent and the face value is $1,000,so the annual coupon is $40.
Presentvalue of semiannual coupons
Presentvalue of $1,000 principal
Theprice of the bond is the sum of the present value of coupons andprincipal
Durationof the Bond

Calculate the proportionate change in the bond price if yield to maturity increases to 6.10% using the following formula
ReferenceList
Bogomolov,R. and Khametov, V., 2016. Bayesian binomial zerocoupon bonds model.AppliedEconometrics,42,pp.100120.
Reher,G. and Wilfling, B., 2014. The valuation of European call options onzerocoupon bonds in the runup to a fixed exchangerate regime.InternationalReview of Economics & Finance,29,pp.483496.
Smith,D.J., 2011. Zero‐CouponBonds. BondMath: The Theory behind the Formulas,pp.2338.