Question

Given a zero coupon bond with maturity of 5 years and yield of 2% (in annualized...

Given a zero coupon bond with maturity of 5 years and yield of 2% (in annualized units)

Calculate the price of this bond in a continuous and discrete models

What are the durations and convexity of this bond in discrete and continuous models?

Assume that the yield goes up by 0.5% calculate the returns directly and using duration convexity approximation

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Answer #1

Assumption in this question is Face value of bond is USD 1000

Price of bond using Discreet method: FV/(1+YTM)^5 i.e 1000/(1+4.00%)^5= USD 905.73

Price of bond using Contineous model:: FV/ exponential rate i.e 1000/1.105=USD 904.83

The Duration of Zero coupon bond under discrete and contineous model is maturity itself i.e 5 years. The convexity under discrete and contineous model is 27.17 and 27.14 respectively.

The price of bond using convexity approximation duration in case of discreet model is USD 884.14 and USD 883.27 under contineous model when yield gose up by 0.50%.

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