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The YTM on a 6-month $20 par value zero-coupon bond is 18%, and the YTM on a 1-year $20 par value zero-coupon bond is 20%. These YTMs are semiannual BEYs. What would be the arbitrage-free price of a 1-year bond with coupon rate of 20% (semiannual payments) and par value of $1000

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Answer: $1,000.83

Explanation:

1 year coupon to be paid is:

= 20% * 1,000 * 1/2 semi annual

= $100

Relevant rates:

Zero coupon YTM to semi annual = 18%/2 = 9%

1 year bond = 20%/2 = 10%

Arbitrage free price:

=( Coupon / (1 + zero coupon rate) ^ no. of periods of zero coupon bond) + ((Coupon + Par value) / (1 + coupon rate of 1 year bond) ^no. of periods)

= (100 / (1 + 9%)¹) + ( (100 + 1,000) / ( 1 + 10%)²)

= $1,000.83

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