Arbitraging a coupon bond against zeros

Two zero-coupon bonds (each $100 face) trade in the market: the 1-year zero at $96.00 and the 2-year zero at $90.00. A 2-year bond with $100 face paying an 8% annual coupon trades at $103.50. A riskless arbitrage exists. What profit (in dollars, to two decimals) can you lock in per coupon bond?

Show hints (2)+
  1. Replicate the coupon bond's cash flows using the two zeros - that cost is its fair value.
  2. Fair value =8×0.96+108×0.90=8\times0.96+108\times0.90; the arb is fair value minus the $103.50 market price.

Answer

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1.38 (± 0.01)

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Asked at: Multi-Strategy Quant, ETF Market-Making

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