Arbitrage Bounds and Resale Pricing for Zero-Coupon Bonds

Summary

The question examines whether prices of two zero-coupon bonds, with different maturities and the same face value, imply an arbitrage opportunity. It challenges the idea that differing maturities alone prevent arbitrage: arbitrage analysis instead compares available cash flows and prices using strategies that can be financed or replicated. With only one- and two-year claims specified, the setup raises whether their quoted prices violate consistent discounting relationships.

It also asks for the fair resale value of the longer bond after six months. That value cannot be pinned down from the initial prices alone without assumptions or additional market information about discounting and the value of remaining future cash flows at that intermediate date. The document contains only the question and the learner’s initial reasoning, not a solution, so it supplies no demonstrated arbitrage trade or definitive interim price.

Key ideas

• Different maturities do not by themselves rule out arbitrage; cash flows and prices must be compared.
• Arbitrage requires a self-financing strategy with nonnegative future payoffs and a positive gain in some state.
• The prices of the stated bonds alone do not determine the longer bond’s resale price at an intermediate date.
• Interim valuation requires assumptions or market data about remaining discount factors.

Tags

# Arbitrage Opportunities in a Two-Zero Coupon Bond Market


# Arbitrage Opportunities in a Two-Zero Coupon Bond Market












Question: Suppose we are in a market where there are only two zero coupon bonds, both with a face value of 100: the first one with a maturity of one year and a price of 90, and the second one with a maturity of two years and a price of 40.

I would like to know if this market is free of arbitrage opportunities. If not, why? Additionally, if I were to purchase the two-year zero coupon bond, what would be the fair price after six months if I intended to resell it?

My Attempt: I don't see how the market could allow for arbitrage opportunities since the maturities are different, and there is no way to start with an initial wealth of 0 and end up with wealth > 0 in the future. Concerning the second question, I do not understand how it is possible to price such a coupon after six months, given that the shortest maturity coupon is only one year.

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