Concave Shape of the Yield Curve and No Arbitrage

TL;DR

This paper explains the concave shape of the yield curve from a trading perspective, addressing a gap in economic theory understanding of its typical concavity.

Contribution

It provides a novel explanation for the yield curve's concavity based on trading perspectives, filling a theoretical gap.

Findings

Yield curve is generally concave across currencies.

The paper offers a new trading-based explanation for the curve's shape.

Addresses the lack of economic theory explanation for concavity.

Abstract

In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30 years. For each currency, the corresponding curve shows the relation between the level of the interest rates (or cost of borrowing) and the time to maturity. For example, the U.S. dollar interest rates paid on U.S. Treasury securities for various maturities are plotted as the US treasury curve. For the same currency, if the swap market is used, we could also plot the swap rates across the tenors which would be called the swap curve.Even the yield curve can be at, upward or downward (inverted), however, yield curve is generally concave. There is a lack of explanation of the concavity of the yield curve shape from economics theory. We offer in this article an explanation of the concavity shape of the yield curve from trading perspectives.