Understanding the Convexity Premium in Long-Dated Bonds

Summary

The document distinguishes the mechanical relationship between a bond’s price and its yield from the market value investors may assign to convexity. Discounted cash flows determine the price implied by a chosen yield; this calculation does not itself judge whether the bond’s convexity is valuable. The discussion instead frames the premium as a market pricing question about how expected gains and losses compare across bonds with different maturities.

A simplified example assumes a flat yield curve and a parallel yield move of one standard deviation. For equal DV01 exposure, a short bond has an approximately linear price response, while a longer bond also benefits from convexity. The explanation suggests that a higher price for the long bond can offset this expected convexity benefit across its life. This is an intuition, not a full valuation method: yield changes vary by maturity, and real yield curves do not always move in parallel. The example does not provide a general formula for estimating the premium.

Key ideas

• Discounted cash flows mechanically map a given yield to a bond price, without separately valuing convexity.
• The convexity premium is a market pricing question about expected returns across bonds.
• For a given DV01 exposure, a long bond can gain from convexity in addition to its linear price response.
• The example relies on parallel yield moves and simplifies the maturity dependence of yield volatility.

Tags

# How to price the convexity premium on a bond?


# How to price the convexity premium on a bond?












It appears to be the case that convexity is a benefit that investors are often willing to pay a premium for. How does this factor into the bond's theoretical price? And why is it not part of the original equation for computing a bond's price given a yield (with discounted cash flows)?

## Answer by dm63 (score 4, accepted)

https://quant.stackexchange.com/a/81196

The relationship between price and yield is purely mechanical- the yield is just the discount rate that makes the present value equal to the price. There is no judgment about convexity within the calculation.

What you are asking is how to figure out the value of convexity in long dated bonds. Here is a simplified model: imagine a 5% flat yield curve so that bonds of all maturities yield 5%. Now imagine a parallel, one standard deviation move in yields (calculated from historical or implied volatilities), and let’s say this is 6bp. We then propose that the expected p/l of all bonds should be the same( for a given dv01 position) . For example the p/l of a very short dated bond will simply be 6xdv01, but the p/l of the long dated bond will be 6xdv01+ a convexity benefit. The point is, the market will increase the price of the long dated bond to offset the convexity benefit of a one standard deviation move, summed over the life of the long dated bond. (Note this is simplified-the one standard deviation is different for different maturities , and yield curve does not move in parallel all the time. But that’s the principle).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.