Risk-Neutral HJM Yields and the Term Premium Distinction

Summary

The note asks whether a government bond yield can be divided into an expectations component and a term premium within the Heath–Jarrow–Morton framework. It distinguishes a real-world view of yields, in which investors may describe yields as expectations plus a premium, from the pricing measure used in arbitrage-free models.

In the risk-neutral measure used by HJM-style pricing, asset values are represented through discounted expectations of future cash flows. This framework is calibrated to bonds or swaps to avoid arbitrage, so it does not directly provide the same real-world term-premium decomposition. The answer is conceptual and brief: it clarifies the role of the pricing measure but gives no estimation procedure for extracting a real-world premium or empirical evidence about its size.

Key ideas

• Some market interpretations decompose government yields into expected rates and a term premium.
• HJM pricing uses a risk-neutral measure to value future cash flows.
• Risk-neutral pricing is designed to remain arbitrage-free relative to calibrated bonds or swaps.
• A risk-neutral model does not itself provide a real-world expectations-plus-term-premium estimate.
• The note explains the conceptual distinction without giving an empirical decomposition method.

Tags

# HJM framework and expectations hypothesis, updated


# HJM framework and expectations hypothesis, updated












Is there a way one can decompose the yield of say a government bond with respect the the HJM framework? (into say an expectations component and a term premium component).

As far as I can see the HJM framework covers the "expectations hypotheses part" but not the term premium part if there is such a decomposition.

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/51561

In the real world, many people believe that the yield of a government bond consists of an expectations part plus a term premium. However financial models such as HJM are built in a “risk -neutral” probability measure, with respect to which every asset is the expectation of future cash flows without regard to any term premium. This is done to ensure the models are arbitrage free versus the bonds or swaps with which it is calibrated.

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