Interpreting Risk and the Market Price of Risk in Bond Models

Summary

The document raises questions about how to interpret the volatility term and market price of risk in a fixed income model. The author connects the negative sign on a risk-related volatility parameter with the inverse relationship between bond prices and yields, and asks why a negative market price of risk would imply a higher premium for holding long-term bonds.

It provides no model equations, definitions, derivation, or answer to these questions, so it does not establish what the signs mean or whether the suggested interpretation follows. The value is mainly in identifying an interpretive problem for readers studying term structure models. Any conclusions would require the model’s conventions and definitions, which are absent from the document.

Key ideas

• The author asks how a negative volatility-related term represents the inverse relationship between bond prices and yields.
• The document asks why a negative market price of risk could correspond to a larger premium for long-term bonds.
• No explanation or derivation is supplied, so the sign interpretation cannot be verified from this material.

Tags

# What is relationship Risk,Market Price of Risk and it's sign?


# What is relationship Risk,Market Price of Risk and it's sign?












Now I'm studying this textbook ( Fixed Income Securities by Veronesi ). But this page gets me some trouble.

I know that yield and Bond Price have negative relationship. But in this image, it says sigma_z(Risk)'s negative sign captures this risk. What does it mean totally? Why it should have negative sign to explain the fact that Bond yield and Bond Price have negative relationship?

Also, See Lambda term. it says lambda(r,t) < 0 would imply the higher risk premium that investors require in order to hold long term bonds. What is the reason? Why below zero imply the higher risk premium that investors require in order to hold long term bonds ?

I'm studying this textbook by myself and the contents is not enough to understand this intuition. I need your help sincerely.

Thanks.

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