Book contents
- Frontmatter
- Dedication
- Contents
- Acknowledgements
- Symbols and Abbreviations
- Part I The Foundations
- Part II The Building Blocks: A First Look
- Part III The Conditions of No-Arbitrage
- Part IV Solving the Models
- Part V The Value of Convexity
- Part VI Excess Returns
- Part VII What the Models Tell Us
- 30 The Doubly Mean-Reverting Vasicek Model
- 31 Real Yields, Nominal Yields and Inflation: The D'Amico–Kim–Wei Model
- 32 From Snapshots to Structural Models: The Diebold–Rudebusch Approach
- 33 Principal Components as State Variables of Affine Models: The PCA Affine Approach
- 34 Generalizations: The Adrian–Crump–Moench Model
- 35 An Affine, Stochastic-Market-Price-of-Risk Model
- 36 Conclusions
- References
- Index
35 - An Affine, Stochastic-Market-Price-of-Risk Model
from Part VII - What the Models Tell Us
Published online by Cambridge University Press: 25 May 2018
- Frontmatter
- Dedication
- Contents
- Acknowledgements
- Symbols and Abbreviations
- Part I The Foundations
- Part II The Building Blocks: A First Look
- Part III The Conditions of No-Arbitrage
- Part IV Solving the Models
- Part V The Value of Convexity
- Part VI Excess Returns
- Part VII What the Models Tell Us
- 30 The Doubly Mean-Reverting Vasicek Model
- 31 Real Yields, Nominal Yields and Inflation: The D'Amico–Kim–Wei Model
- 32 From Snapshots to Structural Models: The Diebold–Rudebusch Approach
- 33 Principal Components as State Variables of Affine Models: The PCA Affine Approach
- 34 Generalizations: The Adrian–Crump–Moench Model
- 35 An Affine, Stochastic-Market-Price-of-Risk Model
- 36 Conclusions
- References
- Index
Summary
A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.” The scientist gave a superior smile before replying, “What is the tortoise standing on?” “You're very clever, young man, very clever,” said the old lady. “But it's turtles all the way down!”
Stephen Hawking, A Brief History of Time, 1988THE PURPOSE OF THIS CHAPTER
If one uses a structural affine model to describe the yield curve, one has to establish an affine relationship between the state variables and the market price of risk. In non-trivial cases (ie, if the affine relationship is not just a constant), the resulting behaviour for the market price of risk is stochastic – because the state variables are stochastic. However, if the values of the state variables are known (in statistical parlance, if one conditions on a particular set of values for the state variables), there can be one and only one possible value for the market price of risk.
So, for instance, if one of the state variables is the slope of the yield curve, and, on the basis of our regression studies, we impose a deterministic (affine) relationship between market price of risk and the yield curve slope, then the instantaneous expected excess return will always be exactly the same whenever the slope has a certain value.
In this chapter we break the deterministic link between the market price of risk and the return-predicting factor. We do so by introducing a model that enforces the regularities uncovered by the empirical investigation on average, but not at each point in time. We argue that this will result in a more realistic decomposition of the observed market yields into an expectation and a riskpremiumcomponent.
- Type
- Chapter
- Information
- Bond Pricing and Yield Curve ModelingA Structural Approach, pp. 688 - 713Publisher: Cambridge University PressPrint publication year: 2018