Suppose that x is the continuously compounded yield to maturity on a zero-coupon bond that pays off $1 at time T. Assume that x follows the process: dx = a (x₁ - x) dt + sx dz where a, x0, and s are positive constants and dz is a Wiener process. What is the process followed by the bond price?

Suppose that x is the continuously compounded yield to maturity on a zero-coupon bond that pays off $1 at time T. Assume that x follows the process: dx = a (x₁ - x) dt + sx dz where a, x0, and s are positive constants and dz is a Wiener process. What is the process followed by the bond price?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Concept explainers

Treasury Market

On-the-run securities are the most recently issued securities in the market depth and are therefore traded at some premium. The off-the-run securities are the ones issued just before the most recent ones. The on-the-run securities have a lower yield to the investor than the off-the-run securities.

Question

Suppose that x is the continuously compounded yield to maturity on a zero-coupon
bond that pays off $1 at time T. Assume that x follows the process:
dx = a (x₁ - x) dt + sx dz
where a, x0, and s are positive constants and dz is a Wiener process.
What is the process followed by the bond price?
Solutions:

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Please step by step solutions
P(4) is the value of a zero-coupon bond O at node (3, 1) and which matures at time T = 7. at node (3, 1) and which matures at time T = 5. at node (4, 1) and which matures at time T = 7. at node (3, 1) and which matures at time T = 4.

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