A one-factor bond pricing model implies that interest-rates of all maturities are driven by a single source of stochastic randomness.For example the system of interest rates may be described by the following equation: $d r ( T ) = \alpha ( r ( T ) , T ) d t + \sigma ( r ( T ) , T ) d W , \quad \forall T$ where $T$ denotes the maturity of different rates.A single-factor model implies that
A)All rates either move up together or all move down together.
B)The yield curve experience parallel shifts.
C)Instantaneous changes in rates of all maturities are perfectly positively or negatively correlated with each other.
D)Twists in shape of the yield curve are not possible.

Question

Quizplus · Accepted Answer

A one-factor model implies that changes in interest rates across different maturities are perfectly correlated, meaning they move together, either positively or negatively.

A One-Factor Bond Pricing Model Implies That Interest-Rates of All dr(T)=α(r(T),T)dt+σ(r(T),T)dW,∀Td r ( T ) = \alpha ( r ( T ) , T ) d t + \sigma ( r ( T ) , T ) d W , \quad \forall Tdr(T)=α(r(T),T)dt+σ(r(T),T)dW,∀T

A One-Factor Bond Pricing Model Implies That Interest-Rates of All $d r ( T ) = \alpha ( r ( T ) , T ) d t + \sigma ( r ( T ) , T ) d W , \quad \forall T$