I am currently reading some notes which state that
For one-factor models, the value of a European option on a coupon bond can be calculated as the sum of European options on zero-coupon bonds (ZCBs). The process is described in Hull Section 31.4. For two-factor models, this doesn’t apply because yield curve changes could cause ZCBs to increase in value at some durations, whilst decreasing in value at other durations.
If I am not mistaken (please correct me if I am), a one factor model cannot produce varying shapes of future yield curve (i.e. it gives rise to parallel shifts in the yield curve over time). By contrast, a two-factor model allows the shape of the yield curve to change over time.
However, I am struggling to understany why this difference means that the value of a European option on a coupon bond can be calculated as the sum of European options on ZCBs for a two factor model. That is, why this would be the case on account of the yield curve being able to change in shape.
Could someone please help me to see why this is the case?