Chapter 18: Term structure of interest rates

Question 1

Term structure

Answer 1

how interest rates for different maturities are related

Question 2

Yield curve theories

Answer 2

• Expectations theory - yong-term rate determined purely by expectations of current and future interest rates
• Liquidity theory - Investors will require additional yield for less liquid (longer term bonds)
• Market segmentations theory - yields at each terms will be determined by supply and demand at that term.

Question 3

Difference between a spot, short and foward rate

Answer 3

• A spot rate refers to the current price or bond yield over a period (T-t)
• A short rate refers to the instantaneous bond yield - it is the limit of the spot rate
• Forward rate refers to the price or yield for the same instrument at some point in the future

Question 4

Desirable characteristics for a term structure model

Answer 4

• Should be arbitage free
• Interest rates should ideally be positive - otherwise there is no incentive to save - but this condition is economy dependent
• The short rate r(t) and other rates should exhibit mean reverting behaviour - for consistency with emperical evidence
• Should either give rise to simple formulae for bond and option prices, or make it straightforward to compute prices using numerical techniques
• Should produce realistic dynamics - emperical evidence and yield curves
• Fit historic data adequately
• Can it be caliberated easily using market data

Question 4

Desirable characteristics for a term structure model

Answer 4

• Should be arbitage free
• Interest rates should ideally be positive - otherwise there is no incentive to save - but this condition is economy dependent
• The short rate r(t) and other rates should exhibit mean reverting behaviour - for consistency with emperical evidence
• Should either give rise to simple formulae for bond and option prices, or make it straightforward to compute prices using numerical techniques
• Should produce realistic dynamics - emperical evidence and yield curves
• Fit historic data adequately
• Can it be caliberated easily using market data
• Is the model flexible enough to cope properly with a range of derivative contracts