Chapter4. Term Structure of Interest Rate || Part.3

Short Rates

• short rates : a simpler way to calculate all future spot rates
  모든 걸 step by step으로 계산하는 건 너무 귀찮아.....한 번에 계산하는 방법임
• Short rate at time k is the forward rate from k to k+1
  k에서 플러스 1만 함(무조건 1년이네)

• spot => 끝나는 점 표기 / forward rate => 시작 + 끝나는 점 표기  / r(short) => 시작일만 표기

• Short rates form a convenient basis for generating all other rates

4.8 Duration

Duration

• duration is a measure of interest rate sensitivity

• In Chapter 3, duration was the sensitivity with respect to yield

• In the term structure framework, yield is not a fundamental quantity
  기간에 따라서 yield는 바꼈었어서 fundamental이 아님

• Instead, we can consider parallel shifts in the spot rate curve
  그래서 spot rate curve를 활용하는 것

음....잘 이해가 안됨

Fisher-Weil Duration

• Best expressed using continuous compounding
• Given a cash flow series (X_t0, X_t1, X_t2, .... X_tn) and spot rate curve s_t, the present value is 

 

• Then, the Fisher-Weil duration is

• Note that this corresponds to the definition of duration as a PV-weighted average of the cash flow times

Summary of Chapter 4

• Yield curve

• Term structure

  • Spot rates and corresponding discount factors •

• Forward rates

  • Implied forward rate calculation

• Expectation dynamics

  • Spot rate forecasts and short rates

• Duration