Forward rate model

Hi folks,

I need some help understanding the economics of this equation

This timeline should help in interpreting the notation:

In the equation above:

  • S(j+k) = spot rate at Year j+k
  • Sj = spot rate at Year j
  • f(j,k) = annualized interest rate for a k-year loan starting in Year j

I need help understanding the economics of the equation. For example, on the left hand side of the equation, why do we use the spot rate at Year j+k for compounding into the future? Isn’t this rate used for discounting?

Thanks in advance, folks.

You have 2 choices for investing money for (j+k) years:

  1. Invest for (j+k) years at the (j+k) spot rate OR
  2. Invest for j years at the j year spot rate and then reinvest for another k years at the k year forward rate at time j

To avoid arbitrage, option 1 and option 2 need to produce the same accumulated value at time j+k.

Thank you @breadmaker

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