Not sure how CFAI defines the Forward Rate Model, but the way I approached these questions was to set 2 investment options: 1. Invest in n-year spot and 2. Invest in n-t year spot and reinvest at the unknown forward rate for t years. The accumulated amount should be identical under both to avoid arbitrage: using that aljibber that @S2000magician talks so much about gets you to the unknown forward rate.
Invest in 2 year spot: accumulated value is (1.055)^2
Invest in 1 year spot, reinvest at unknown forward rate: 1.05 * (1 + 1f1)
1.055^2 = 1.05 * (1 +1f1)
Aljibber happens here
1f1 = 6.0023%
Forward rate model: invest j year spot, reinvest at forward rate for k years has identical value to investing at (j+k) year spot rate.
So the variable S is the price of the spot rate bond for both j or k? i.e. there are two prices, each price is associated with j and the other price with k.
S looks like an interest rate in this context. I know S is often used for price in the CFA readings.
S for “spot”??
It must be a rate since this is the Forward Rate model. I like to learn verrrry slowly.
I’m starting to get the hang of this…