The forward
pricing model states that two investors should be indifferent between
paying P for a j+k year zero coupon, $1 FV contract and paying the PV of a j
year zero coupon $1 FV forward contract maturing in k years at a price of F_{j+k.}

P_{(j+k)} = P_{j}F_{(j,k) }

Or F_{(j,k)} = P_{(j+k)}/P_{j}

The forward rate model relates forward and spot rates as follows:

[1 + S_{(j+k)}]^{(j+k)} = (1 + S_{j})^{j }[1
+ *f*(j,k)]^{k}

or

[1 + *f*(j,k)]^{k} = [1 + S_{(j+k)}]^{(j+k)} /
(1 + S_{j})^{j}

This equation suggests that the forward rate *f*(2,3)
should make investors indifferent between buying a five-year zero-coupon bond
versus buying a two-year zero-coupon bond and at maturity reinvesting the
principal for three additional years.

If the yield curve is upward sloping, [i.e., S(j+k) > Sj], then the forward rate corresponding to the period from j to k [i.e., f(j,k)] will be greater than the spot rate for maturity j+k [i.e., S(j+k)]. The opposite is true if the curve is downward sloping.