# Module 34.1 LOS 34.b: Calculate forward and spot prices using the forward pricing and forward rate models

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 Fj+k­.

P(j+k) = PjF(j,k)

Or F(j,k) = P(j+k)/Pj

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

[1 + S(j+k)](j+k) = (1 + Sj)[1 + f(j,k)]k

or

[1 + f(j,k)]k = [1 + S(j+k)](j+k) / (1 + Sj)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.