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LOS 34.b: Describe the forward pricing and forward
   rate models and calculate forward and spot prices                                          READING 34: THE TERM STRUCTURE AND
   and rates using those models.                                                                               INTEREST RATE DYNAMICS
                                                                                        MODULE 34.1: SPOT AND FORWARD RATES, PART 1
    THE FORWARD PRICING MODEL
    It values forward contracts based on arbitrage-free pricing. Consider two investors:




                                          Investor A purchases a $1 face value, zero-coupon                      EXAMPLE: Forward
                                            bond maturing in 2+3 years at a price of P (2+k3 .                   pricing: Calculate
                                                                                                                 the forward price two
                                                                                                                 years from now for a
                                                                                                                 $1 par, zero-coupon,
                                                                                                                 three-year bond
                               Investor B enters into a j =2 year forward contract to purchase a $1 face
                               value, zero-coupon bond maturing in k = 3 years at a price of F (2,3)             given the following
                                                                                                                 spot rates:
                                                                                                                 • two-year spot rate,
                                                                                                                    S = 4%;
                                                                                                                     2
        Investor B’s                                                                                             • five-year spot rate,
        cost today is the                                                                                           S = 6%.
        present value of the                                                                                         5
        cost: PV[F (2,3) ] or PF  .
                          j (2,3)



                                                                                        In other words, $0.8082 is the price agreed to
                                 F (2,3)  =  1/(1.06) ^ 5   =     0.7473  =   0.8083    today, to pay in two years, for a three-year bond
                                          1/(1.04) ^ 2              0.9246
                                                                                        that will pay $1 at maturity.

          Alternatively, calculate discount factors P and P   (j+k) .   The forward price of a three-year bond in two years, F   (2,3)
                                                       j
          P j  = P = 1 / (1 + 0.04) = 0.9246                            F (j,k) = P (j+k)  / P j
                                    2
                   2
                                     5
          P (j+k)  = P = 1 / (1 + 0.06) = 0.7473                        F (2,3)  = 0.7473 / 0.9246 = 0.8082
                   5
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