Summary: Forward Pricing & Valuation: Investment Assets with Known Dollar Income

Table 2.3. Forward Pricing & Valuation: Investment Assets with Known Dollar Income

Notations:
T = Forward contract maturity I0 = PV0(the income during the period (0, T)) , discounted back to time 0 It = PVt(the income during the period (t, T)), discounted back to time t S0 = spot price of the underlying at t=0 St = spot price of the underlying at t > 0, but before maturity F(t,T) = price at t (any time before maturity) of a forward contract with maturity T Vt2(t1,T) = The present value as of t2 of F(t1,T), t1 ≤ t2 ≤ T
Pricing of a forward at  t = T:
F(t,T) = (St – It) · EXP(rt,T  · (T-t))       continuous compounding F(t,T) = (St – It) · (1+ rt,T)(T-t)             discrete compounding Note:  When t=0, the two equations yield: F(0,T) = (S0 – I0) · EXP(r0,T · T) F(0,T) = (S0 – I0) · (1+r0,T)T
Value of an existing long forward, F(0,T), discounted back to time t (0 < t < T):
Vt (0,T)= St - It – F(0,T)/EXP(rt,T · (T-t))     continuous compounding Vt (0,T)= St - It – F(0,T)/(1+rt,T)(T-t)           discrete compounding