Summary: Forward Pricing & Valuation: Investment Assets with Known Yields

Table 2.4. Forward Pricing & Valuation: Investment Assets with Known Yields

Investment Assets with Known Yields, discrete number of times
Dividends paid n times at known dividend rates of q1, q2, … qn  at t1 < t2 < . . . < tn < T Pricing of a forward price at t = 0: F0 = S0 (1 - q1) (1 - q2) . . . (1 - qn)erT Value at t = t1 of an existing forward long position, F0, discounted back to time t (0 < t < T): Vt1  = (Ft1 – F0 )e–r(T-t1) where Ft1 = St1Πi(1 - qi) where  Πi  (Xi) = Xi · Xi+1 · Xi+2 · . . . · XT · for all i such that t1 < i < T
Investment Assets with a Known Yield, continuous time
Dividends paid continuously at an annual rate of δ (delta) Pricing of a forward price at t = 0: F0 = S0 e(r – δ)T Value at t = t1 of an existing forward long position, F0, discounted back to time t (0 < t < T): Vt1  = (Ft1 – F0 )e–r(T-t1) = St1e- δ (T-t1) – F0 e–r(T-t1)