Lesson 3 of 7 · 12 min

Forwards on assets with costs and benefits

When holding the underlying brings income or costs, adjust the spot price by the present value of the remaining income (subtract) and costs (add), both at inception and when marking to market.

In short

  • Cost of carry = net of all costs and benefits of owning the underlying.
  • Forward price: F0(T)=(S0−PV0(I)+PV0(C))(1+r)TF_0(T) = (S_0 - PV_0(I) + PV_0(C))(1+r)^T. Income lowers the forward price; costs raise it.
  • MTM value of a long at t: Vt(T)=(St−PVt(I)+PVt(C))−F0(T)(1+r)−(T−t)V_t(T) = (S_t - PV_t(I) + PV_t(C)) - F_0(T)(1+r)^{-(T-t)}.
  • Only cash flows still to come between t and T count; income already paid is gone.
  • Value is still zero at inception and equal to ST−F0(T)S_T - F_0(T) at maturity, because the forward price already reflects the carry.

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Forwards on assets with costs and benefits · Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities