Lesson 4 of 6 · 13 min

The cost of carry: income and costs of owning the underlying

The forward price is the spot price plus the net cost of carrying the asset to delivery: financing and other costs push it up, income and other benefits push it down.

In short

  • The cost of carry is the net of all costs and benefits of owning the underlying for the life of the contract.
  • The opportunity cost (risk-free rate) applies to every asset. Other costs (storage, insurance) raise F; benefits (dividends, coupons) lower it.
  • Known amounts, discrete: F0(T)=[S0−PV0(I)+PV0(C)](1+r)TF_0(T) = [S_0 - PV_0(I) + PV_0(C)](1+r)^T.
  • Rates, continuous: F0(T)=S0e(r+c−i)TF_0(T) = S_0 e^{(r + c - i)T}, e.g. an equity index with a dividend yield.
  • Costs > benefits → F > S. Benefits > costs → F < S. Equal → F = S.

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The cost of carry: income and costs of owning the underlying · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives