Time value, rates and linear products

The no-arbitrage forward

Prices a forward from carry alone, enforced by a trade anyone can put on today.

F0=(S0−D)erT,F0=S0e(r−q)TF_0 = (S_0 - D)e^{rT}, \qquad F_0 = S_0 e^{(r-q)T}

Where

DD
Present value of income received while holding.
qq
Continuous dividend yield, for an index.

Assumptions

  • Frictionless borrowing, shorting and storage. Add storage cost and subtract convenience yield for commodities.

Sanity check. It is not a forecast. Contango is positive carry, not an expectation of higher prices.

Where this is taught