Futures & Basis Exercises

Derivatives Theory Futures Pricing: Cost of Carry, Basis and Cash-and-Carry Arbitrage Futures & Basis Exercises

Market Making Trainer ~10 min

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Overview

The Futures & Basis Drills train pricing a future from its spot. With simple interest the fair future is spot times one plus net carry times time, where net carry is financing minus the income the asset pays. The basis is future minus spot and shrinks to zero at delivery. The exercises isolate fair value and basis (including how the basis converges), carry and the curve (net carry, contango and backwardation, the commodity case with storage and convenience yield) and cash-and-carry arbitrage (rich or cheap against fair value, which legs lock it, profit per unit and per contract). The scenario run follows one index future from carry to settlement: fair value, the arbitrage, the ETF route into the basket, quoting, hedging a fill, basis decay halfway to delivery, a dividend shock and the final P&L.

What's Covered

Fair value & basis F = S × (1 + (r − q) × T). Basis = F − S, and it decays in proportion to time left.

Carry & the curve Net carry = financing − income (plus storage, minus convenience yield for commodities). Positive carry means contango, negative means backwardation.

Cash-and-carry arb Future rich: buy spot, sell the future, carry to delivery. Future cheap: the reverse. Profit per unit is the gap to fair value, per contract times the multiplier.

Scenario run One index future taken from carry to settlement against the clock. You price it, spot the arb, route through the ETF, quote, hedge a fill, watch the basis decay, absorb a dividend change and book the P&L, with the working shown at the end.