Lesson 3 of 6 · 11 min

Exploiting a mispriced forward, and the role of r and T

If a quoted forward price differs from S0(1+r)TS_0(1+r)^T, one replication strategy is cheaper than the other and the gap can be locked in as riskless profit.

In short

  • Forward too high: borrow, buy the asset, sell the forward. Profit at T = quoted F − S0(1+r)TS_0(1+r)^T.
  • Forward too low: short-sell the asset, lend the proceeds, buy the forward. Profit at T = S0(1+r)TS_0(1+r)^T − quoted F.
  • A higher risk-free rate or a longer time to delivery widens the gap between forward and spot when r > 0.
  • If r < 0, (1+r)T<1(1+r)^T < 1 and the forward price is below the spot price.
  • For most market participants the relevant borrowing rate is the repo rate, on funds collateralised by liquid securities.

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Exploiting a mispriced forward, and the role of r and T · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives