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Explain the pricing of equity forwards and futures, and work out their no-arbitrage value and say what it means

CFA® Level II · Derivatives and Risk Management · Pricing and Valuation of Forward Commitments · L2.DE.1.a

The idea

An equity forward price is the cost of buying the share now and carrying it to delivery, less what it pays you meanwhile. With discrete dividends, the spot price net of the dividends' present value is carried to delivery: F0 = (S0 − PV of dividends) × (1 + r)^T. With a continuous dividend yield δ, the yield is netted from the continuously compounded rate: F0 = S0 × e^((rc − δ)T). The contract starts at zero value. Later, the long is worth Vt = St − PV(remaining dividends) − F0 ÷ (1 + r)^(T − t). Futures price the same way when rates are not random, but reset to zero value at each daily settlement. The trap is forgetting to discount F0, or discounting it over the original rather than the remaining term.

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