Pricing, Valuation and Cost of Carry
Futures fair value
Futures are priced from the spot price plus the cost of carry less income. For a financial asset, a common continuous-compounding formula is F = S × e^((r − q)T), where r is the risk-free rate, q is the dividend or income yield and T is time to expiry. If carry exceeds income, the futures trades above spot; if income exceeds carry, it trades below spot.
Basis and convergence
Basis is the difference between spot and futures. At expiry, basis converges to zero because the futures price equals the settlement price. Contango describes an upward-sloping futures curve; backwardation describes a downward-sloping curve. The exam tests whether you can identify the direction of the curve and the sign of the carry.
Options valuation
An option premium has intrinsic value and time value. Black-Scholes inputs are spot, strike, time, volatility, risk-free rate and dividends. The Greeks describe sensitivities: delta, gamma, theta, vega and rho. Put-call parity links European calls and puts: c + Ke^(−rT) = p + S. Volatility affects the premium but not the direction of the underlying.
Worked example
An index is at 12,000, the risk-free rate is 3%, the dividend yield is 4% and expiry is six months. F = 12,000 × e^((0.03 − 0.04) × 0.5) = 12,000 × e^(−0.005) ≈ 11,940. The reasoning is that dividend income exceeds financing cost, so the futures price is below spot.
Traps
Adding dividends instead of subtracting them; mixing simple and continuous compounding; assuming high volatility means a bullish view; and forgetting that basis converges at expiry.