Valuation models

Futures and forwards

Equity and commodity forwards and futures by cost of carry, FX futures by covered interest parity, interest rate futures from the forward curve, bond forwards and bond futures from the cheapest to deliver, with value and PV01.

Inputs

Results

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Methodology

Conventions

  • Forwards are worth the discounted gain of the fair forward over the contract price; futures are margined, so undiscounted.
  • No futures convexity adjustment and no bond future delivery option.

References

  • Hull, Options, Futures, and Other Derivatives, ch. 5–6

Formulas

Cost of carry
F = S e^((r + u − q − y) T)
FX
F = S · D_base(T) / D_quote(T)
Rate future
P = 100 (1 − F(t1, t2))
Bond forward
F = Σ_{t_i > T} c_i D(t_i) / D(T) − AI(T)