• Global Frameworks: CFA Level 2 (Derivatives Pricing), ACCA Advanced Financial Management (AFM).

1. The Arbitrage-Free Baseline (The Principle of No-Arbitrage)
 
Forward contract pricing does not depend on subjective forecasts of where an asset’s price will move. Instead, it relies on the Principle of No-Arbitrage. This principle states that if two identical investments yield the same cash flows in the future, they must sell for the same price today. If prices disconnect, market participants will execute risk-free trades that instantly eliminate the mispricing and restore equilibrium.
 
2. Forward Pricing for Underlying Assets with Zero Storage Costs
The forward price (Fâ‚€) is the delivery price set today that forces the initial market value of the forward contract to exactly zero. For a non-income-producing asset (like a growth stock or zero-coupon bond), the forward price is calculated by compounding the spot asset price (Sâ‚€) to maturity at the risk-free rate (r):
F₀ = S₀ × e^(r × T)
 
Where T is the time to contract maturity in years, utilizing continuous compounding conventions.
 
3. Forward Pricing Adjustments for Costs and Benefits
If holding the underlying asset generates cash inflows (e.g., stock dividends, bond coupons) or costs (e.g., commodity storage fees), these items must be factored into the pricing matrix:
  • Discrete Dividends / Inflows: Income reduces the net cost of holding the asset over the contract’s lifespan. The present value of this income (I) is subtracted from the spot price:

    F₀ = (S₀ − I) × e^(r × T)
  • Continuous Income Yield (q): For assets like stock indices or currencies that pay a continuous yield, the formula scales to:

    F₀ = (S₀ − I) × e^(r × T)
  • Storage Costs (u) and Convenience Yield (y): For physical commodities, storage costs increase the forward price, while the Convenience Yield (the operational advantage of physically holding the inventory during shortages) reduces the forward price:

    F₀ = S₀ × e^((r + u − y) × T)

4. Valuation of a Forward Contract Over Time
While the initial value of a forward contract is zero, its value (\(V_{t}\)) fluctuates as the underlying spot price changes. For a long forward position at time t, the valuation equation is:

V_t = S_t − [F₀ × e^(−r × (T − t))]
 
PreviousNext