Module 6 · Derivatives

Pricing and Valuation of Futures Contracts

EN: Futures price, basis, contango/backwardation, daily mark-to-market.
VN: Giá tương lai, basis, contango/backwardation, mark-to-market hằng ngày.

1. Futures Price Core

About: Same formula as forwards in theory. In practice futures-forward divergence small unless rates strongly correlate with the underlying.Tóm tắt: Giống forward về lý thuyết. Thực tế chênh lệch nhỏ trừ khi rate tương quan mạnh với underlying.

\[ F_0(T) = S_0 \cdot (1 + r)^{T} - FV(\text{benefits}) + FV(\text{costs}) \]

Same formula as forwards. In practice, futures and forwards prices may diverge slightly due to daily MTM and correlation between the underlying and interest rates.

Practice problem

Spot $200, r = 3%, T = 0.5 yr, no income. Compute theoretical futures price.

Show solution

F = 200 × (1.03)$^{0.5}$

= 200 × 1.0149

F ≈ $202.98

2. Basis Core

About: Basis = spot − futures. Converges to 0 at expiration. Basis risk = imperfect convergence between hedge and exposure.Tóm tắt: Basis = spot − futures. Hội tụ về 0 tại expiry. Basis risk = không hội tụ hoàn hảo.

\[ \text{Basis} = S_t - F_t \]

Basis converges to zero at expiration. Basis risk arises when hedging with a related but non-identical contract.

Practice problem

Spot $52, current futures $50.50. Compute basis.

Show solution

Basis = 52 − 50.50

Basis = $1.50 (positive → backwardation-like locally)

3. Contango vs Backwardation Concept

About: Contango: futures > spot (typical for storables). Backwardation: futures < spot (tight supply, high convenience yield). Drives roll yield.Tóm tắt: Contango (F > S, hàng dự trữ được). Backwardation (F < S, supply chặt). Quyết định roll yield.

Contango Futures price > expected future spot. Typical for storable commodities.
Backwardation Futures price < expected future spot. Often when supply is tight or convenience yield is high.

4. Daily Settlement Concept

About: Daily MTM eliminates counterparty default risk. Cash impact: gains/losses settle daily — interest-rate effect causes small futures-forward divergence.Tóm tắt: Daily MTM loại counterparty risk. Tác động: lời/lỗ settle hàng ngày — gây chênh lệch nhỏ với forward.

Each day, gains/losses are credited/debited to margin accounts. The daily settlement reduces counterparty risk but causes interest-rate effects on cash flows that distinguish futures from forwards.

Practice problem Practice

Practice problem

Crude oil spot = $80, 3-month futures = $78. Is the market in contango or backwardation?

Show solution

Futures < spot → backwardation.

Often signals tight supply / high convenience yield.

Backwardation