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Financial Derivatives from First Principles

A derivative is a contract whose value is derived from an underlying — a currency, a commodity, an equity, an index or a rate. The contract itself creates no new asset; it defines future cash flows between two parties. Three questions organize everything: what is the underlying, when does settlement occur, and who bears counterparty risk?

نویسنده: FinScope Derivatives Editorial Team · آخرین به‌روزرسانی: ۱۶ آبان ۱۴۰۵

اهداف یادگیری

  • Distinguish the four contract families: forwards, futures, swaps and options
  • Explain how central clearing and margining compress counterparty risk
  • Separate the three uses of derivatives with worked examples

The four contract families

A forward is a bilateral obligation to buy or sell the underlying at a future date at a price agreed today; it trades over the counter (OTC) with counterparty credit risk. A future is the same obligation, standardized and exchange-traded: fixed size and tick, daily mark-to-market settlement, and a central counterparty (CCP) guaranteeing performance. A swap exchanges periodic cash flows — the interest rate swap (fixed-vs-floating) is the most traded OTC instrument in existence. An option is different in kind: the buyer pays a premium for the right (not the obligation) to buy (call) or sell (put) at a strike. Right versus obligation changes the entire risk profile: an option buyer's loss is capped at the premium; a seller's loss scales with the market.

Clearing, margin and the compression of counterparty risk

OTC trades leave each party exposed to the other's default. The CCP absorbs this with three mechanisms: legal novation (it becomes buyer to every seller and seller to every buyer), initial margin sized to cover a bad day, and daily settlement that realizes gains and losses before they compound. When equity falls below maintenance margin, a margin call restores the position to the initial level; failing to fund it forces liquidation. This machinery works quietly in normal times and consumes liquidity violently in stressed ones — which is why institutional desks keep cash buffers above the minimum requirement.

Daily P&L (long future) = (F_t − F_{t−1}) × multiplier × contracts
Margin call = initial margin − equity (when equity < maintenance)
Daily settlement changes no cumulative P&L — it pulls the timing of cash forward and compresses credit exposure to one day.

Worked example: daily settlement on one futures contract

  1. A trader buys one gold futures contract for 100 oz at $2,000/oz.
  2. Day 2 close: $2,020 → +100 × 20 = +$200 credited to the margin account.
  3. Day 3 close: $1,995 → −100 × 25 = −$250 debited.
  4. Cumulative P&L: −$50, exactly the change in contract value from entry.

نتیجه: Daily settlement does not change cumulative P&L — it changes its timing, compressing counterparty exposure from the contract's life to one day. That compression is the architecture of trust in futures markets.

Three uses: hedging, arbitrage, speculation

Hedging offsets an existing risk: an exporter with dollar revenue sells currency futures to lock the conversion rate. Arbitrage builds a zero-investment, risk-free profit from mispriced pairs — buy spot, sell futures when the forward trades above its cost-of-carry fair value; this pressure pins futures to spot. Speculation deliberately accepts risk for return; it is the liquidity provider of last resort, and the most dangerous seat at the table. The same person may hedge operational revenue and run speculative views at the same time — the roles are positions, not identities.

پرسش‌های متداول

What is the core difference between futures and forwards?

Futures are standardized, exchange-traded, daily-settled and centrally cleared; forwards are customized OTC agreements with bilateral credit risk. Standardized exposures are easier to hedge with futures; exact amounts and dates are easier with forwards.

When is a margin call triggered?

When the account equity falls below the maintenance margin the exchange sets for that contract; the call restores equity to the initial margin level. Size positions for the worst plausible daily move, not for the minimum.

Which instrument should I hedge with?

Match the tool to the loss profile: standardized risk → futures; exact dates/amounts → forwards; protect from losses but keep upside → options. Always price in basis risk — the residual that remains after the best hedge.

منابع

  1. Hull, J. C. (2022). Options, Futures, and Other Derivatives (11th ed.), Ch. 1–2. Pearson.
  2. BIS, OTC Derivatives Statistics (quarterly).
  3. CME Group, Contract Specifications and Clearing documentation.

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