Chapter 6 · Derivatives

A financial instrument whose value is DERIVED from an underlying — equity, index, bond, interest rate, FX rate, commodity, or credit event. Derivatives do NOT represent direct ownership of the underlying.

• Hedging — use derivatives to OFFSET an existing risk exposure. Farmer sells wheat futures to lock in a price ahead of harvest.
• Speculation — take a directional bet on the underlying, typically with LEVERAGE built in. Small initial outlay controls a much larger notional.
• Arbitrage — exploit small price differences between related instruments (e.g. index future vs constituent basket) for low-risk profit.

Same instruments; different intent.

A small initial outlay (margin, or an option premium) controls a much LARGER notional exposure to the underlying. £10k margin can control a £100k futures position.

Cuts both ways — magnifies gains AND losses. Why retail-friendly derivative products (CFDs, spread bets) are heavily regulated.

Pre-fees: one side's gain = the other side's loss. Different from equities (where all shareholders can profit from a company's growth) or bonds (where coupons come from outside the contract). Important for framing risk.

A standardised, exchange-traded contract obliging the BUYER to purchase (and the SELLER to deliver) a specified asset at a specified price on a specified future date.

Note the word OBLIGATION. Both sides are locked in. Compare with options (where only the writer has an obligation; the buyer has a right).

LONG the future = buyer / agreed to TAKE delivery. Profits when the underlying rises.

SHORT the future = seller / agreed to DELIVER. Profits when the underlying falls.

KEY feature: contract specs (size, expiry, deliverable) are STANDARDISED. This enables exchange trading + central clearing. The clearing house (CCP) becomes the counterparty to both sides — eliminating bilateral counterparty risk.

Trade-off: less flexibility than an OTC forward.

A small deposit (typically 5–15% of the notional value) lodged with the exchange / clearing house as SECURITY against losses. Held by the CCP for the life of the position; returned at expiry net of profit/loss. Sized to cover 1–3 days of potential adverse moves under stress.

Futures positions are marked-to-market DAILY. Profits and losses are credited/debited from the margin account each day. If margin falls below a maintenance level, a MARGIN CALL demands a top-up.

Purpose: prevents large losses building up. Losers pay winners daily rather than at expiry.

The MINIMUM price movement allowed on a contract. Each contract specifies its tick size + tick value. Enables consistent P&L calculation.

Physical settlement: actual delivery of the underlying (e.g. commodity futures — oil, wheat).

Cash settlement: settle in cash based on the difference between contract price and final index value. Used for index futures (S&P 500, FTSE 100) where physical delivery of 500 stocks would be impractical.

Most futures positions are CLOSED OUT before expiry via an offsetting trade — the counterparty rarely takes delivery.

Forward: OTC (bespoke), custom terms, settled at expiry, counterparty risk.
Future: standardised, exchange-traded, central clearing, daily mark-to-market, tick size, standard expiries.

Economically similar; operationally very different.

The BUYER of an option has the RIGHT (but not the obligation) to buy or sell an underlying at a specified strike price on or before a specified date.

The buyer pays a PREMIUM upfront for that right. May or may not exercise.

CALL: right to BUY the underlying at the strike. Used to speculate that the underlying will RISE, or hedge a future purchase.

PUT: right to SELL the underlying at the strike. Used to speculate that the underlying will FALL, or hedge an existing holding (protective put).

• Strike price (exercise price): pre-agreed price at which the buyer may buy (call) or sell (put) the underlying.
• Premium: price paid by the buyer to the writer for the option. Buyer's maximum LOSS = premium paid. Writer's maximum PROFIT = premium received.
• Expiry: last date the option can be exercised.

The seller of an option is called the WRITER. Receives premium upfront. Takes on the OBLIGATION to deliver (call writer) or buy (put writer) if the holder exercises.

Asymmetric: writer has limited upside (the premium) + potentially uncapped downside.

American-style: can be exercised at any time UP TO expiry.
European-style: can only be exercised AT expiry.

The names are conventions — both styles trade globally on global exchanges. American flexibility is at least as valuable as European, so an American option premium ≥ the equivalent European premium.

Total option premium = Intrinsic value + Time value.

Intrinsic value = the amount the option is currently ITM (zero if at- or out-of-the-money). Always ≥ 0.

Time value = the portion of the premium above intrinsic value. Reflects the time remaining to expiry + probability the option moves further ITM. DECAYS as expiry approaches (theta). Out-of-the-money options have ALL their value in time value.

Buy a 100-strike call for a £5 premium. At expiry the underlying is at £108.

• Exercise the call: buy at 100, sell in market at 108 → +£8 gross
• Subtract £5 premium paid → +£3 net profit per share
• Break-even = strike + premium = £105

Buy a 100-strike put for a £4 premium. At expiry the underlying is at £88.

• Exercise the put: sell at 100, buy in market at 88 → +£12 gross
• Subtract £4 premium paid → +£8 net profit per share
• Break-even = strike − premium = £96

Covered call: own the underlying + WRITE calls against it. Generates premium income. If underlying stays below strike, keep the premium. If it rises above, shares get called away — capped upside. Popular income strategy for long-only holders.

Protective put: own the underlying + BUY puts on it. Like insurance — puts gain if shares fall. Caps loss to (strike − current price − put premium). Costs the premium.

Higher expected volatility of the underlying INCREASES both call AND put premiums. Wider distribution of possible expiry prices = more chance of ending deep ITM. Market's real-time pricing of this is called implied volatility. The VIX tracks S&P 500 implied vol — the "fear gauge".

An OTC agreement where two parties exchange streams of interest payments on a NOTIONAL principal. Plain-vanilla: one party pays a FIXED rate, the other pays a FLOATING rate.

Principal is NEVER exchanged — only the net difference in coupons is paid periodically.

A company with floating-rate debt that wants to LOCK IN its interest cost enters a pay-fixed, receive-floating swap.

• Pays fixed on the swap ✓
• Receives floating on the swap, which OFFSETS the floating on its debt ✓
• Net result: pays a synthetic FIXED rate

This is a hedge against RISING rates — if floating rates rise, the company is protected.

Notional: the REFERENCE amount used to calculate interest payments. Never actually changes hands.

A £100m IRS has £100m notional — but the daily mark-to-market value moves only by changes in fixed-vs-floating expectations. Globally, derivatives notional outstanding is measured in hundreds of trillions of USD, while their market value is a small fraction of that.

A credit derivative. The protection BUYER pays a periodic premium to the protection SELLER. In exchange, the seller agrees to compensate the buyer if a specified "credit event" (default) on a reference entity occurs.

Like insurance against corporate/sovereign default. Buyer can be a bondholder hedging credit risk — or a speculator with no underlying exposure.

Payment direction:

• Buyer: PAYS premium (the "CDS spread") → BENEFITS if the reference entity defaults
• Seller: RECEIVES premium → LOSES if the reference entity defaults

Note that customers must NEVER be told they are the CDS reference — it's a market instrument, not an intent to see them fail.

AIG's Financial Products division had written enormous CDS protection on subprime mortgage-backed securities — without adequate reserves. When those defaulted, AIG's payouts dwarfed its capital. The 2008 bailout of AIG (~US$180bn) was largely about honouring these CDS obligations.

The CDS spread is the annual premium paid by the buyer, expressed in basis points of notional. A 200bp CDS = the buyer pays 2% pa. Widens as perceived credit risk rises; narrows when credit improves. Real-time indicator of distress — heavily watched in fixed-income markets.

Post-2008 reforms (US Dodd-Frank, EU EMIR) pushed many standardised OTC swaps through mandatory central clearing.

After matching a cleared trade, the CCP steps into the middle — becoming the BUYER to every SELLER and the SELLER to every BUYER. Both original counterparties now face the CCP, not each other. The CCP collects margin from both sides to absorb default losses.

• CME Group (Chicago) — futures on equity indices, treasuries, FX, commodities
• ICE Futures — oil (Brent) + gas + softs; also owns NYSE
• Eurex — European bond + equity derivatives
• HKEX — Asian derivatives hub
• LIFFE was acquired by ICE

• Efficient risk transfer (hedging)
• Leverage / capital efficiency
• Access to markets and strategies otherwise unavailable (easier to short via a future than physically short-sell)
• Isolate specific exposures (buy volatility, buy delta, buy vega separately)

• Complexity — mispricing / model risk
• Leverage — small adverse moves can wipe out capital
• Counterparty risk (OTC)
• Operational risk — margining, collateral management

• Barings Bank (1995) — Nick Leeson's Nikkei futures trades, £827m loss, bank collapsed
• LTCM (1998) — leveraged model-based bond arbitrage, $4.6bn loss, Fed-orchestrated bailout
• Société Générale (2008) — Jérôme Kerviel rogue trader, €4.9bn
• AIG (2008) — CDS on subprime MBS, ~$180bn US government bailout
• JP Morgan London Whale (2012) — credit derivatives, $6.2bn
• Archegos Capital (2021) — total return swaps, $10bn+ combined bank losses

Common thread: concentrated positions + leverage + poor risk oversight.