3.1.3 Markets, Products & Contract Mechanics

Basic Prerequisites: 02 · Options Mechanics & Payoffs.

1. Intuition & Practical Objective

The previous two pages described contracts; this one describes where they live and how the plumbing constrains their prices. The practical objective: know the difference between an exchange-traded contract (standardised, cleared, margined daily) and an OTC contract (bespoke, bilateral or CCP-cleared, collateralised under an ISDA/CSA), know what a contract specification pins down, and know the conventions - multiplier, day-count, cost-of-carry - that silently change every number you compute.

The reason this is a fundamentals topic and not fine print: two contracts with the same payoff can trade at different prices if their market structure differs. Futures settle daily and their variation margin earns no interest; OTC forwards settle once at $T$ ; the same payoff under the two structures has slightly different value (the convexity difference, Hull §5.8 and Ch 6). And a contract’s specification - the deliverable, the settlement, the multiplier - determines which asset you can hedge with and hence what “the” price even means.

The one-sentence essence. “A derivative price is the price of a replicating portfolio; the market structure (exchange vs OTC, clearing, margin, day-count, multiplier) determines which instruments are actually available to build that portfolio - so structure is part of the model, not a footnote to it.”

2. Mathematical Ground Truth & Derivations

2.1 Exchange vs OTC - the structural difference (Hull Ch 1, 2)

	Exchange-traded	OTC
Terms	Standardised (fixed expiry cycle, size, strikes)	Negotiated per trade
Clearing	Central counterparty (CCP)	Bilateral, or a CCP with margin
Margin	Initial + daily variation, marked to market	Collateral under an ISDA credit-support annex (CSA)
Cash flows	Realised daily; variation margin does not earn interest	Realised at maturity (or on margin calls, which do earn interest)
Scale (Dec 2019)	$\approx$ $96.5T notional	≈$558.5T notional (gross market value $\approx$ $11.6T)

2.2 Contract specification - what gets pinned down (Hull Ch 2.1)

An exchange contract specifies the asset (and any grade/deliverable choice), the contract size (multiplier), the delivery months / expiries, the settlement procedure (physical vs cash), price quotes, and price/position limits. Option-specific items (Hull Ch 10.4):

Expiration cycle: standard equity options expire on the third Friday; strikes are spaced $2.50 / $5 / $10; a class shares the underlying, a series is one strike & expiry.
Settlement: index options are cash-settled and quoted at $100 \times$ the index; equity options are $100 \times$ the premium.
Adjustments: cash dividends normally do not adjust the contract; splits adjust strike and size by $K \to K \cdot m / n$ , shares $\to n / m$ ; stock dividends and rights issues are handled ad hoc.
FLEX options allow bespoke terms within the exchange framework.

2.3 Margin mechanics (Hull Ch 2.2, 10.7)

Futures. At the trader level the maintenance margin is about $75%$ of the initial margin; the account is marked to market daily and any balance above the initial margin may be withdrawn. In the delivery month the contract converges to spot, because otherwise a cash-and-carry (or its reverse) locks a profit.

Options (short positions). Buying an option requires full payment, no margin (options with life $< 9$ months). Writing a naked option ties up margin:

naked call margin = max (100 c + 20% S - 100 max (K - S, 0), 100 c + 10% S),

naked put margin = max (100 c + 20% K - 100 max (S - K, 0), 100 c + 10% K),

with the second term the floor. Broad-index obligations use $15%$ instead of $20%$ in the first term. The $max (\cdot)$ structure is exactly the “at least the out-of-the-money discount, but never less than the 10% floor” rule.

2.4 The cost-of-carry dictionary - one master formula (Haug §1)

Every vanilla European model is the same formula with one variable changed:

c = S e^{(b - r) T} N (d_{1}) - X e^{- r T} N (d_{2}), ⎩ ⎨ ⎧ b = r b = r - q b = 0 b = r - r_{f} non-dividend stock (BSM 1973) index / continuous yield q (Merton 1973) futures / forward (Black-76) currency (Garman-Kohlhagen)

This is the reason §3 exposes the carry $b$ as an explicit function argument. Feed the wrong $b$ and you misprice by exactly the missing $e^{- qT}$ or $e^{- r_{f} T}$ factor.

2.5 Day-count and quote conventions (Hull Ch 6.1)

Interest accrues under a day-count convention: Actual/Actual (US Treasuries), $30/360$ (US corporates), Actual/360 (US money market); Actual/365 in Australia/Canada/NZ. Bonds quote a clean price; the cash paid is the dirty price $=$ clean price $+$ accrued interest. Rate futures are quoted as $100 - R$ with a fixed dollar value per basis point: $25 per bp for a $1M three-month contract, $41.67 per bp for a $5M one-month SOFR (Hull Ch 6.3).

3. Computational Implementation - the conventions in numbers

Standard library only. This turns the specification, margin and day-count rules into concrete cash amounts.

The naked-call number decomposes cleanly: $100 \times 5$ premium $+ 20% \times 100 \times 55 =$ $1,100 of stock cover, minus zero OTM discount = $1,600; the $10%$ floor is $1,050, so the 20%$ branch binds. The margin is not a fee - it is collateral, and its size is set by the exchange to cover a plausible one-day move.

4. Failure Modes & First-Principles Breakdowns

Wrong carry $b$ . The single most common pricing bug: using $b = r$ for an index (should be $r - q$ ), for futures ( $0$ ), or for FX ( $r - r_{f}$ ). The error is a multiplicative factor $e^{(b_{wrong} - b_{right}) T}$ on the forward leg.
Futures $\neq =$ forward when rates are stochastic. Equal only when $r$ is constant (Hull §5.8); otherwise futures are slightly higher/lower, and for interest-rate futures the difference is the convexity adjustment (Hull Ch 6.3). Treating them as identical silently misprices long-dated rate hedges.
Margin vs premium confusion. Buying an option is a cash outflow of the full premium ($325); writing one is collateral ($1,600) plus a contingent liability. Conflating the two wrecks both the cash-flow model and the risk model.
Ignoring settlement-timing differences. Futures variation margin earns no interest; OTC/CCP variation margin does. Over long horizons this timing difference is exactly what separates forward and futures prices.
Day-count sloppiness. Actual/360 vs Actual/365 changes the accrued interest of a rate instrument by a factor of $\approx 365/360$ - small per trade, material across a book.
Assuming standardisation is universal. Only exchange contracts are standard; the OTC market (the larger one, $\approx$ $558.5T notional) negotiates every term, so “the” market price may not exist - only a dealer quote with a bid/ask.

5. References

Hull, Options, Futures, and Other Derivatives
Haug, The Complete Guide to Option Pricing Formulas
Hull & White (via Hull

6. Connected Graph Bridges

Back: 02 · Options Mechanics & Payoffs · Index Hub
Next: 04 · No-Arbitrage & Bounds
Structure $\to$ pricing: BSM · The Pricing Formulas (the $b$ dictionary in closed form)
Clearing & collateral: Counterparty Risk & XVA · Interest Rate & Term Structure

Kwant Atlas

Explorer