What a derivative is and why they exist

A derivative is a contract between two parties whose value is defined by reference to something else. That something else — the underlying — can be a share, an index, a bond, a currency pair, a barrel of oil, an interest rate, or an abstraction like realised volatility. The contract itself has no intrinsic content. It is a rule for who pays whom, how much, and when, expressed as a function of the underlying's future level.

That sounds academic until you notice the consequence: because the payoff is a function, you can choose the function. Owning an asset gives you one shape — you make money linearly when it rises, lose linearly when it falls, and you cannot separate the two. A derivative lets you cut that line apart and keep only the piece you want, or sell the piece you do not. Everything else in this course is a variation on that single idea.

Four families, two shapes

The instrument zoo is large; the underlying structure is not. Almost every derivative belongs to one of four families.

A forward is an agreement made today to exchange an asset at a fixed price on a fixed future date. Both sides are obliged. It is bilateral, negotiated, and settled once, at the end.

A future is a forward that has been standardised — fixed contract size, fixed expiry dates, a named exchange — and routed through a clearing house that settles gains and losses daily. Lesson 2 covers that machinery, which is where most of the practical difficulty lives.

A swap is a sequence of forwards bundled together: an agreement to exchange one stream of cash flows for another over time, most commonly a floating interest rate for a fixed one.

An option is different in kind. It gives one party the right but not the obligation to transact at a set price, and obliges the other party to perform if the right is exercised. Lesson 4 takes this apart properly.

Underneath the four families there are only two payoff shapes. Forwards, futures and swaps are linear: your profit changes one-for-one with the underlying, in both directions, and you are committed. Options are asymmetric: the buyer's loss is capped at the premium paid, the upside is not, and the price of that asymmetry is the premium itself. Once you can see which of the two shapes an instrument has, you can reason about it even when the marketing material is opaque.

Why anyone wanted these in the first place

Derivatives were not invented by quantitative finance. They were invented by people with inventory.

A farmer with a crop in the ground and a miller who needs flour in six months face mirror-image risks: the farmer is hurt by a falling price, the miller by a rising one. Neither wants a view on grain; both want a known number in a budget. A forward contract between them removes the uncertainty for both sides at once, and does so without either party needing capital, insurance, or a bank. The Dojima rice market in Osaka was trading standardised forward claims on rice in the eighteenth century, and the Chicago Board of Trade, founded in 1848, formalised the same logic for American grain.

This is the first and most defensible economic function: risk transfer. Derivatives let risk move from someone who is stuck with it to someone willing to be paid to hold it. That is genuinely productive. It is why an airline can quote fares a year out, why a mortgage lender can offer a fixed rate, and why a Swiss industrial exporter can sign a contract in euros without betting the margin on the franc.

The second function is price discovery. A liquid futures curve is a public statement about what the market expects, and about what it costs to carry the asset through time. Central banks, treasurers and analysts read those curves precisely because they aggregate the views of participants who have money at stake.

The third function is capital efficiency, and it is the one that gets people hurt. Because a derivative requires only a good-faith deposit rather than the full value of the underlying, a small amount of capital controls a large exposure. Used deliberately, that frees capital for productive use. Used carelessly, it converts an ordinary market move into an account-ending event.

A worked hedge, with the numbers

Take a Zurich software company that will invoice a German client EUR 1,000,000, payable in six months. Assume spot is 0.95 CHF per euro, the six-month Swiss franc rate is 0.5% per annum, and the six-month euro rate is 2.5%.

The fair forward rate is not a forecast. It is set by the interest differential, because anyone quoting a different number could borrow in one currency, lend in the other, and lock a risk-free profit. Over half a year:

F = 0.95 × (1 + 0.0025) ÷ (1 + 0.0125) = 0.95 × 0.99012 = 0.9406 CHF per euro

Selling the euros forward locks in CHF 940,617 — visibly less than the CHF 950,000 that today's spot rate implies. That CHF 9,383 gap is not a fee and not a prediction that the euro will fall. It is the cost of holding the higher-yielding currency for six months, and it is the structural reason forward rates on the franc sit below spot when Swiss rates are lower than foreign ones.

Now test it. If the euro falls to 0.90, the unhedged invoice is worth CHF 900,000, and the forward pays (0.9406 − 0.90) × 1,000,000 = CHF 40,617. Total: CHF 940,617. If the euro instead rises to 0.98, the invoice is worth CHF 980,000, and the forward loses CHF 39,383. Total: CHF 940,617.

That is the whole point and the whole discipline. The hedge did not make money in one scenario and lose money in the other — it produced the same number in both. A treasurer who congratulates himself in the first case and apologises in the second has misunderstood what he bought.

The leverage arithmetic that catches people

Consider an equity index future. Suppose the contract multiplier is CHF 10 per index point and the index stands at 12,000. The contract's notional value — the economic exposure it represents — is 12,000 × 10 = CHF 120,000. The clearing house does not ask for CHF 120,000. It asks for a performance bond sized to cover a plausible one- or two-day move, which for an equity index is typically a single-digit to low-teens percentage of notional and is raised when volatility rises.

Say the requirement is CHF 9,000. A 2% index move is 240 points, or CHF 2,400 — a 27% swing on the capital posted. Nothing unusual has happened in the market. What changed is the denominator you are measuring against.

This is why the sentence "I only put down CHF 9,000" is a category error. You are exposed to CHF 120,000 of index. Position sizing has to be done against notional, never against margin, and the fact that the broker permits the trade is a statement about the broker's collateral model, not about your ability to survive the outcome.

Counterparty risk, and the plumbing built to contain it

A derivative is a promise, and a promise is only as good as the party making it. This is the risk that does not appear in the payoff diagram.

Exchange-traded derivatives handle it by inserting a central counterparty between buyer and seller. Once a trade is registered, you no longer face the person on the other side; you face the clearing house, which requires collateral from everyone and marks positions to market daily so that losses are settled while they are small.

Over-the-counter derivatives — negotiated bilaterally, still the larger part of the market by notional — historically did not. The 2008 crisis was in significant part a demonstration of what happens when a dense web of bilateral obligations sits behind a small amount of collateral. The regulatory response was global: mandatory clearing for standardised contracts, trade reporting to repositories, and margin requirements for the rest. In Switzerland this is codified in the Financial Market Infrastructure Act (FinfraG/FMIA), supervised by FINMA, which imposes clearing, reporting and risk-mitigation duties broadly parallel to the EU's EMIR regime.

One statistic is worth internalising, and the Bank for International Settlements publishes it twice a year: the notional amount outstanding in OTC derivatives runs into the hundreds of trillions of dollars, while the gross market value — what the contracts are actually worth to the winning side — is a low single-digit percentage of that. Notional measures the size of the reference; market value measures the money genuinely at risk. Headlines that quote the first as if it were the second are describing a different and much scarier world than the one that exists.

What you are not getting

A derivative gives you a payoff, not ownership, and the difference has consequences that matter in Switzerland specifically.

Hold a Swiss share and you receive the dividend, from which 35% federal withholding tax (Verrechnungssteuer) is deducted and which a Swiss-resident private investor reclaims through the annual tax return. Hold a call option or a future on that share and you receive no dividend and have nothing to reclaim — the expected dividend is instead priced into the contract, silently, as a discount. You have not escaped the dividend; you have been paid it in advance, net, without the reclaim.

You also do not get the shareholder. A call option on a Swiss listed company carries no vote at the annual general meeting, no subscription right in a capital increase, and no entry in the share register. The payoff tracks the share; the membership rights stay with whoever actually holds it.

Swiss disclosure law, interestingly, does not accept that separation. Under the Financial Market Infrastructure Act, anyone whose holding in a company with shares listed in Switzerland crosses one of the statutory thresholds — 3, 5, 10, 15, 20, 25, 33⅓, 50 and 66⅔ per cent of voting rights — must notify the company and the exchange, and the regime deliberately captures more than shares. Derivatives conferring a right or an obligation to acquire the underlying are reportable as an acquisition position, and those on the other side as a disposal position, precisely so that an economic stake cannot be built through options and warrants while remaining invisible. The lesson generalises beyond the disclosure rules: a derivative separates the payoff from the ownership, and regulators, counterparties and tax authorities each decide independently which of the two they care about. Do not assume the answer is the same in all three places.

What to take away

• A derivative is a contract whose payoff is a chosen function of an underlying, which is why it can isolate one piece of a risk — direction, timing, volatility — and leave the rest behind.
• Forwards, futures and swaps commit you symmetrically; options do not, and the premium is the explicit price of that asymmetry.
• A forward price is arithmetic on interest rates and carry, not a forecast: the CHF 9,383 gap in the worked example is the interest differential, and a correctly executed hedge produces the same result whether the market rises or falls.
• Size positions against notional, never against margin — the CHF 9,000 deposit in the index example controls CHF 120,000 of exposure, and a routine 2% move is a 27% move on posted capital.
• Holding a derivative gives you the payoff without the ownership: no dividend, no Swiss withholding tax reclaim, no vote and no subscription right — yet Swiss disclosure law still counts options and other acquisition rights towards the shareholding thresholds.

Sources

• John C. Hull, Options, Futures, and Other Derivatives — the standard reference text; the opening chapters cover contract mechanics and the economic rationale for derivative markets.
• Bank for International Settlements, semiannual OTC derivatives statistics — the primary source for notional amounts outstanding versus gross market value.
• Bank for International Settlements, Quarterly Review — recurring analysis of central clearing, margin practices and derivatives market structure.
• Swiss Financial Market Infrastructure Act (FinfraG / FMIA) and FINMA guidance on OTC derivatives clearing, reporting and risk mitigation.
• European Market Infrastructure Regulation (EMIR), European Commission and ESMA materials on the post-2008 clearing and reporting framework.
• Eurex contract specifications for Swiss and European equity index futures and options — the authoritative source for multipliers, expiries and settlement conventions.
• Financial Market Infrastructure Act (FinfraG / FMIA), provisions on the disclosure of shareholdings, and SIX Exchange Regulation guidance on reportable acquisition and disposal positions.
• Fischer Black and Myron Scholes (1973), "The Pricing of Options and Corporate Liabilities", Journal of Political Economy; Robert C. Merton (1973), "Theory of Rational Option Pricing", Bell Journal of Economics and Management Science.