Four purposes, and the useful version of each names a case rather than a category.
The first is risk transfer, and it is the purpose that justifies the market's existence. An Indian chemicals exporter with dollar receivables and rupee costs holds a currency exposure it did not choose and has no view on. Someone else, a dollar-funded investor who wants rupee assets, holds the mirror image. A currency swap moves the exposure from the party that cannot price it to the party that wants it, and both balance sheets get simpler.
Then price discovery. The forward curve, the cap volatility surface and the swaption grid are prices at which someone will actually trade, and they aggregate views that no survey collects. The forward-starting swap rate of 4.9628% in the module's opening is not an opinion about future rates. It is the rate at which the market is indifferent today, and any forecast worth having has to explain why it differs.
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Third comes the operational and cost advantage, which is the one desks feel daily. Selling one index futures contract adjusts a portfolio's market exposure in a second, at a spread measured in a basis point or two, with no custody instruction, no securities lending and no capital-gains event. Selling the underlying basket costs far more and takes days, so the exposure gets adjusted where adjusting it is cheap.
Fourth, and rarest, is market completeness. Some exposures cannot be taken any other way. A pure position in the volatility of the five-year swap rate, long if it moves and short if it does not, does not exist in the cash market. A swaption straddle is that position, and it can be priced.
None of those four is an argument for using derivatives. They are the reasons the instruments exist. Whether a particular book should hold any of them is a sizing decision, and Phase 9's answer to almost every version of it is to own less rather than to hedge more.
What goes wrong: five risks, five mechanisms
"Derivatives are risky" is a claim with no operational content. Five separate claims, each with a mechanism, do have content, and each is managed by a different control.
Leverage is the first, and it means that a small premium controls a large sensitivity. The payer swaption priced on the swaption page costs $900,201.39 on a $50 million notional, and a 100 basis point rise in the forward swap rate changes the underlying swap's value by $2,063,271.31, which is 2.2920 times the premium. That ratio is the attraction of the instrument for a hedger and the trap for a speculator, because the same multiple applies to the loss when the option has been sold rather than bought. Barings Bank failed in 1995 on exchange-traded index futures and options positions whose notional was many multiples of the bank's capital, and the exchange margin calls arrived long before anyone reconciled the trades.
Next is basis risk, which lives in the gap between the hedge instrument and the exposure. A cap on a three-month reference rate does not hedge a loan that reprices off a different index, and a currency swap priced off two domestic curves does not match a dealer's quote, because the dealer prices the cross-currency basis as well. Basis risk is measured rather than eliminated, and the minimum-variance hedge ratio DV1.03 derives is the measurement.
Then liquidity and funding risk, where a hedge can be economically right and still fail, because the cash it demands arrives before the cash it protects. Metallgesellschaft's US subsidiary in 1993 held long oil futures against long-dated fixed-price supply contracts. The economics were arguably sound. The futures leg nonetheless required variation margin in cash as prices fell, and the supply contracts produced no offsetting cash for years, so the position was closed at a loss reported at more than a billion dollars.
Counterparty risk is the reminder that over-the-counter contracts are promises by named institutions. AIG's Financial Products unit had written credit protection whose collateral terms were tied to AIG's own rating, so a downgrade produced immediate collateral demands the firm could not meet, and the US government provided support in September 2008 on a scale that is public record. Central clearing and collateral agreements exist because of that mechanism, and they convert it into the liquidity risk above.
Last, and hardest to see from inside a single book, is systemic risk. Positions that are individually hedged can be collectively directional, and the hedging behaviour itself moves the market. A book of sold options that is delta-hedged mechanically sells into falls and buys into rallies, so a crowded short-gamma position amplifies whatever is already happening. No single participant can observe that from their own position, which is the reason for trade repositories and position-limit regimes.
Notice what the list is not. None of these five is "the model is wrong", because model risk is a separate thing and it is handled by the verification identities rather than by risk limits.