Equity Derivatives

The market at a glance

Equity derivatives are contracts whose value derives from stocks and indices. The listed side alone is enormous: global exchange-traded equity options and futures turn over billions of contracts a year (US option volume has repeatedly broken records above 40 million contracts a day), while the OTC side — swaps, exotics, structured products — adds trillions in notional. Since 2020, retail option trading has exploded: on many days, more premium changes hands in short-dated options than in the underlying shares.

Three tribes populate the market: hedgers (funds insuring portfolios, corporates managing stakes), yield manufacturers (structured-product desks converting optionality into retail coupons), and volatility traders (market makers and funds trading turbulence itself as an asset).

The one idea underneath everything

Every product here is assembled from two primitives: linear exposure (futures, forwards, swaps — payoff proportional to the move) and optionality (payoffs with a kink — the right without the obligation). Once you can price those two, everything from a warrant to an autocallable is a combination with packaging.

The pricing revolution — Black, Scholes and Merton, 1973 — showed that an option can be replicated by dynamically trading the stock, so its price depends not on anyone's forecast but on the cost of replication, driven by one unobservable input: volatility. That insight turned volatility itself into the traded quantity — option markets are, at bottom, volatility markets.

Interactive: Black–Scholes option pricer

Price a European call and put and see the Greeks. Play with volatility and watch premium respond — that's vega, the heart of the options business.

Spot S Strike K Expiry T (years) Volatility % Rate r % Dividend yield q %

Call price

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Put price

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Call delta

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Gamma

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Vega (per vol pt)

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Theta ($/day)

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Textbook Black–Scholes with continuous dividend yield. Real desks price on a full volatility surface — but every quote you'll ever see is a conversation with this formula.

How the products fit together

Options are the foundation — learn the Greeks there. Index futures and forwards are the linear workhorses; equity swaps and total return swaps rebuild ownership as financing. Variance swaps trade pure turbulence; dividend futures strip out payouts. On the packaged shelf: convertibles (bond + option), warrants (options as securities), autocallables (sold crash insurance as coupons) and CFDs (leveraged retail mirrors).

Concepts that separate professionals from tourists

• Implied vs. realised volatility — options are bets on the gap between the turbulence you paid for and the turbulence that happens.
• The skew — crash insurance costs extra; downside strikes trade at higher implied vol, and that asymmetry prices every structured product.
• Gamma/theta trade-off — long options bleed daily and win on big moves; short options harvest daily and die occasionally. Neither is free money.
• Dealer positioning feedback — when the street is short gamma, hedging amplifies moves; when long, it dampens them. Modern market microstructure runs through the options market.