Equity Option
Also known as: Call, Put, Vanilla option
The right — not the obligation — to buy or sell a stock at a fixed price. The atom of derivatives.
1 · SnapshotThe one idea to remember
2 · BeginnerWhat is it, really?
An option is a contract that gives you a choice. A call lets you buy a stock at a fixed price (the strike) until a set date (expiry); a put lets you sell at the strike. You pay a premium up front for that choice, and you only use ("exercise") it if it benefits you.
Buy a call with a $100 strike and the stock rockets to $130 — you buy at 100, an instant $30 of value. The stock falls to $80 instead? You walk away, losing only the premium. That asymmetry — capped loss, open-ended gain — is what people pay for.
The seller (writer) of the option takes the other side: they collect the premium and hope the choice expires worthless. Selling options is a business of collecting many small premiums while wearing rare large losses.
Want to see what happens when you combine several options into one position — spreads, straddles, condors? The strategy builder draws the combined payoff live, leg by leg.
Point at a line to pick it out from the others.
a paymentsomething deliveredonly if a condition is metnot a payment
The buyer's worst case is fixed on day one. The seller's is not, and that asymmetry is the whole instrument.
At the trade
- Option buyer → Option seller Paid once and never returned. It is the most the buyer can lose, whatever happens next.
While the position is open
- Option seller → Option buyer A short option is an open-ended obligation rather than a position with a purchase price, so the seller's broker calls for more collateral as the market moves against it.
If the buyer exercises
- Option buyer → Option seller Paid for shares the buyer now wants at a price now better than the market.
- Option seller → Option buyer On a single-stock contract the seller must deliver. On an index contract the difference is settled in cash instead.
If not
- Option seller → Option buyer The seller's profit is capped at the premium. That is the trade: a small certain gain against a large uncertain loss.
Clearing, margin and the assignment nobody choosesafter the trade
a paymentonly if a condition is metnot a payment
From the first minute
- Option buyer → Clearing house Neither side faces the other. Both face the clearing house, which is why an option can be closed against anybody rather than only against the person who wrote it.
- Option seller → Clearing house Held against the open-ended obligation and called for whenever the model says it is short.
On exercise
- Clearing house → Option seller The clearing house picks a short position to deliver against by a published rule. Nobody decides that it should be yours and no warning arrives first.
At expiry
- Clearing house → Option buyer Index contracts settle against a price built from an auction or from opening prints, so the index level at the moment of expiry can differ from the number the contract pays against.
- Asset class
- Equity derivatives
- Instrument type
- Option (call / put)
- Traded
- Exchange (listed) and OTC
- Typical users
- Hedgers, income sellers, speculators, market makers
Which risks decide the outcome
Not how risky this is, and not a rating — there is deliberately no total. It says which of five failure modes drives what happens here, in the same order on all 129 products so they can be compared. This publication's own reading; see the notice below.
- Marketdecides it
- Creditmatters
- Liquiditybarely applies
- Fundingmatters
- Operationaldecides it
What decides it here. Market risk for the buyer, whose loss is capped at the premium. For the seller it is funding: the obligation is open-ended and the margin call arrives on somebody else's timetable.
3 · IntermediateHow it works in practice
The vocabulary
- Moneyness: in-the-money (exercising pays), at-the-money (strike ≈ spot), out-of-the-money.
- Intrinsic value = payoff if exercised now; time value = premium − intrinsic. Time value melts to zero at expiry ("theta decay").
- American vs. European: American options can be exercised any day; European only at expiry. Most single-stock listed options are American.
- Implied volatility (IV): the volatility number that makes a pricing model match the market premium — the market's forecast of turbulence, and the actual unit in which traders quote options.
The Greeks — how the price moves
| Greek | Sensitivity to | Long call sign |
|---|---|---|
| Delta (Δ) | Stock price | + (0 to 1) |
| Gamma (Γ) | Delta itself (convexity) | + |
| Vega | Implied volatility | + |
| Theta (Θ) | Passage of time | − (you bleed) |
| Rho (ρ) | Interest rates | + |
4 · AdvancedPricing & valuation
Black–Scholes–Merton
Under the BSM assumptions (lognormal spot, constant volatility \(\sigma\), continuous hedging), the price of a European call on a non-dividend stock is
What the symbols mean
- Cthe price of a call option
- Sthe price of the underlying today
- Nthe normal distribution, or a count
- Kthe strike: the price written into the contract
- rthe interest rate, per year
- Tmaturity, in years
with \(N(\cdot)\) the standard normal CDF; the put follows from put–call parity \(C - P = S_0 - Ke^{-rT}\). The derivation's core is not the formula but the idea: a continuously rebalanced portfolio of \(\Delta = N(d_1)\) shares replicates the option, so its price is the cost of replication — independent of anyone's forecast of direction.
Where the model bends
- Volatility smile/skew: equity IV rises for low strikes (crash insurance). The market prices a whole surface \(\sigma(K,T)\), not one \(\sigma\); models like local vol (Dupire) or stochastic vol (Heston) fit it.
- Dividends: discrete dividends lower forward price; American calls on dividend payers may be exercised early just before ex-dates, American puts early when deep ITM (priced on binomial/finite-difference grids).
What a desk actually does
Market makers run delta-hedged books: buy the option, short \(\Delta\) shares, rebalance. Their P&L over a hedge interval is the classic gamma-theta tradeoff:
What the symbols mean
- Gammahow fast Delta itself changes
- Sthe price of the underlying today
- sigmavolatility, the standard deviation of returns
- deltaa small change in whatever follows
- ta point in time
— long options make money when realised volatility beats the implied vol paid, and vice versa. Options are, at bottom, a market for volatility.
The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.
5 · Desk notesHow practitioners think about it
Now say it back
Close the page and give Equity Option in four sentences. It takes a minute and it is the only way to find out whether reading it was enough.
- Who wants what — two parties wanted opposite things badly enough to write it down.
- What the contract obliges, and when — not the payoff; the obligation.
- Where the money comes from — name the source, or you have described a hope.
- What makes it lose — the ordinary way, not the dramatic one.
Put Equity Option beside any other instrument →
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