Markets03
Derivatives basics
Options get taught backwards. Most courses open with Black-Scholes, which prices something the reader cannot yet picture. Start with the picture. Once the payoff diagram is obvious, the pricing model is a way of putting a number on a shape you already understand.
The four positions
| Profits when | Max gain | Max loss | |
|---|---|---|---|
| Long call | Spot rises above strike plus premium | Unlimited | The premium |
| Long put | Spot falls below strike less premium | Strike less premium | The premium |
| Short call | Spot stays below strike plus premium | The premium | Unlimited |
| Short put | Spot stays above strike less premium | The premium | Strike less premium |
The asymmetry is the whole point. A buyer pays a known amount for an unknown payoff. A seller receives a known amount and takes on an unknown obligation. Every option strategy is a combination of those two shapes.
Draw them
The dashed line is the payoff, which ignores what you paid. The solid line is profit, which is the payoff shifted down by the premium for a long position and up for a short one. The vertical line is the break-even.
Two-leg structures
A call spread buys one call and sells a higher-struck one. The sold call pays for part of the bought one, so the position costs less and gives up the upside above the second strike. It is a directional bet with both ends capped.
A straddle buys a call and a put at the same strike. It profits from a large move in either direction and loses the whole premium if nothing happens. It is a bet on rather than direction.
Both are in the tool above as presets. Switch between them and watch the shape change, which is a faster way to understand them than any description including this one.
Where options show up in corporate finance
- Employee options. The in the is an option calculation, and it behaves exactly like the payoff above: worth nothing below the strike, dilutive above it.
- Convertible .A bond plus a call on the issuer's stock, which is why they pay a lower than straight debt.
- in a levered company.Merton's insight: shareholders in a company with debt hold something like a on the assets, struck at the of the debt. If the assets are worth less than the debt they walk away, and if they are worth more they keep the difference. That reframing explains why equity in a distressed company can still trade above zero.
Test yourself
01Draw the payoff for a long call struck at $100, bought for $5.
Flat at negative $5 for every spot price up to $100, because the option expires worthless and you lose the premium. Above $100 it rises one for one with the spot, crossing zero at $105. Maximum loss $5, maximum gain unlimited. The interviewer is checking whether you draw the kink at the strike and the break-even at the strike plus premium, which are two different points.
02Why would anyone sell a call?
For the premium, which is received up front and kept if the option expires worthless. The seller is taking a capped gain against an uncapped loss, which is only sensible if they think the probability-weighted outcome favors them, or if they already own the stock and are willing to sell it at the strike. Selling calls without owning the underlying is a position that loses more than the account contains if the stock moves far enough.
03What is a straddle betting on?
Movement, in either direction, larger than the combined premium. A long straddle buys a call and a put at the same strike, so it profits from a large move and loses the full premium if the stock sits still. It is a bet on volatility rather than on direction, which is why they get bought before earnings and why they are usually expensive right then.
A tutor that knows this lesson. It asks before it explains, and it will not tell you what to do with your own money.
Every figure in this lesson that names a company comes from Target Corporation's Form 10-K for Fiscal 2025, the year ended 2026-01-31, filed 2026-03-11. Educational material, not investment advice.