Option Theory

The whole unit on one sheet: the buyer-versus-writer asymmetry that every hedge, speculative, and spread strategy in this chapter reshapes.

Which Two Roles Does Every Option Have?

• The buyer (holder, long) pays the premium and acquires a right: a call is the right to go long the future at the strike; a put is the right to go short at the strike. The buyer is never obligated.
• The writer (seller, grantor, short) receives the premium and takes on an obligation: if assigned, the writer must take the other side at the strike. Assignment is not optional.
• The underlying is a futures contract, not stock. Exercising a call delivers a long futures position to the buyer and a short futures position to the assigned writer. Exercising a put delivers a short futures position to the buyer and a long futures position to the assigned writer.

What Can the Long Side Win and Lose?

• Maximum loss = the premium paid, and not a cent more. The buyer posts no margin, because the risk is prepaid and closed-ended.
• A total loss of the premium is a routine outcome, not a rare one: an out-of-the-money (OTM) expiration is worthless.
• Breakeven: long call = strike plus premium; long put = strike minus premium.
• Maximum profit: long call is unlimited (the future has no price ceiling); long put is strike minus premium (the future can only fall to zero).

What Can the Short Side Win and Lose?

• Maximum gain = the premium received, kept whether or not the option is assigned. The writer must post a performance-bond margin, because the obligation is open-ended.
• A naked short call is the truly unlimited-risk case: the future has no ceiling, so the loss climbs without bound. This mirrors the long call's unlimited profit.
• A naked short put is large but bounded: maximum loss = strike minus premium, reached only if the future falls to zero. It is not literally unlimited.

Which Numbers Matter Most?

Which Gotchas Trip Students Up?

• Calling a naked short put "unlimited": only the naked short call earns that label. The put's floor at zero bounds it.
• Flipping the margin rule: the buyer posts none because the premium is paid in full up front; the writer must post margin because the obligation is open-ended.
• Reading "limited risk" as "safe": the premium can still be lost in full, and often is.
• Forgetting the underlying is a futures contract: exercise opens a futures position, it does not move shares. A put holder who exercises goes short, not long.

What Is the Memory Aid for Buyer Versus Writer?

Buyer equals Bounded loss and Big upside. The writer is the reverse: a small, capped gain against open-ended risk. The buyer paid for the good side of the trade; the writer sold it.

One-Breath Recap

Every option position is one of two roles: the buyer pays the premium for a right and can lose no more than that premium, though losing it in full is routine, while the return runs large, unlimited on a long call and capped at strike minus premium on a long put; the writer collects the premium as the maximum possible gain but carries an open-ended obligation, unlimited on a naked short call because the future has no price ceiling and bounded at strike minus premium on a naked short put because the future can only fall to zero, and only the buyer's risk is prepaid and margin-free while the writer must post a performance bond.

Need more than the recap? Read the full Option Theory unit.