Long Put

Core Thesis

A Long Put is bearish convexity with capped loss. It is used for directional downside trades and for tactical hedging when downside tails are underpriced relative to expected realized volatility.

Structure and Capital Model

• Buy 1 put at strike $K$ and expiration $T$.
• Capital at risk is premium $P_0 \times 100$.
• No assignment risk from the long leg itself.

Expiration Payoff Mathematics

$$\Pi_T = \max(K - S_T, 0) - P_0$$

• Max loss: $P_0$.
• Break-even at expiration: $K - P_0$.
• Max profit: $K - P_0$ (if underlying goes to zero).

Greek Profile

• Delta: negative; approaches -1.00 as put moves deeper ITM.
• Gamma: positive; downside acceleration is beneficial.
• Theta: negative; strongest drag when option is near ATM and near expiry.
• Vega: positive; long puts generally benefit from volatility expansion.

Strike and Tenor Design

• Swing bearish view: 30-90 DTE, delta around -0.35 to -0.60.
• Crash hedge: further-dated options improve persistence but cost more carry.
• Event short: avoid paying peak IV unless you expect realized move beyond implied distribution.

Execution and Risk Controls

• Define both a price trigger and a time stop.
• Hedge intent differs from speculation: hedge positions should map to portfolio beta/dollar exposure.
• Exit partials into panic spikes; put skew can normalize quickly.

Institutional Failure Modes

• Chasing downside after realized selloff (buying puts when skew is already extreme).
• Holding short-dated puts as theta accelerates after momentum stalls.
• Over-hedging and destroying carry over long periods.

Practical Checklist

• Is downside target below $K - P_0$ during your holding window?
• Are you buying volatility efficiently relative to regime and catalyst?
• Is this a speculative short or a portfolio hedge with explicit coverage ratio?