Long Put

Overview

A Long Put is the mirror image of a long call. It is an asymmetric contract that gives you the right—but not the obligation—to sell 100 shares of an underlying stock at a specific Strike Price ($K$) before a specific Expiration Date.

This is the professional's tool for profiting from a market decline or protecting an existing portfolio from a crash. Like the long call, your Maximum Risk is limited to the premium ($P_0$) you paid up front.

[!TIP] While a long call has unlimited profit potential, a long put's profit is finite because a stock price cannot go below zero. However, for most traders, a 100% drop in stock price is close enough to "unlimited"!

Mechanics of the Trade

When you buy a put:

1. The Entry: You pay the premium. You are now "Short Delta"—you want the stock price to go down.
2. The Hold: If the stock price falls, the right to sell at the (higher) strike becomes more valuable.
3. The Exit: You can sell the put back to the market for a profit, or exercise it to sell shares at the strike price.

The "Moneyness" Spectrum for Puts

Note that the conditions are reversed compared to calls:

Payoff and Break-even

At expiration, the value of your put is:

$$\text{Value} = \max(K - S_T, 0)$$

Your Profit accounts for the cost of entry:

$$\text{Profit} = \max(K - S_T, 0) - P_0$$

Break-even Point

Since you need the stock to fall enough to cover the premium, your break-even is:

$$\text{Break-even} = \text{Strike} - \text{Premium}$$

If you buy a $100 strike put for$4, your break-even is **$96**. If the stock is at$98 at expiration, you actually lose $2, even though the stock went down!

The Greeks: Bearish Edition

The Greeks behave slightly differently for puts, particularly Delta.

1. Delta ($\Delta$): The Downside Magnet

Delta for a long put is negative (between 0 and -1).

• An ATM put has a Delta of roughly -0.50.
• As the stock falls, Delta moves toward -1.00, meaning the put gains $1 for every$1 the stock loses.
• This is why puts are used for "hedging"—the negative delta of the put offsets the positive delta of your shares.

2. Vega ($\nu$): The "Crash" Multiplier

Puts are highly sensitive to Implied Volatility (IV).

• In the stock market, volatility usually spikes when prices crash.
• This means put buyers often get a "double win": the price move helps (Delta) and the rising panic/volatility helps (Vega).

3. Theta ($\Theta$): The Cost of Insurance

Like calls, puts lose value every day. If you buy a put to protect your portfolio, think of Theta as your "insurance premium" that you pay daily for peace of mind.

Strategic Variations

1. Protective Puts: Buying a put while owning the underlying stock. This creates a "floor" for your losses.
2. Speculative Puts: Buying OTM puts expecting a sudden, sharp crash. These are cheap but have a low probability of success.
3. Deep ITM Puts: Used as a "synthetic short" stock position. They have very high delta and behave almost exactly like shorting shares, but with capped risk.

Checklist for Entry

• Is my target price significantly below Strike - Premium?
• Am I prepared for Theta to erode my position if the crash is delayed?
• Is the IV low enough that I'm not overpaying for the "insurance"?
• Have I considered if a Put Spread might be more cost-effective?

Put-Call Parity: The Golden RuleRead more

One of the most important relationships in options is Put-Call Parity. It states that for European options:

$$C - P = S_0 - K e^{-rT}$$

This means a Call minus a Put is equivalent to Stock minus the discounted Strike Price.

If this relationship breaks, arbitrageurs will move in to fix it. It also explains why Call and Put premiums are mathematically linked—you can't have one be "cheap" without the other also being affected.