Understand calls and puts — Stock-Market notes

Overview

Options are contracts that give you the right, but not the obligation, to buy or sell an underlying asset (usually a stock) at a predetermined strike price before or on an expiration date. The two fundamental types are calls and puts, which represent opposite directional bets.

[!intuition] Core Mental Model

Think of options like insurance or reservations:

Call option = A reservation to BUY something at today's price, even if the price shoots up tomorrow. You're betting the asset will go UP.
Put option = An insurance policy that lets you SELL something at today's price, even if the market crashes. You're betting the asset will go DOWN.

WHY do these exist? Options separate direction from commitment. You can express a market view with limited downside (only lose the premium you paid) while keeping unlimited upside (calls) or substantial downside protection (puts).

Key asymetry: Your maximum loss is capped at the premium paid, but profit potential is theoretically unlimited (call) or large (put, down to zero).

[!definition] Call Option

A call option is a contract giving the holder the right to BUY the underlying asset at the strike price $K$ on or before expiration.

Components:

Underlying asset: The stock/commodity the option controls (usually 100 shares per contract)
Strike price ( $K$ ): The price at which you can buy
Premium ( $C$ ): What you pay upfront for the right
Expiration date: Last day the option is valid
Long call: You BUY the call (bullish)
Short call: You SELL the call (bearish or neutral, obligated to sell if exercised)

[!definition] Put Option

A put option is a contract giving the holder the right to SELL the underlying asset at the strike price $K$ on or before expiration.

Components:

Strike price ( $K$ ): The price at which you can sell
Premium ( $P$ ): What you pay upfront for the right
Long put: You BUY the put (bearish)
Short put: You SELL the put (bullish or neutral, obligated to buy if exercised)

[!formula] Payoff Derivation from First Principles

Long Call Payoff

Setup: You pay premium $C$ today for the right to buy at strike $K$ . At expiration, stock price is $S_T$ .

Decision logic:

If $S_T > K$ : Exercise! Buy at $K$ , immediately sell at $S_T$ , profit = $S_T - K$
If $S_T \leq K$ : Don't exercise (you'd lose money buying above market), let it expire worthless

Payoff at expiration: $\text{Intrinsic Value} = \max(S_T - K, 0)$

Profit/Loss (accounting for premium paid): $\text{P/L}_{\text{call}} = \max(S_T - K, 0) - C$

WHY this formula? The $\max$ function captures the optionality: you only exercise when profitable. The $-C$ adjusts for sunk cost.

Breakeven: $S_T = K + C$ (stock must rise enough to cover both strike and premium)

Long Put Payoff

Setup: You pay premium $P$ today for the right to sell at strike $K$ . At expiration, stock price is $S_T$ .

Decision logic:

If $S_T < K$ : Exercise! Buy at market $S_T$ , sell using put at $K$ , profit = $K - S_T$
If $S_T \geq K$ : Don't exercise (you'd lose money selling below market), let it expire worthless

Payoff at expiration: $\text{Intrinsic Value} = \max(K - S_T, 0)$

Profit/Loss: $\text{P/L}_{\text{put}} = \max(K - S_T, 0) - P$

Breakeven: $S_T = K - P$ (stock must fall enough that your gain exceds the premium)

[!example] Worked Example 1: Long Call

Scenario: You buy a call option on XYZ stock.

Current stock price: $50
Strike price $K = 55$
Premium paid $C = 3$
Expiration: 1 month

Question: What's your P/L if stock ends at (a) $60, (b)$ 55, (c) $50?

Solution:

(a) $S_T = 60$ :*

Intrinsic value = $\max(60 - 55, 0) = 5$
P/L = $5 - 3 = +2$ per share = $200 profit (per contract of 100 shares)
WHY? Stock rose above strike + premium, you're in the money

(b) $S_T = 55$ :

Intrinsic value = $\max(55 - 55, 0) = 0$
P/L = $0 - 3 = -3$ per share = $300 loss
WHY? At-the-money at expiration has no intrinsic value, you lose the full premium

(c) $S_T = 50$ :

Intrinsic value = $\max(50 - 55, 0) = 0$
P/L = $0 - 3 = -3$ per share = $300 loss
WHY? Stock didn't move enough (or moved down), option expires worthless

Breakeven calculation: $K + C = 55 + 3 = 58$ . Stock must reach $58 to break even.

[!example] Worked Example 2: Long Put

Scenario: You buy a put option on ABC stock.

Current stock price: $100
Strike price $K = 95$
Premium paid $P = 4$
Expiration: 2 months

Question: What's your P/L if stock ends at (a) $85, (b)$ 95, (c) $105?

Solution:

(a) $S_T = 85$ :

Intrinsic value = $\max(95 - 85, 0) = 10$
P/L = $10 - 4 = +6$ per share = $600 profit
WHY? Stock dropped significantly below strike, your insurance paid off

(b) $S_T = 95$ :

Intrinsic value = $\max(95 - 95, 0) = 0$
P/L = $0 - 4 = -4$ per share = $400 loss
WHY? At-the-money, no intrinsic value, premium lost

(c) $S_T = 105$ :

Intrinsic value = $\max(95 - 105, 0) = 0$
P/L = $0 - 4 = -4$ per share = $400 loss
WHY? Stock went up, put is worthless (you wouldn't sell at $95 when market is$ 105)

Breakeven calculation: $K - P = 95 - 4 = 91$ . Stock must fall below $91 to profit.

[!example] Worked Example 3: Comparing Call vs Put on Same Stock

Scenario: DEF stock trades at $50. You can buy:

Call: $K = 52$ , $C = 2$
Put: $K = 48$ , $P = 2$

If stock goes to $60:

Call P/L = $\max(60-52, 0) - 2 = 8 - 2 = +6$ ✅
Put P/L = $\max(48-60, 0) - 2 = 0 - 2 = -2$ ❌

If stock goes to $40:

Call P/L = $\max(40-52, 0) - 2 = -2$ ❌
Put P/L = $\max(48-40, 0) - 2 = 8 - 2 = +6$ ✅

WHY this matters: Direction is everything. Call = bullish, Put = bearish. They're mirror images in philosophy.

[!mistake] Common Misconception: "Options are Obligations"

Wrong idea: "If I buy an option, I must exercise it."

Why it feels right: The word "contract" suggests a binding commitment, and you're paying money upfront.

Steel-man: The confusion arises because the seller (short side) IS obligated if the buyer exercises. But as the buyer (long side), you're only purchasing a right.

The fix:

Long (buy) = RIGHT, not obligation. You can walk away, losing only the premium.
Short (sell) = OBLIGATION. You must fulfill if exercised.

Mnemonic: "Long = Liberty, Short = Shackled."

[!mistake] Confusing Intrinsic Value with Profit

Wrong idea: "My call has intrinsic value of $5, so I made$ 5."

Why it feels right: The math shows $S_T - K = 5$ , which looks like profit.

Steel-man: Intrinsic value IS the gross payoff, but you forgot the sunk cost.

The fix: Always subtract the premium paid: $\text{Profit} = \text{Intrinsic Value} - \text{Premium}$

If premium was $3, your net profit is$ 5 - 3 = 2 $, not$ 5.

[!recall]- Feynman Explanation (Explain to a 12-Year-Old)

Imagine you're at a carnival. There's a game where you can win a giant teddy bear, but the bear's price changes every hour—sometimes it's $10, sometimes$ 50, sometimes $5.

Call option is like this: You pay $2 to get a special ticket that says "I can buy the tedy bear for$ 20anytime in the next week, no matter what the actual price is." If next Tuesday the bear costs $40, you use your ticket, pay$ 20, and get a $40 bear—you win! If the bear only costs$ 15all week, you just throw away your $2 ticket and buy the bear normally.

Put option is the opposite: You pay $2 for a ticket that says "I can sell my tedy bear for$ 20 anytime this week, no matter what it's worth." If you already own a bear and the carnival starts buying them back for only $5, you use your ticket and get$ 20—you protected yourself! If the bear's value goes up to $30, you don't use the ticket (why sell at$ 20 when you can get $30?), and you just lose the$ 2.

Key point: The $2 ticket (premium) is the most you can lose. But if the bet works out, you can win a lot more!

[!mnemonic] Remember Calls vs Puts

CALL = Can Acquire Low, Long bullish

Call = Calls go UP (the letter C is a smile, going up!)
You CALL someone to invite them OVER (buy)

PUT = Price Undermined Totally, Long bearish

Put = Prices go DOWN (the letter P is upside-down, falling!)
You PUT something down (sell)

[!recall] Active Recall Questions

What is the key difference between a call and a put option?
Derive the payoff formula for a long call from first principles.
If you buy a call with $K=100$ , $C=5$ , and stock ends at $110, what's your profit per share?
Why is the maximum loss for a long option position capped?
What is the breakeven price for a long put with $K=50$ , $P=3$ ?

Connections

Intrinsic vs Time Value: Options have two value components; calls/puts both exhibit this
Option Greeks: Delta tells you how much call/put price changes with stock price
Covered Calls: Combines owning stock with selling a call
Protective Puts: Buying puts as insurance for long stock positions
Put-Call Parity: Mathematical relationship between call and put prices
American vs European Options: Exercise rules affect calls and puts differently
Moneyness: ITM/ATM/OTM status determines intrinsic value

#flashcards/stock-market

What gives a call option holder the right to do? :: Buy the underlying asset at the strike price before expiration.

What gives a put option holder the right to do?

Sell the underlying asset at the strike price before expiration.

Formula for long call profit/loss?

\text{P/L} = \max(S_T - K, 0) - C

Formula for long put profit/loss?

\text{P/L} = \max(K - S_T, 0) - P

Breakeven for a long call with strike

K

and premium

C

S_T = K + C

Breakeven for a long put with strike

K

and premium

P

S_T = K - P

Maximum loss on a long call or put?

The premium paid (limited downside).

When should you exercise a call option at expiration?

When

S_T > K

(stock price above strike).

When should you exercise a put option at expiration?

When

S_T < K

(stock price below strike).

Who has an obligation in an options contract?

The option seller (short position), not the buyer (long position).

What does "intrinsic value" mean for a call?

\max(S_T - K, 0)

—the immediate exercise value.

What does "intrinsic value" mean for a put?

\max(K - S_T, 0)

—the immediate exercise value.

If you're bullish on a stock, do you buy a call or put?

Buy a call.

If you're bearish on a stock, do you buy a call or put?

Buy a put.

What happens to an out-of-the-money option at expiration?

It expires worthless; intrinsic value is zero.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Options samajhne ke liye sabse pehle yeh jano: yeh ek contract hai jo tumhe aq deta hai (obligation nahi). Call option matlab tumhe right milta hai stock ko kharidne ka ek fixed price pe (strike price), chahe market mein stock ka price kitna bhi upar chala jaye. Put option ulta hai—tumhe right milta hai stock ko bechne ka fixed price pe,agar market crash ho jaaye tab bhi. Premium wo paisa hai jo tum upfront dete ho is right ke liye.

Imagine karo tum ek property dekhne gaye ho. Builder kehta hai, "Aaj price50 lakh hai, lekin agar tumhe 2 mahine bad confirm karna hai, toh 2 lakh dedo as booking—main tumhe 50 lakh pe hi dunga chahe future mein price 70 lakh ho jaaye." Yeh call option jaisa hai.Agar 2 mahine baad price 70 lakh ho gaya, tum 50 lakh deke property le sakte ho aur turant 20 lakh profit! Agar price 40 lakh pe gir gaya, toh tum booking cancel kar sakte ho, bas 2 lakh token money chali gayi. Maximum loss limited hai, profit unlimited.

Put option bhi aise hi, lekin opposite direction. Yeh insurance jaisa kaam karta hai. Maan lo tumhare pas alreadyek stock hai jo100 rupaye ka hai. Tum sochte ho, "Agar yeh gir gaya toh?" Toh tum 4 rupaye dekar ek put khareed lete ho jisse tum apna stock 95 rupaye pe bech sakte ho, chahe market 50 pe gir jaaye. Yeh traders aur investors ke liye protection ka tarika hai. Options isliye powerful hain kyunki limited risk ke sath directional bets le sakte ho—bullish ho toh call lo, bearish ho toh put.

Core formula yad rakho: Call profit = max(Stock price - Strike price, 0) minus premium paid. Put profit = max(Strike price - Stock price, 0) minus premium. Agar option "in the money" nahi hai expiration pe, toh zero value hai aur premium pura loss. Diagram dekho toh call aur put ki payoff lines clearly samajh ayegi—call right side mein profit kamata hai (stock upar jaye), put left side mein (stock neeche jaaye).

Test yourself — Options Basics