Understand option buyer vs seller payoffs

5.2.5 · Stock-Market › Options Basics

Core Definitions

Payoff Structure: Call Options

Call Buyer Payoff (Long Call)

First principles se derivation:

Expiration par, call buyer ko right hai $K$ strike par buy karne ka jab market price $S_T$ ho.

1. Agar $S_T>K$: Exercise karo! $K$ par buy karo, $S_T$ par sell karo, intrinsic value = $S_T-K$
2. Agar $S_T\le K$: Worthless expire hone do, sirf premium $C_0$ jaata hai

Profit/Loss = Intrinsic value at expiration − Premium paid

Yeh formula kyun?

• $\max (S_T-K,0)$: Tum sirf tab exercise karte ho jab profitable ho; warna floor zero hai
• $-C_0$: Break even ke liye upfront cost recover karni padegi

Breakeven: Payoff = 0 set karo → $S_T-K-C_0=0$ → ==Breakeven = $K+C_0$==

Call Seller Payoff (Short Call)

Seller ka payoff mirror image hai (zero-sum):

Kyun? Seller ko $C_0$ upfront milta hai. Agar buyer exercise kare ($S_T>K$), seller ko stock deliver karni padti hai, $S_T-K$ ka loss hota hai.

Payoff Structure: Put Options

Put Buyer Payoff (Long Put)

Expiration par, put buyer $K$ par sell kar sakta hai jab market $S_T$ ho.

1. Agar $S_T<K$: Exercise karo! $K$ par sell karo, $S_T$ par buy karo, intrinsic = $K-S_T$
2. Agar $S_T\ge K$: Worthless expire hota hai, premium $P_0$ jaata hai

Breakeven: $K-S_T-P_0=0$ → ==Breakeven = $K-P_0$==

Put Seller Payoff (Short Put)

Phir se mirror image:

Seller $P_0$ rakhta hai agar worthless expire ho. Agar assigned ho jaaye ($S_T<K$), toh $K$ par buy karna padta hai (overpriced).

Visual Summary

Diagram se key observations:

1. Buyer curves zero ke neeche se shuru hoti hain (premium paid), seller curves zero ke upar se (premium received)
2. Slopes: Buyer breakeven ke upar $1:1$ gain karta hai; seller $1:1$ lose karta hai
3. Asymmetry: Buyer ka loss capped hai; seller ka loss open-ended (calls) ya large (puts) hota hai

Worked Examples

Common Mistakes & Steel-manning

Active Recall Practice

Memory Aids

Connections

• 5.2.01-What-are-options-and-why-use-them – Foundation: rights vs obligations
• 5.2.03-Call-options-explained – Call mechanics ki deep dive
• 5.2.04-Put-options-explained – Put mechanics ki deep dive
• 5.3.01-Covered-calls-strategy – Sellers risk kaise limit karte hain (covered position)
• 5.3.02-Cash-secured-puts-strategy – Sellers assignment ke liye kaise prepare karte hain
• 5.4.01-Understanding-the-Greeks – Premiums kyun change hote hain (breakevens affect karta hai)
• 5.5.01-Option-pricing-Black-Scholes-intuition – Premium value kya determine karta hai
• 6.2.01-Risk-reward-ratios – Options vs stocks mein asymmetric risk/reward

Flashcards

#flashcards/stock-market

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