Chapter 5: Options Contracts, Mechanism and Applications (Part 2 of 3)

1. Section 5.3: Options Payoffs Overview

The optionality inherent in option contracts leads to non-linear (asymmetrical) payoff profiles. This fundamental feature distinguishes options from forward and futures contracts, which feature linear or symmetrical payoffs.

• Buyer's Perspective: The buyer of an option pays an upfront premium to cap their maximum potential loss strictly at the premium amount, while retaining potentially unlimited upside profit.
• Writer's Perspective: The writer (seller) receives the upfront premium but assumes the opposite risk profile—maximum gains are strictly capped at the premium received, while potential losses are virtually unlimited.

The six basic positions in derivative and spot markets are:

1. Long Asset (Spot)
2. Short Asset (Spot)
3. Long Call Option
4. Short Call Option
5. Long Put Option
6. Short Put Option

2. Section 5.3.1: Payoff Profile for Buyer of Asset (Long Asset)

2.1 Concept and Mechanism

In a long asset position, an investor purchases the underlying asset (such as the Nifty index portfolio) in the spot market at an initial price and holds it to sell at a future date at an unknown spot price (St).

• Market View: Bullish.
• Payoff Structure: Linear / Symmetrical.
• Payoff Equation: Payoff = St - Initial Asset Price

2.2 Numerical Illustration

Consider an investor who goes long on the Nifty index at a level of 2220.

• If Nifty rises above 2220 (e.g., to 2280), the position generates a profit of 2280 - 2220 = +60.
• If Nifty falls below 2220 (e.g., to 2160), the position incurs a loss of 2160 - 2220 = -60.

Long Asset Summary (Entry Price = 2220): - Spot Price = 2280 --> Profit = +60 - Spot Price = 2220 --> Payoff = 0 (Break-even) - Spot Price = 2160 --> Loss = -60

Key Risk Metrics: - Maximum Profit : Unlimited (as spot price rises) - Maximum Loss : 2220 (if spot price drops to zero) - Break-Even Point: 2220

3. Section 5.3.2: Payoff Profile for Seller of Asset (Short Asset)

3.1 Concept and Mechanism

In a short asset position, an investor sells an asset in the spot market at an initial price (often via short selling or borrowing mechanisms) with the intention of buying it back later at a lower price.

• Market View: Bearish.
• Payoff Structure: Linear / Symmetrical.
• Payoff Equation: Payoff = Initial Selling Price - St

3.2 Numerical Illustration

Consider an investor who goes short on the Nifty index at 2220.

• If Nifty falls below 2220 (e.g., to 2160), the position generates a profit of 2220 - 2160 = +60.
• If Nifty rises above 2220 (e.g., to 2280), the position incurs a loss of 2220 - 2280 = -60.

Short Asset Summary (Entry Price = 2220): - Spot Price = 2160 --> Profit = +60 - Spot Price = 2220 --> Payoff = 0 (Break-even) - Spot Price = 2280 --> Loss = -60

Key Risk Metrics: - Maximum Profit : 2220 (if spot price drops to zero) - Maximum Loss : Unlimited (as spot price rises) - Break-Even Point: 2220

4. Section 5.3.3: Payoff Profile for Buyer of Call Options (Long Call)

4.1 Concept and Mechanism

A long call position gives the buyer the right, but not the obligation, to purchase the underlying asset at a specified strike price (K) on or before expiration by paying an upfront premium.

• Market View: Bullish.
• Payoff Structure: Non-linear.
• Gross Payoff: Max[0, St - K]
• Net Profit / Loss: Max[0, St - K] - Option Premium Paid

4.2 Numerical Illustration

An investor buys a 3-month Nifty call option with a Strike Price (K) of 2250 at a Premium of 86.60.

• Scenario 1 (Nifty Closes at 2400): Spot > Strike. The option is exercised.
  • Gross Payoff = 2400 - 2250 = 150
  • Net Profit = 150 - 86.60 = +63.40
• Scenario 2 (Nifty Closes at 2250): Spot = Strike. The option expires worthless.
  • Net Loss = -86.60 (Premium lost)
• Scenario 3 (Nifty Closes at 2100): Spot < Strike. The option expires un-exercised.
  • Net Loss = -86.60 (Maximum loss strictly capped at premium paid)

Long Call Metrics (Strike = 2250, Premium = 86.60): - Break-Even Spot Price : Strike + Premium = 2250 + 86.60 = 2336.60 - Maximum Profit : Unlimited - Maximum Loss : 86.60 (Limited to Premium Paid)

5. Section 5.3.4: Payoff Profile for Writer of Call Options (Short Call)

5.1 Concept and Mechanism

A short call position obligates the seller/writer to sell the underlying asset at the strike price (K) if the option buyer chooses to exercise. In exchange for accepting this unhedged obligation, the writer collects and keeps the upfront premium.

• Market View: Neutral to Bearish.
• Payoff Structure: Non-linear.
• Gross Payoff: -Max[0, St - K]
• Net Profit / Loss: Option Premium Received - Max[0, St - K]

5.2 Numerical Illustration

An investor writes/sells a 3-month Nifty call option with a Strike Price (K) of 2250 receiving a Premium of 86.60.

• Scenario 1 (Nifty Closes at 2100): Spot < Strike. The buyer lets the option expire worthless.
  • Net Profit = +86.60 (Writer retains full premium).
• Scenario 2 (Nifty Closes at 2400): Spot > Strike. The buyer exercises the option.
  • Gross Loss = -(2400 - 2250) = -150
  • Net Loss = 86.60 - 150 = -63.40

Short Call Metrics (Strike = 2250, Premium = 86.60): - Break-Even Spot Price : Strike + Premium = 2250 + 86.60 = 2336.60 - Maximum Profit : 86.60 (Limited to Premium Received) - Maximum Loss : Unlimited

6. Section 5.3.5: Payoff Profile for Buyer of Put Options (Long Put)

6.1 Concept and Mechanism

A long put position gives the buyer the right, but not the obligation, to sell the underlying asset at the specified strike price (K) on or before expiration by paying an upfront premium.

• Market View: Bearish.
• Payoff Structure: Non-linear.
• Gross Payoff: Max[0, K - St]
• Net Profit / Loss: Max[0, K - St] - Option Premium Paid

6.2 Numerical Illustration

An investor buys a 3-month Nifty put option with a Strike Price (K) of 2250 at a Premium of 61.70.

• Scenario 1 (Nifty Closes at 2100): Spot < Strike. The option is exercised.
  • Gross Payoff = 2250 - 2100 = 150
  • Net Profit = 150 - 61.70 = +88.30
• Scenario 2 (Nifty Closes at 2300): Spot > Strike. The option expires worthless.
  • Net Loss = -61.70 (Maximum loss strictly limited to premium paid)

Long Put Metrics (Strike = 2250, Premium = 61.70): - Break-Even Spot Price : Strike - Premium = 2250 - 61.70 = 2188.30 - Maximum Profit : Strike - Premium = 2250 - 61.70 = 2188.30 (If spot drops to 0) - Maximum Loss : 61.70 (Limited to Premium Paid)

7. Section 5.3.6: Payoff Profile for Writer of Put Options (Short Put)

7.1 Concept and Mechanism

A short put position obligates the seller/writer to buy the underlying asset at the strike price (K) if the option holder exercises their right. The writer earns and keeps the upfront premium as compensation for taking on this obligation.

• Market View: Neutral to Bullish.
• Payoff Structure: Non-linear.
• Gross Payoff: -Max[0, K - St]
• Net Profit / Loss: Option Premium Received - Max[0, K - St]

7.2 Numerical Illustration

An investor writes/sells a 3-month Nifty put option with a Strike Price (K) of 2250 receiving a Premium of 61.70.

• Scenario 1 (Nifty Closes at 2300): Spot > Strike. The buyer lets the option expire worthless.
  • Net Profit = +61.70 (Writer retains full premium).
• Scenario 2 (Nifty Closes at 2100): Spot < Strike. The buyer exercises the option on the writer.
  • Gross Loss = -(2250 - 2100) = -150
  • Net Loss = 61.70 - 150 = -88.30

Short Put Metrics (Strike = 2250, Premium = 61.70): - Break-Even Spot Price : Strike - Premium = 2250 - 61.70 = 2188.30 - Maximum Profit : 61.70 (Limited to Premium Received) - Maximum Loss : Strike - Premium = 2250 - 61.70 = 2188.30 (If spot drops to 0)

8. Summary Matrix of Basic Payoff Positions

9. Key Takeaways & Exam Summary Terms

• Non-Linear Payoffs: The core defining characteristic of options where profit/loss curves bend at the strike price, separating capped losses from open-ended gains or vice versa.
• Zero-Sum Game: The net payoff of a long option position and a short option position with the exact same strike and expiry equals zero—the buyer's profit is strictly equal to the writer's loss.
• Break-Even Point (Calls): Strike Price + Premium.
• Break-Even Point (Puts): Strike Price - Premium.
• Maximum Loss for Put Writers: Occurs if the underlying asset price drops all the way to zero, resulting in a maximum net loss equal to Strike Price - Premium Received.