Option Basics & Terminology: Definitions, Types, and Mechanics

TAKEAWAYS:

• Options are contracts granting the buyer the right (not obligation) to buy/sell an asset at a fixed price by a set date, with the seller obligated to fulfill the contract.
• Call options profit if the underlying asset’s price rises; put options profit if it falls, with intrinsic value = (Stock Price – Strike Price) for calls or (Strike Price – Stock Price) for puts.
• At-the-money (ATM), in-the-money (ITM), and out-of-the-money (OTM) classify options based on their relationship to the current stock price, directly affecting their premiums.
• American vs. European options differ in exercise timing (anytime vs. expiration), while covered vs. naked positions describe the seller’s risk exposure.
• Dividends and stock splits adjust option strike prices and premiums, requiring recalculations (e.g., a 2-for-1 split halves the strike price).
• Time value (premium – intrinsic value) decays over time (theta), while volatility (vega) and interest rates (rho) influence option pricing.

1. What Are Options? The Core Definition

Options are derivative contracts where the buyer pays a premium to acquire the right (but not the obligation) to:

• Buy (call option) or sell (put option) an underlying asset (stock, commodity, currency, etc.) at a predetermined strike price by a specific expiration date.

Key Parties:

• Buyer (Holder): Pays the premium; benefits if the option is profitable.
• Seller (Writer): Receives the premium; risks unlimited loss if the option is exercised against them.

2. Call vs. Put Options: Side-by-Side Comparison

FIGURE 1: Call vs. Put Payoff Diagrams

Call Option Payoff:

flowchart TD
    A["Stock Price"] -->|"< K"| B["Call Value = 0"]
    A -->|"K"| C["Call Value = S - K"]
    A -->|"> K"| D["Call Value = S - K"]

Put Option Payoff:

flowchart TD
    A["Stock Price"] -->|"< K"| B["Put Value = K - S"]
    A -->|"K"| C["Put Value = 0"]
    A -->|"> K"| D["Put Value = 0"]

• $S$ = Stock price
• $K$ = Strike price

3. Intrinsic vs. Extrinsic Value

• Intrinsic Value: The immediate profit if the option were exercised today.
  • Call: $\text{Intrinsic}=\text{Max}(S-K,0)$
  • Put: $\text{Intrinsic}=\text{Max}(K-S,0)$
• Extrinsic Value (Time Value): The premium beyond intrinsic value, driven by:
  • Time to expiration (theta).
  • Volatility (vega).
  • Interest rates (rho).

Example: For a call option on Chandragiri Hills (Rs 2,500 stock), strike price Rs 2,400, selling for Rs 50:

• Intrinsic value = $2,500-2,400=\text{Rs 100}$.
• Extrinsic value = Rs 50 – Rs 100 = –Rs 50 (unusual; likely due to low volatility).

4. Moneyness: ATM, ITM, and OTM

Options are classified based on their relationship to the current stock price:

FIGURE 2: Moneyness and Intrinsic Value

Call Option:

flowchart TD
    A["Stock Price"] -->|"< K"| B["OTM: Intrinsic = 0"]
    A -->|"K"| C["ATM: Intrinsic = 0"]
    A -->|"> K"| D["ITM: Intrinsic = S - K"]

Put Option:

flowchart TD
    A["Stock Price"] -->|"< K"| B["ITM: Intrinsic = K - S"]
    A -->|"K"| C["ATM: Intrinsic = 0"]
    A -->|"> K"| D["OTM: Intrinsic = 0"]

5. Expiration and Exercise Styles

• Expiration Date: The last day the option can be exercised (European) or exercised (American).
• American Options: Can be exercised anytime before expiration (common for stocks).
• European Options: Can only be exercised on expiration (common for indices).

Example: A put option on NEPSE’s NEPSE-100 Index (European-style) expires on March 31. If the index drops below the strike price on that date, the holder can exercise it.

6. Dividends and Stock Splits: Adjusting Options

A. Dividends

• Call Options: Dividends reduce the call’s intrinsic value (since the buyer gains the dividend but the seller loses it).
  • Adjustment: Subtract the dividend from the stock price when calculating intrinsic value.
• Put Options: Dividends increase the put’s value (since the buyer avoids the dividend cost).

B. Stock Splits

• Rule: The strike price is adjusted divided by the split ratio.
  • Example: If ABC Ltd. splits 2-for-1 (Rs 170 → Rs 85), a call with strike Rs 170 becomes Rs 85.

Worked Example: Stock Split Impact

• Scenario: RK Company stock splits 2-for-1 (Rs 230 → Rs 115). Original call option: strike Rs 200, premium Rs 45.
• Adjusted Strike: $\frac{200}{2}=\text{Rs 100}$.
• New Premium: Typically recalculated based on the new split-adjusted price (not simply halved).

7. Covered vs. Naked Options

FIGURE 3: Covered vs. Naked Call Seller Payoffs

Covered Call:

flowchart TD
    A["Stock Price"] -->|"< K"| B["Profit = Premium"]
    A -->|"K"| C["Profit = Premium"]
    A -->|"> K"| D["Profit = Premium + (K - S)"]

Naked Call:

flowchart TD
    A["Stock Price"] -->|"< K"| B["Loss = Premium"]
    A -->|"K"| C["Loss = Premium"]
    A -->|"> K"| D["Loss = (S - K) - Premium"]

8. Real-World Applications in Nepal

In the Real World

1. NEPSE Investors Hedging Stock Drops

   • Product: NEPSE-listed stocks (e.g., Ncell, NTC).
   • Idea: Investors buy put options to lock in a minimum price (e.g., a put with strike Rs 1,200 on Ncell stock when the market is volatile).
   • Why: Protects against sudden price declines (e.g., during political uncertainty).

2. Banks and Microfinance Institutions (MFIs) Using Options

   • Product: Loan defaults hedging (e.g., by NMB Bank).
   • Idea: Banks buy put options on loan portfolios to insure against borrower defaults (e.g., a put with strike Rs 500,000 on a Rs 600,000 loan).
   • Why: Limits losses if borrowers default (common in agriculture loans).

3. E-commerce Platforms Managing Supply Risks

   • Product: Daraz’s inventory purchases.
   • Idea: Daraz might use call options on commodity prices (e.g., rice, electronics) to lock in future purchase prices, avoiding supply chain shocks.

Worked Example: Daraz’s Rice Purchase Hedging

• Scenario: Daraz needs to buy 10,000 kg of rice in 6 months. Current price: Rs 25/kg. Daraz buys a call option with:
  • Strike price: Rs 28/kg.
  • Premium: Rs 1.50/kg.
• Outcome:
  • If rice price rises to Rs 30/kg: Daraz exercises the call, paying Rs 28/kg (saving Rs 2/kg).
  • If price drops to Rs 22/kg: Daraz lets the option expire, paying Rs 25/kg (saving Rs 3/kg minus premium).

9. Common Exam Questions and Pitfalls

Exam Tip:

• Focus on:
  1. Definitions: Clearly distinguish call/put, intrinsic/extrinsic value, and moneyness.
  2. Calculations: Master intrinsic value formulas and adjustments for dividends/splits.
  3. Real-world ties: Relate options to Nepal’s markets (e.g., NEPSE, banks) or global platforms (e.g., WhatsApp’s volatility hedging).
  4. Multiple-choice traps:
     • "Maximum value of American put is the exercise price." → False. It’s $\text{Max}(K-S,0)$ or the present value of the strike price (for dividends).
     • "At-the-money put has zero intrinsic value." → True (but only if no dividends).

FIGURE 4: Exam Formula Cheat Sheet

Option Intrinsic Value:

flowchart TD
    A["Call Option"] -->|"Intrinsic"| B["Max(S - K, 0)"]
    A -->|"Extrinsic"| C["Premium - Intrinsic"]
    D["Put Option"] -->|"Intrinsic"| E["Max(K - S, 0)"]
    D -->|"Extrinsic"| F["Premium - Intrinsic"]

10. Fully Worked Numerical Example

Scenario: Kathmandu Retail Ltd. (KRL) stock trades at Rs 1,200. You buy a put option with:

• Strike price: Rs 1,100.
• Premium: Rs 80.
• Expiration: 3 months.

Questions:

1. What is the intrinsic value if KRL’s stock drops to Rs 1,000?
2. If KRL splits 1-for-2, what is the new strike price?
3. What is the maximum gain/loss for the buyer/seller?

Solution:

1. Intrinsic Value: $\text{Intrinsic}=\text{Max}(1,100-1,000,0)=\text{Rs 100}$.

   • Total Value = Intrinsic + Premium = Rs 100 + Rs 80 = Rs 180.

2. Stock Split Adjustment:

   • Original strike: Rs 1,100.
   • After 1-for-2 split: $\frac{1,100}{2}=\text{Rs 550}$.

3. Max Gain/Loss:

   • Buyer (Holder):
     • Max gain: Strike price – Stock price = Rs 1,100 – Rs 0 = Rs 1,100 (if stock crashes to Rs 0).
     • Max loss: Premium = Rs 80 (if stock > Rs 1,100).
   • Seller (Writer):
     • Max gain: Premium = Rs 80.
     • Max loss: Unlimited (if stock < Rs 0, but capped by strike price in practice).

TABLE: Payoff Summary

Exam Tip: How This Unit Is Tested

1. Definitions: Expect 1–2 MCQs on call/put, intrinsic/extrinsic value, or moneyness.

   • Example: "An OTM put option has _____ intrinsic value." → Zero.

2. Calculations: Always solve for intrinsic value or adjusted strike prices.

   • Example: "A stock splits 3-for-1. Original strike Rs 500. New strike?" → Rs 500/3 ≈ Rs 166.67.

3. Real-world scenarios: Tie options to Nepal’s context (e.g., NEPSE, banks, Daraz).

   • Example: "How would a bank use put options to hedge loan defaults?"

4. True/False traps: Watch for absolute statements (e.g., "American put’s max value is the strike price" is false unless dividends are zero).

5. Diagrams: Sketch payoff diagrams for calls/puts or moneyness states.

Pro Tip: Memorize the intrinsic value formulas and practice adjustments for splits/dividends. Use NEPSE data (e.g., current stock prices) in examples to stay grounded in Nepal’s markets.