Option Pricing – Simple Numerical Problems

1. Concept: Moneyness

Before solving, remember:

• In-the-Money (ITM): Has value (Profitable to exercise).
• At-the-Money (ATM): Spot = Strike.
• Out-of-the-Money (OTM): Useless (Spot < Strike for Call). Intrinsic Value is 0.

Problem 1: Payoff for Call Option Holder

Question:

• Mr. X buys a Call Option on Reliance.
• Strike Price: ₹ 2000.
• Premium Paid: ₹ 50.
• Calculate Net Profit/Loss if:
  1. Spot Price at expiry = ₹ 1900.
  2. Spot Price at expiry = ₹ 2200.

Solution:

1. Scenario A (Price = 1900):

   • Strike (2000) > Spot (1900). Market is cheaper.
   • Action: Lapse (Don't exercise).
   • Gross Payoff: 0.
   • Net Profit: 0 - Premium (50) = Loss of ₹ 50.

2. Scenario B (Price = 2200):

   • Spot (2200) > Strike (2000). Market is costlier.
   • Action: Exercise (Buy at 2000, Sell at 2200).
   • Gross Payoff: 2200 - 2000 = ₹ 200.
   • Net Profit: 200 - Premium (50) = Profit of ₹ 150.

Problem 2: Break-Even Point (BEP)

Question:

• Put Option Strike = ₹ 500.
• Premium = ₹ 20.
• Calculate the Market Price at which the buyer Breaks Even.

Solution:

• For Put Option (Right to Sell), you profit if price goes down.
• You paid ₹ 20. So you need to recover ₹ 20 from price fall.
• BEP = Strike Price - Premium.
• BEP = 500 - 20 = ₹ 480.
  • Proof: If price is 480, Payoff = (500-480) = 20. Net = 20 - 20 = 0.

3. Exam Notes: Formula Cheat Sheet

1. Call Payoff: Max(Spot - Strike, 0) - Premium.
2. Put Payoff: Max(Strike - Spot, 0) - Premium.
3. Call Break-Even: Strike + Premium.
4. Put Break-Even: Strike - Premium.

4. Quiz Time! 🎯

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