Derivatives

• Topic 01

  Derivative Markets and Instruments

  25 questions
• Topic 02

  Forward Contracts: Pricing and Valuation

  21 questions
• Topic 03

  Futures Contracts

  21 questions
• Topic 04

  Swap Contracts

  21 questions
• Topic 05

  Options Fundamentals

  24 questions
• Topic 06

  Options Strategies and Payoffs

  24 questions
• Topic 07

  Options Pricing: Binomial Model

  21 questions
• Topic 08

  Black-Scholes-Merton Model

  24 questions

A few questions from this unit, with the answer and a full explanation. The complete bank is available when you start practising.

1. An investor owns a stock purchased at USD 50 and writes a call option with a strike price of USD 55, receiving a premium of USD 3. What is the maximum profit of the covered call position?

   • A
     USD 5 per share
   • B
     USD 0 per share, because the call premium covers all upside forgone
   • C
     USD 3 per share
   • D
     USD 8 per share
     Correct answer
   Explanation

   The maximum profit of a covered call is capped at the point where the short call is exercised (when S_T ≥ X). At that point, the investor delivers the stock at the strike price of USD 55.

   Maximum profit = (Strike price – Stock purchase price) + Premium received = (55 – 50) + 3 = USD 8

   Above USD 55, any further stock appreciation is offset by the loss on the short call (the investor must deliver shares at USD 55 regardless of how high the stock rises). The upside is capped, not unlimited. USD 3 is only the premium (ignores the stock gain). USD 5 is the stock gain alone (ignores the premium).

2. Why must the futures price converge to the spot price at the contract's expiration date?

   • A
     The futures price converges because regulators require the two prices to be equal on the final trading day
   • B
     The futures price converges to the spot price because the clearinghouse adjusts prices daily until they match
   • C
     If they diverged at expiry, an arbitrageur could buy the cheaper and simultaneously sell the more expensive, earning a riskless profit at no cost
     Correct answer
   • D
     Convergence is optional and occurs only when the contract allows physical delivery
   Explanation

   Convergence at expiry is enforced by arbitrage. At expiration, if the futures price is above the spot price, any trader can simultaneously buy the underlying at the spot price and sell the futures at the higher futures price, delivering the underlying to close the futures position — earning a riskless profit. This arbitrage immediately drives the futures price down and the spot price up until they converge. If the futures price is below spot, the reverse arbitrage (buy futures, short spot) enforces convergence from below. This arbitrage is riskless and costless (in theory), guaranteeing that F_T = S_T at expiry. Convergence is not optional or contractual — it is enforced by market forces.

3. A portfolio manager holds 10,000 shares of a stock at USD 45 per share. She writes a covered call with X = USD 50 and receives a premium of USD 2.50 per share. An unexpected earnings announcement causes the stock to jump to USD 62 before expiry. What is the manager's total profit and loss per share, and what is the opportunity cost of the covered call strategy?

   • A
     Total profit = USD 5.00 per share; opportunity cost = USD 9.50 per share
   • B
     Total profit = USD 7.50 per share; opportunity cost = USD 9.50 per share (the gain foregone above the strike minus the premium)
     Correct answer
   • C
     Total profit = USD 7.50 per share; opportunity cost = USD 12 per share (the full stock gain from USD 45 to USD 57)
   • D
     Total profit = USD 17 per share; no opportunity cost because the covered call outperforms in all scenarios
   Explanation

   Covered call profit at S_T = 62:

   • Stock gain: 62 – 45 = USD 17
   • Short call loss (assignment): –(62 – 50) = –USD 12
   • Premium received: +USD 2.50
   • Net profit = 17 – 12 + 2.50 = USD 7.50 per share

   Opportunity cost (vs. holding the stock outright):

   • Stock outright gain: USD 17
   • Covered call gain: USD 7.50
   • Opportunity cost = USD 17 – USD 7.50 = USD 9.50 per share

   The opportunity cost is the gain surrendered above the call strike due to assignment, reduced by the premium received: (62 – 50) – 2.50 = 12 – 2.50 = USD 9.50. This is the hidden cost of writing covered calls in sharply rising markets.