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Financial Instruments, Markets and Conventions / A First Look at Options: Payoffs, Bounds, and the Binomial Model

Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets

Every forward and futures contract studied so far commits both sides to a transaction: the long is obligated to buy, the short is obligated to sell. The option breaks this symmetry. The buyer of an option has the right but not the obligation to transact; the seller (writer) has the obligation to transact if the buyer chooses to exercise. This asymmetry has a price — the option premium — paid up front by the buyer to the writer.
Why does asymmetry matter to a quant? An option's payoff is a non-linear function of the underlying. A forward's profit is linear in ST−FS_T - F; a call's payoff is max⁡(ST−K,0)\max(S_T - K, 0) — it is convex in STS_T. That convexity means the delta (sensitivity to the underlying) changes as SS moves, which is the source of both the hedging difficulty and the pricing complexity. Every subsequent note in this topic builds on the mechanical understanding developed here.
Learning objectives. After this note you should be able to:
  • write down the payoff formulas for long/short call/put positions;
  • distinguish European from American exercise and state when each is relevant;
  • define moneyness (ITM/ATM/OTM), intrinsic value, and time value;
  • describe how exchange-traded options are specified (contract size, expiration dates, strike price spacing);
  • explain the OCC's role as central counterparty and how exercise is assigned;
  • compute the initial margin required for a naked written call (CBOE formula);
  • distinguish exchange-traded options from OTC options in terms of customisation, counterparty risk, and liquidity;
  • identify how warrants and employee stock options differ from exchange-traded calls.

In this lesson

  1. Call options
  2. Put options
  3. European vs. American options
  4. Underlying assets and option types
  5. Exchange specification of stock options
  6. Moneyness, intrinsic value, and time value
  7. Trading mechanics: market makers and open interest
  8. Margin requirements for option writers
  9. The Options Clearing Corporation (OCC)
  10. Warrants and employee stock options
  11. OTC options markets

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