P1.T3.22.24. Stock option features and variations

David Harper CFA FRM

David Harper CFA FRM
Staff member
Learning objectives: Explain how dividends and stock splits can impact the terms of a stock option. Describe the application of commissions, margin requirements, and exercise procedures to exchange-traded options and explain the trading characteristics of these options. Define and describe warrants, convertible bonds, and employee stock options.


22.24.1. At yesterday's market open, the stock of a certain company jumped up dramatically. Consequently, the exchange introduced a new call option with a specific (higher) strike price and expiration date. The open interest for this particular option, therefore, started at zero. Subsequently, during the day the following five trades were placed by participants Albert (A), Bart (B), Cheryl (C), and Denise (D).
  • Albert (A) buys to open 10 contracts; Bart (B) sells to open 10 contracts
  • Albert (A) buys to open 5 contracts; Cheryl (C) sells to open 5 contracts
  • Albert (A) sells to close 6 contracts; Denise (D) buys to open 6 contracts
  • Albert (A) sells to close 3 contracts; Bart (B) buys to close 3 contracts
  • Denise (D) exercises 4 option contracts that are assigned to Cheryl (C)
At the end of the day, what was the open interest?

a. Zero
b. Five
c. Eight
d. Fifteen

22.24.2. The valuation of a stock option on a non-dividend-paying stock requires only five inputs (six if we include the dividend yield). Three of these are not contractual and vary over time: the stock's price, the stock's volatility, and the riskfree rate assumption. Consequently, a stock option can be described with a limited number of specifications, namely the strike price and the expiration date. (The contract size is typically 100 options).

Despite this relatively basic set of specifications, stock options as trading instruments have several interesting variations and associated features. In regard to margin requirements and instrument variations (i.e., warrants and employee stock options), each of the following statements is TRUE except which is FALSE?

a. Unlike naked options, a written covered call does not obligate the option seller with a margin requirement
b. Unlike exchange-traded options (e.g., CBOE), warrants and employee stock options (ESO) increase the number of the company's shares outstanding upon their exercise
c. If the price of an at-the-money (ATM; i.e., S = K) call option is equal to the price of an ATM put option on the same stock with identical maturity (i.e., if we assume the riskfree rate is zero, then put-call parity ensures c = p when S = K), then their initial margins is also equal
d. Agency theory suggests that better alignment between employees and shareholders (aka, reduction of the principal-agent problem) is achieved when restricted shares are replaced with incentive stock options (ISOs) that can be sold immediately after grant because shareholders do have the right to trade their shares

22.24.3. Every year, Acme Corporation grants stock options to its executives and employees. Like most of its peers, the employee stock options (ESOs) vest over four years and always have a 10-year term. In the event of termination, depending on the particulars, options sometimes accelerate and sometimes are forfeited. Newly recruited executives often receive abnormally large, front-loaded option grants. All option grants always have a fixed strike price, and to date, Acme has never re-priced grants. In the majority of cases, Acme grants at-the-money (ATM) options; in rare cases, Acme grants out-of-the-money (OTM) options. However, Acme never grants in-the-money (ITM) ESOS. To value ESOs, the company has developed basic and advanced versions of both the Black-Scholes-Merton (BSM) and the binomial (aka, lattice) models.

Which of the following statements is TRUE?

a. In theory, the binomial model is better than the BSM model to price the company's ESOs
b. The ESO grants do not dilute the company's shareholders because the company never grants in-the-money options
c. The ESO grants do not reduce the company's reported profit because the ESOs have zero intrinsic value at grant
d. The fair market value (FMV) of the ESOs is equal to the standard BSM value assuming a 10-year term; i.e., c = c(S,K, sigma, 10, r, q)

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