CFA Level II ExamDerivativesMedium
A financial analyst is evaluating an out-of-the-money European call option with a strike price of $55, expiring in three months. The underlying stock currently trades at $50, pays no dividends, and has a volatility of 25%. The risk-free rate is 4% per annum, compounded continuously. Using the Black-Scholes-Merton model, the analyst calculates the option premium. Which of the following statements about the option's sensitivity to a small change in the underlying stock price is most accurate?
- AThe delta of the option will be close to 1.
- BThe delta of the option will be close to 0.
- CThe delta of the option will be negative.
- DThe delta of the option will be positive but less than 0.5.
Show answer & explanationAnswer & explanation
Correct answer: D. The delta of the option will be positive but less than 0.5.
For an out-of-the-money call option, delta is positive but less than 0.5. As the stock price is well below the strike price, the probability of exercise is low, resulting in a delta closer to 0 than to 0.5 or 1.
Why the other options are wrong
- A. Delta approaches 1 for deep in-the-money call options.
- B. Delta approaches 0 for deep out-of-the-money call options, but this option is not extremely far out-of-the-money.
- C. Delta for a call option is always positive.
Option Delta (Call Option)
Delta measures the sensitivity of an option's price to a $1 change in the underlying asset's price.
- Call option delta ranges from 0 to 1.
- It represents the probability of the option expiring in-the-money.
- Out-of-the-money calls have delta < 0.5; in-the-money calls have delta > 0.5.
Memory trick: Delta 'Drives' option price changes from 'Dollars' in stock price.