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Derivatives

Financial instruments whose value is derived from an underlying asset.

Derivatives are financial instruments whose value is derived from an underlying asset, such as stocks, bonds, commodities, or currencies. Examples include options, futures, forwards, and swaps. Derivatives are used for hedging, speculation, and risk management purposes. Analysts must understand the mechanics and risks associated with derivatives to effectively use them in investment strategies.
5 minutes 5 Questions

Concepts covered: Valuation of Contingent Claims, Pricing and Valuation of Forward Commitments

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CFA Level 2 - Derivatives Example Questions

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Question 1

XYZ Company has a one-year European call option on a non-dividend paying stock. The current stock price is $50, the strike price is $55, the risk-free rate is 5%, and the volatility of the stock's returns is 30%. According to the Black-Scholes-Merton model, which of the following statements is most likely true about the value of the call option if the time to expiration is increased from one year to two years, assuming all other factors remain constant?

Correct Answer: The value of the call option will increase as the time to expiration increases, due to the increased probability that the stock price will exceed the strike price at expiration.

The value of the call option will increase as the time to expiration increases. This is because a longer time to expiration provides more opportunity for the stock price to rise above the strike price, making the option more valuable. The other two answers are incorrect: The second answer suggests that the decrease in the present value of the strike price offsets the increased probability of the stock price exceeding the strike price. However, the effect of the increased probability typically dominates, leading to a higher option value. The third answer incorrectly states that the probability of the stock price exceeding the strike price is independent of the time to expiration. In reality, a longer time horizon gives the stock price more chances to rise above the strike price, increasing the option's value.

Question 2

When pricing a European put option using the Black-Scholes-Merton model, which of the following is true about the effect of increased volatility on the option's value?

Correct Answer: Increased volatility will increase the value of the put option.

Increased volatility will increase the value of a European put option when using the Black-Scholes-Merton model. This is because higher volatility implies greater potential price fluctuations in the underlying asset, which increases the probability that the put option will expire in-the-money. The other two answers are incorrect: The second answer states that increased volatility will decrease the put option's value, which is the opposite of the correct relationship between volatility and put option value. The third answer incorrectly states that volatility is not a factor in the Black-Scholes-Merton model. Volatility is, in fact, one of the key inputs in this option pricing model.

Question 3

Under the binomial model for valuing options, which of the following is true about the value of an American call option?

Correct Answer: It is equal to the value of an otherwise identical European call option plus the early exercise premium.

The correct answer is that the value of an American call option is equal to the value of an otherwise identical European call option plus the early exercise premium. This is because an American call option gives the holder the right to exercise the option at any time before expiration, while a European call option can only be exercised at expiration. The early exercise feature of the American call option adds value, known as the early exercise premium. The other two answers are incorrect: - It is not always equal to the value of an otherwise identical European call option, because early exercise can be optimal in certain situations, such as when the underlying stock pays a large dividend. - The value of an American call option is not equal to the European call option value minus an early exercise premium. The early exercise feature adds value to the American call option, it does not reduce it.

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