Two Stocks a and B Both Have a Current Price

question 19

Multiple Choice

Two stocks A and B both have a current price of $100 and are identical in every way except that the risk-neutral probability of default of A in three months is 10%, and that of B is zero. Assume a CRR-style jump-to-default model in which the volatility of both stocks is 30%. The risk-free rate is 2%. Consider the price of three-month at-the-money call options on these two stocks in a one-period jump-to-default tree model. Which of the following statements is valid?

• A) The call option on A is worth less than the call option on B.
• B) The call option on A is worth the same as the call option on B.
• C) The call option on A is worth more than the call option on B.
• D) There is insufficient information to determine which option is worth more.

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Definitions:

Passive Activity

Financial activities in which the taxpayer does not materially participate, often generating passive income or losses for tax purposes.

Rental Losses

Financial losses incurred from renting out property, often deductible under specific conditions on a taxpayer's return.

Active Income

Earnings received from direct labor or active business activities, as opposed to passive income from investments.

Portfolio Income

Income from investments, including dividends, interest, and capital gains, excluding active business income.