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:

Well-Diversified Portfolios

Investment portfolios constructed to spread out risk by including a variety of asset classes and securities.

Mispriced Securities

Financial instruments whose market price does not accurately reflect their intrinsic value, potentially leading to buying or selling opportunities.

Risk Arbitrage

Speculation on perceived security mispricing, often in connection with merger and acquisition targets.

One-Factor APT

A financial model that describes the relationship between a security's returns and a single factor affecting all securities, used to predict performance.