1. Consider a stock whose future price is log-normally distributed. The required rate of return on the stock in the real world is 15% per annum, and its volatility is 20%. The current stock price is $100. The risk-free interest rate is 5% per annum. What is the real probability that the future stock price in year 3 is greater than $150?

A.0.084

B. 0.181

C. 0.482

D. 0.518

2. A non-dividend-paying stock currently sells for $280. A 2-year European call option on the stock with the strike price of $260 sells for $40. The risk-free rate is 2% per annum. If there is no arbitrage, what should be the price of the 2-year European put option with the same strike price?

A. 9.805

B. 12.174

C. 14.851

D. 29.805

3. A bank tries to construct a protected principal note, where it receives $100 from its clients and guarantees to pay back $100 two years later. In this strategy, the bank first buys a two-year risk-free bond. Also, it considers buying a two-year European put option on a non-dividend-paying stock that currently sells for $80. The risk-free interest rate is 4%. Which of the following puts is certainly infeasible for the bank under no-arbitrage condition?

A. Put with a strike price of $96

B. Put with a strike price of $94

C. Put with a strike price of $92

D. All of the above puts are feasible.

4. A company's current value of assets is $300 million, and the volatility of the asset value is 20% per annum. The future value of assets is log-normally distributed. The company has issued a debt whose face value is $240 million, and it needs to repay the debt in one year. The risk-free interest rate is 5% per annum.

Q1: What is the current value of the company's equity? Use the Black-Scholes-Merton model.

Q2 : What is the default probability under the risk-neutral probability?