Problem
1. The price of a European put option is 1.20 euros. The underlying asset has a spot price of 20, and the exercise price of this option is 18. The option expires in three months. The risk-free rate is 1%.
a. What is the price of the call option using the put-call parity?
b. Which option is in the money, and which is out of the money?
c. Explain the factors that determine the price of a call option (using the Black-Scholes formula).
2. The price of a non-dividend paying stock is £10 pounds today. The risk free-rate is 2%. The price of a 6-month future on this stock is 12. Are there any arbitrage opportunities, and if yes, which strategy you would follow to realize riskless profit?
3. Describe the approach that the Merton model takes in producing credit ratings. What is the most crucial parameter in the determination of corporate default probability in the Merton model?
4. Describe how banks use the Receiver Operating Characteristic (ROC) curves to gauge the credibility of potential borrowers.