Derivatives

Sample Questions for Option Pricing Models FA2011

1. A company’s current stock price is $50, and expected to increase 30% at a probability of 0.8, or to decrease 10% at a probability of 0.2 for the next one year. A European call option with one-year maturity was issued on this stock, and its exercise price is $54. The risk-free rate of return is 10%.

a. Find the equilibrium price of the call option.

b. Find the equilibrium price of a put option with the same conditions as the call.

c. You currently hold 100 shares of the company. How many call options you need to buy or sell to make your portfolio to be risk-free?

d. How many put options you need to buy or sell to make your portfolio to be risk-free?

e. Now, assume all conditions are equal except that the maturities of the options are two years. Find the equilibrium price of the call option.

f. If you want to maintain your portfolio to be risk-free until the end of two years, what will be your hedge ratios for both cases where the stock price increases and decreases after one year?

g. Using the results from the above question, find the call option values after one year for Cu and Cd.

h. Using the results from above, find the call option price today and the hedge ratio to maintain his portfolio to be risk-free.

i. If the put option is an American option, and you can exercise either one year or two years later. What will be the price of the put today?

2. A company’s current stock price is $100 with its standard deviation of 20%, and the exercise price of a call option issued on this stock is $100 with its maturity remaining for 6 months. The risk free rate is 8%.

a. Find the call option price using Black-Scholes model.

b. Find the price of a put option issued on this stock under the same conditions as the call.

c. An investor holds one share of this company. How many call options she has to sell to...