1.Short-term interest rates are 5%. An at-the-money six-month $95 call sells for $7. What is the parity value for a six-month at-the-money put, assuming the underlying stock pays no dividends?
2. One-year interest rates are 5%. A stock currently sells for $40 and will either rise to $50 or fall to $35 in six months. Using the binomial option pricing model, determine the fair value of a $45 call.
3. Your company owns coastal land worth $1 million. Pending the outcome of a regulatory decision, in six months the land will either increase in value by exactly 60% or remain unchanged in value. A real estate speculator offers your firm $50,000 for the right to buy the land anytime within the next six months for $1.3 million. The interest rate is 8% per year.
Evaluate this offer and recommend whether or not your company should accept it.
4. A $50, one-year call sells for $4; a $50 one-year put sells for $6.45. If the one-year interest rate is 8%, calculate the implied stock price.
5. Suppose one-year interest rates are 6%. A stock currently sells for $100 and at the end of one year will sell for either $110 or $95.
a. Using binomial pricing, calculate the value of a $105 call.
b. Using your answer to part a and the theory of put call parity, calculate the value of a $105 put.
6. Indicate whether the option premium will rise or fall:
|
Increase in interest rates
|
Call à
|
_____
|
Put à
|
_____
|
|
Decrease in time until expiration
|
Call à
|
_____
|
Put à
|
_____
|
|
Decrease in stock volatility
|
Call à
|
_____
|
Put à
|
_____
|
|
Unexpected increase in cash dividends
|
Call à
|
_____
|
Put à
|
_____
|