Assignment
1) A three-month call option is the right to buy a stock at $20. Currently the stock is selling for $22 and the call is selling for five dollars. You are considering buying 100 shares of the stock ($2200) or one call option ($500).
A) the price of the stock rises to $29 within three months what would be the profits or losses on each position? What would be the percentage gains or losses?
B) if the price of the stock declines to $18 within three months, what would be the profits or losses on each position? What would be the percentage gains or losses?
C) if the price of the stock remains stable at $22, what would be the percentage gains or losses at the expiration of the call option?
2) A particular call is the option to buy stock at $25. It expires in six months and currently sells for $4 when the price of the stock is $26.
a) What is the intrinsic value of the call? What is the time premium paid for the call?
b) What will the value of this call be after six months if the price is $20? $25? $30? $40?
c) If the price of the stock rises to $40 at the expiration date of the call, what is the percentage increase in the value of the call? Does his example illustrate favorable leverage?
d) If an individual buys the stock and sells this call, what is the cash outflow (i.e, net cost) and what will the profit on the position be after six months if the price of the stock is $10? $15? $20? $25? $26? $30? $40?
e) If an individual sells this call naked, what will the profit or loss be on the position after six months if the price of the stock is $20? $26? $40?
3)A particular put is the option to sell stock at $40. It expires after three months and currently sells for $2 when the price of the stock is $42.
a) If an investor buys the put, what will the profit be after three months if the price of the stock is $45? $40? $35?
b) What will the profit from selling this put be after three months if the price of the stock is $45? $40? $35?
c) Compare the answers to a) and b). What is the implication of the comparison?
A call option is the right to buy stock at $50 a share. Currently the option has six months to expiration, the volatily of the stock (standard deviation) is .30, and the rate of interest is 10 percent
A) What is the value of the option according to the Black-Scholes model if the price of the stock is $45, $50, or $55?
B) What is the value of the option whne the price of the stock is $50 and the option expires in six months, three months, or one month?
C) What is the value of the option when the price of the stock is $50 and the interest rate is 5 percent, 10 percent, or 15 percent?
D) What is the value of the option when the price of the stck is $50 and the voliaty of the stock is .40, .30, or .10?
E) What generalzation can be derived from the solutions to these problems?
Black scholes demonstrates that the value of a put option increases the longer the time to expiration. Currently the price of a stock is $100 and there are two put options to sell the stock at $100. The three month option sells for 7.00 and the six month option sells for 4.50.
a. what would you recommened and why?
b. how much do you earn or lose after the first three months at the following prices of the underlying stock ($85, $90, $95, $100, $105, and $110) Assume the worse case scenario.
c. is there any reason to anticipate earning a higher return than your answers in (b) ? (this answer may use straddle.