Question

Assume all rates are per annum continuously compounded

Consider the following three European call options, all expiring in one year. Option A has strike $17.00 and premium $7.00; Option B has strike $22.00 and premium $4.00; Option C has strike $27.00 and premium $2.00. Suppose the price on the stock today is $22.00.

(a) Which call(s) is(are) in-the-money?
A. Option A

B. Option B

C. Option C

D. None of the above

(b) Which call(s) is(are) out-of-the-money?
A. Option A

B. Option B

C. Option C

D. None of the above

(c) Suppose the risk-free rate is 4.7%. What is the maximum possible profit of the butterfly?

Answer 1

a. If the Strike price of an option is less than the Spot price of underlying security, then that option is in the money option.

Option A is correct. (Option with strike price of $17)

b. If the Strike price of an option is more than the Spot price of underlying security, then that option is out of the money option.

Option C is correct (Option with strike price of $27)

c) Butterfly with call option can be done by selling 2 call option of strike price $22 and buying one call option of strike price $17 and $27 each

Maximum Payoff happens when spot price expires at $22

Cash inflow or Outflow at beginning of the year = Premium Received by selling option- Premium paid by buying call option

=2*4-7-2=-$1

At the end of the year Call Option of strike price $27 and $22 will expire

Option payoff from option with strike price $17= 22-17=5

EAR= e^(4.7%.1)-1=4.81% (As Interest rate is continuously compounding)

Future Value of maximum profit=-1*(1+4.81%)+5=$3.95