Under what circumstances would the option be exercised?

Problem Set 3
1. A European put with a strike price of $60 has a premium of $8 is held
until maturity.
(a) When does the short position make money?
(b) Under what circumstances would the option be exercised?
2. A trader buys a call with a strike price of $45 and a put with a strike
price of $40. Both options mature on the same date. The call premium
was $3, and the put premium was $4. Diagram the trader’s profit.
3. The current price of the underlier is $40. A one-year Euro put with
X = 30 is quoted at $7, and a one-year call with X = 50 is quoted at
$5.
(a) An investor buys 100 shares, shorts 100 calls and buys 100 puts.
Diagram her profit.
(b) What if she buys 100 shares, shorts 200 calls and buys 200 puts?
4. Use the Black Scholes European Option Calculator to value a European
call option on a non-dividend paying stock with a current price of $52,
a strike price of $50, risk free rate of 3%, volatility of 30%, and time to
maturity of 12 months.
(a) What is the option’s intrinsic value?
(b) What is it’s time value?
(c) Suppose the actual market price is $8.35. What is the implied
volatility?
5. Use the Black Scholes European Option Calculator to value a European
put option on a non-dividend paying stock with a current price of $15,
a strike price of $32, risk free rate of 4%, volatility of 30%, and time to
maturity of 18 months.
(a) What is the option’s intrinsic value?
(b) What is it’s time value?
(c) Is this possible if the option were American?