Assume you short a call option on a stock with a strike price of $25. The expiration is 3 months. The option premium is $2. Create a table showing the net gains/losses at expiration date at different stock prices. What is the breakeven price (i.e. the price at which the net gain is 0)?

Assume you buy a put option on a stock at a strike price of $30. You also sell a call option on the same stock at a strike price of $40. Both options have the same expiration date. The premium on the put is $2.5 and the premium on the call is $3.00. Draw a diagram showing the net gains/losses at different prices.

You currently own a stock, which you previously bought at a price of $60. Since the market has been up you now have some unrealized gains. However, you are uncertain about the immediate direction of the market, so you decide to protect your stock from any price decline. You buy a put option at a strike price of $70 at a premium of $5. The expiration is 6 months. Draw a diagram showing the net gains/losses of the combined position at different price levels of the stock at the expiration date.

Binomial tree. A stock price is currently $40. It is known that at the end of 1 month it will be either $42 or $38. The risk-free rate is 8% per annum with daily compounding. What is the value of a 1-month European call option with a strike price of $39?

Binomial tree. Use the same information as Problem 5. But calculate the value of a 1-month European put option with a strike price of $39. [Hint: Use exactly the same procedure as the call option but evaluate the put option payoffs instead].

Black-Scholes Model. What is the price of a European call option on a stock when the stock price is $52, the strike price is $50, the risk-free rate is 12% per annum, the volatility is 30% per annum, and the time to expiration is 3 months?

Put-call Parity. Using the result of Problem 7, calculate the price of a European put option.