2) The current price of a stock is $84. A one-month call option with a strike price of $87 currently sells for $2.80. An investor who feels that the price of the stock will increase is trying to decide between two strategies that require the same upfront cost: Buying 100 shares or buying 3,000 call options (30 call option contracts). How high does the stock price have to rise for the option strategy to be more profitable? 3) In March, a US investor instructs a broker to sell one July put option contract on a stock. The current stock price is $45 and the strike price is $44. The option price is $3. Explain what the investor has agreed to. Under what circumstances will the trade prove to be profitable? What are the risks? 1) An eight-month European put option on a dividend-paying stock is currently selling for $3. The stock price is $30, the strike price is $32, and the risk-free interest rate is 8% per annum. The stock is expected to pay a dividend of $2 three months later and another dividend of $2 six months later. Explain the arbitrage opportunities available to the arbitrageur by demonstrating what would happen under different scenarios. 2) The volatility of a non-dividend-paying stock whose price is $45, is 20%. The risk-free rate is 3% per annum (continuously compounded) for all maturities. Use a two-step tree to calculate the value of a derivative that pays off (max(S- 48,0) where S, is the stock price in four months? 3) A stock is expected to pay a dividend of $0.70 per share in one month, in four months and in seven months. The stock price is $30, and the risk-free rate of interest is 7% per annum with continuous compounding for all maturities. You have just taken a short position in an eight-month forward contract on the stock. Six months later, the price of the stock has become $34 and the risk-free rate of interest is still 7% per annum. What is the value your position six months later