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Question 1
You observe the shares on ABC trading at $61.00. Call and put options on ABC shares are also trading. Each option contract is written over 1000 shares. A three month call option at a strike price of $60.00 is trading at $3.00 while the put option is trading at $1.08. Show that there is an arbitrage profit to be made, and give explicit details of how the mispricing will be arbitraged and what the profit (in dollars) of your arbitrage strategy will be. You must show the exact strategy and present the cashflows from the strategy in a table. Assume that the risk-free rate is 4.5% p.a. (continuously compounded).

Question 2
A trader decides to protect her portfolio with a put option. The portfolio is worth $150 million and the required put option has a strike price of $145 million with a maturity of 24 weeks. The volatility of the portfolio is 15% and the dividend yield on the portfolio is 3% per annum. The risk-free rate is 4%. Because the option is not available on exchanges, the trader decides to create an option by maintaining a position in the underlying portfolio with the required delta. What percentage of the original portfolio should be sold and invested at the risk-free rate:
a. Initially at time zero?
b. After one week, when value is $145 million?
c. After two weeks when value is $148 million?