关于期权套利问题

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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?

I just give the basic idea. I am too lazy to give the entire answer.

Q1:  Use put call parity. It should have some arbitrage opportunities. Construct two portfolios. If you find C-P>S-Kexp(-rT), you can move S to the left and construct a synthetic bond C-P-S>-Kexp(-rT), you short the overpriced and long the underpriced, you get the arbitrage profit. And if "<" vice versa.

Q2: A put option can be replicated by shorting Delta shares of underlying and deposit the rest of the money with a risk free rate. So initially you should first calculate the put option's value. Then you short delta share of the underlying and deposit the money you get from shorting+the puts value at risk free rate.

After that , whenever the underlying's price changes, you have to calculate a new delta and calculate the additional share you are going to short ( this can be negative means you should buy back some shares) and the money for the additional shares is from the deposit account. You must always keep balance (self-financing)

best,