The Bid and Ask prices of the XYZ Companys stock are $100.10 and $100.25 respectively. Consider European Call and European Put options on the stock, both with maturities of 12 months and strike prices of $105. The lending and borrowing rates are 0.05% and 6.5% per annum respectively.

(a) Assume the Bid and Ask prices of the Put option are $10.80 and $11.10 respectively. What range of call option prices (Bid and Ask) will NOT allow arbitrage opportunities? Show the details of your calculations to justify your answer. Hint: Find a condition on the call option bid price that would not allow arbitrage opportunities due to overpricing of the call option; then, find another condition on the call option ask price that would not allow arbitrage opportunities due to underpricing of the call option. Combine the two to get the range of prices needed.

(b) Assume you just purchased 1,000 shares of XYZ stock for $100.25 a share and you would like to hedge the downside risk of this equity portfolio. Assume the delta of the call option, , is 0.3405 and the delta of the put option, , is -0.6595. How many options, and what kind of options, would you buy or sell to delta-hedge the downside risk of your equity portfolio?