Problem
The current price of a share is $30. In half a year, this share price can either increase to $34 or decrease to $26. You want to sell European call options on this share that pay $1 if the share price increases and nothing if the share price decreases. The risk free rate is 7% per annum compounding continuously. You may assume that there are no arbitrage opportunities and that shares are infinitely divisible.
i. Calculate the number of shares (Δ) that will need to be bought in order to keep the portfolio riskless. Give your answer to 3 decimal places.
ii. Calculate the amount you should charge for each call option. Give your answer in dollars and cents to the nearest cent.