You hold shares in company X for investment, and you are willing to sell some of your shares or buy more to exploit arbitrage opportunities in $4-$month forward contracts. After the contracts expire, you want to have the same shareholdings as before the arbitrage.

A$.$ Suppose that the shares are currently priced at $$150.$ You can borrow at $4\%$ or lend at $2\%,$ continuously compounded. You are very confident that Company X stock will pay no dividends in the next $4$ months. Within what price range can forward contracts trade without allowing you arbitrage opportunities?

B$.$ Now suppose that when you buy shares in the spot market, you pay the ask price of $$150\mathrm{.}25.$ If you sell, you receive the bid of $$149\mathrm{.}75.$ You also must pay a commission of $$5$ plus $$\mathrm{.}005$ per share each time you buy or sell. Retain the $4\%$ borrowing, $2\%$ lending assumption. For part B$,$ assume that the forward contracts are cash$-$settled and that there is a $$200$ transaction fee for entering the forward contract at time $0.$ Also, assume that whatever the ending price ST$,$ which will be used for settling the forward contract, turns out to be$,$ the bid will be $$\mathrm{.}25$ lower and the ask $$\mathrm{.}25$ higher. $($The ask and bid prices apply to the purchase and sale of shares, not to the forward contract.$)$ What are the no$-$arbitrage bounds on the forward price now, assuming you can buy or sell $10,000$ shares?