Consider a non-dividend paying stock. Recall that we have found the forward price of a stock supposing that the market is perfect. In particular, we assumed that the borrowing rate equals the saving rate and that there is no bid-ask spread in trading the stock. Suppose now that the effective borrowing rate is not equal the effective saving rate, in particular, rb(t,T) >rs(t,T). Suppose in addition that the bid price (when you sell or sell short a stock) is lower than the ask price (when you buy the stock), Sask(t) >Sbid(t).
(a) Use, for example, the standard arguments and derive the upper and lower no-arbitrage boundaries on the stock's forward price. Check that there is a range of forward prices under these conditions such that the arbitrage is possible only when the forward price lies outside of this range.
(b) Suppose that Sbid(t) = 49, Sask(t) = 50, the effective borrowing and saving rates are rb(t,T) = 6% and rs(t,T) = 4%. Find out whether or not there are arbitrage opportunities in the market for the following forward prices: (1) 52; (2) 54. In case there are arbitrage opportunities, describe the strategy that exploits them