a$)$ Following exchange rates are quoted in Auckland $($New Zealand$),$ Gaborone $($Botswana$)$ and London $($U$.$K$.)$

Exchange rate Mid$-$quotes

BWP$/$GBP $13\mathrm{.}9604$

NZD$/$GBP $2\mathrm{.}0173$

BWP$/$NZD $6\mathrm{.}9187$

Show if there is any arbitrage opportunity? If yes, how can you exploit it with an initial arbitrage capital of $10,000,000$ BWP$?$

b$)$ Assume that there are transaction costs in each market as shown in the table below.

Show whether you can make any arbitrage profit?

Exchange rate Bid quotes Ask quotes

BWP$/$GBP $13\mathrm{.}958413\mathrm{.}9624$

NZD$/$GBP $2\mathrm{.}01682\mathrm{.}0178$

BWP$/$NZD $6\mathrm{.}91626\mathrm{.}9212$

c$)$ Discuss why different currency pairs have different bid$-$ask spreads.