agentleintroduction國際金融香港大學(xué)wongka-在線瀏覽
2025-01-30 09:46本頁面
【正文】 HKD z = the transaction cost the bank will charge you 34 If I observe S(HKD/ bid USD) and S(HKD/ ask USD), can I conclude that the exchange rate of transaction cost is [ S(HKD/ bid USD) + S(HKD/ ask USD) ] / 2 ? In other words, x = z ? 35 Suppose HKD =1 USD, fixed by HKMA S(HKD/ bid USD) 1 USD ( x) HKD S(HKD/ ask USD) 1 USD ( + z) HKD 36 Nonzero transaction cost ?With nonzero transaction cost, S(j/ask k) S(j/bid k) in general ?S(j/ask k) = 1/S(k/bid j) ?S(j/bid k) = 1/S(k/ask j) ?Noarbitrage condition gives only ?S(1/ask 3) ? S(1/bid 2)S(2/bid 3) 37 S(HKD/USD) ? S(HKD/JPY) S(JPY/USD) without transaction cost A HKD AB JPY ABC USD S(JPY/HKD)=B S(USD/JPY)=C S(HKD/USD)=A 1 USD A HKD 38 Positive arbitrage profit if ? ABC 1 ? S(HKD/USD)*S(JPY/HKD)*S(USD/JPY) 1 ? S(JPY/HKD)*S(USD/JPY) 1/S(HKD/USD) ? S(JPY/HKD)*S(USD/JPY) S(USD/HKD) ? No arbitrage in this direction if ABC ? 1 Note that when transaction cost is zero 1/S(HKD/USD) =S(USD/HKD) 39 How do the arbitrage activities eliminate the arbitrage opportunities? ?Note that we have three markets: ? 1. USD HKD, 2. HKD JPY, 3. JPY USD ? arbitrage opportunities are present if ABC = S(HKD/USD)*S(JPY/HKD)*S(USD/JPY) 1 ?if ABC1 the route of arbitrage is USD ? HKD ? JPY ? USD ? HKD ? .... 40 If ABC1 the route of arbitrage is USD ? HKD ? JPY ? USD ? HKD ? .... ?In the USD HKD market, we sell (supply) USD and buy (demand) HKD. S(HKD/USD) = A will decrease. ?In the HKD JPY market, we sell (supply) HKD and buy (demand) JPY. S(JPY/HKD) = B will decrease. ?In the JPY USD market, we sell (supply) JPY and buy (demand) USD. S(USD/JPY) =C will decrease. ?Now ABC decreases because A, B and C decrease as arbitrage activities occur. ?The arbitrage activities continues until ABC = 1. 41 S(HKD/USD) ? S(HKD/JPY) S(JPY/USD) without transaction cost (reversing the previous strategy) A HKD AB JPY ABC USD S(HKD/JPY)=1/B S(JPY/USD)=1/C S(USD/HKD)=1/A 1 USD A HKD 42 Positive arbitrage profit if ? ABC 1。 . ABC 1 ? Positive arbitrage profit only if S(JPY/bid USD)*S(HKD/ bid JPY)*S(USD/bid HKD) 1 Note that S(JPY/bid USD) S(JPY/ask USD) = 1/S(USD/bid JPY) = 1/C Thus, it may happen that S(JPY/bid USD)*S(HKD/ bid JPY)*S(USD/bid HKD) 1 but ABC1. 50 Why is S(j/ask k) S(j/bid k) in general? A HKD AB USD S(USD/bid HKD)=B S(HKD/bid USD)=A 1 USD A HKD 51 Why is S(j/ask k) S(j/bid k) in general? ?No arbitrage if AB ? 1 ?S(HKD/ bid USD)*S(USD/bid HKD) ? 1 ?S(HKD/bid USD) ? 1/S(USD/bid HKD) ?S(HKD/bid USD) ? S(HKD/ask USD) because S(j/ask k) = 1/S(k/bid j), from their definitions. 52 Can we claim: S(2/bid 3) S(1/bid 2) S(1/bid 3)? ?We know from the noarbitrage condition: S(2/bid 3) S(1/bid 2) ? S(1/ask 3) ?Also S(1/bid 3) S(1/ask 3) ?Ho
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