agentleintroduction國(guó)際金融香港大學(xué)wongka(存儲(chǔ)版)
【正文】 annot last long. ?If S(1/3) S(1/2)S(2/3) and there is no transaction cost, everyone will try to take the sure profit ?Thus, there will be a huge demand for currency 1 and a huge supply of currency 3 until S(1/3) = S(1/2)S(2/3) 27 Cross exchange rates ?Thus, there will be a huge demand for currency 1 and a huge supply of currency 3 until S(1/3) = S(1/2)S(2/3) ?Thus, there will be a huge demand for HKD and a huge supply of USD ?HKD appreciate relative to USD, . ?S(HKD/USD) decreases ? until S(HKD/USD) = S(HKD/JPY)S(JPY/USD) 28 The Principle of No Arbitrage S(1/3) = S(1/2)S(2/3) Given exchange rates S(1/2) and S(2/3), one can easily pute S(1/3) or Given exchange rates S(j/k) and S(k/m), one can easily pute S(j/m) 29 Nonzero Transaction Costs ?S(j/ask k) offer or ask rate is the price that must be paid to the bank to buy one unit of currency k with currency j. ?S(j/bid k) bid rate is the number of currency j received from the bank for the sale of one unit of currency k for currency j. S(j/ask k) S(j/bid k) 30 Nonzero Transaction Costs ?S(USD/ask HKD) is the amount of USD paid to the bank to buy 1 HKD. ?S(HKD/ask USD) is the amount of HKD paid to the bank to buy 1 USD. ?S(USD/bid HKD) is the amount of USD received from the bank for the sale of 1 HKD. ?S(HKD/bid USD) is the amount of HKD received from the bank for the sale of 1 USD. 31 Suppose HKD =1 USD, fixed by HKMA and you sell 1 USD to the bank for HKD S(HKD/ bid USD) 1 USD ( x) HKD x = the transaction cost the bank will charge you 32 Suppose HKD =1 USD, fixed by HKMA and you buy 1 USD from the bank using HKD S(HKD/ ask USD) (1/ y) USD 1 HKD y = the transaction cost the bank will charge you 33 Suppose HKD =1 USD, fixed by HKMA and you buy 1 USD from the bank using HKD S(HKD/ ask USD) 1 USD ( + z) 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/U
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