agentleintroduction國(guó)際金融香港大學(xué)wongka-全文預(yù)覽
【正文】 ates ?S(j/k) is the number of units of currency j per unit of currency k in the spot exchange market ?., j=Hong Kong dollars。 ., 1/(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) 43 Thus, without transaction cost, we must have ? 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) 44 with transaction cost A HKD AB JPY ABC USD S(JPY/bid HKD)=B S(USD/bid JPY)=C S(HKD/bid USD)=A 1 USD A HKD 45 Positive arbitrage profit if ? ABC 1 ? S(HKD/bid USD)*S(JPY/ bid HKD)*S(USD/bid JPY) 1 ? S(JPY/ bid HKD)*S(USD/bid JPY) 1/S(HKD/bid USD) ? S(JPY/ bid HKD)*S(USD/bid JPY) S(USD/ask HKD) ? No arbitrage opportunity if ? S(JPY/ bid HKD)*S(USD/bid JPY) ? S(USD/ask HKD) ?., S(2/bid 3) S(1/bid 2) ? S(1/ask 3) where 1=USD, 2=JPY, 3=HKD. 46 No arbitrage profit if ?S(JPY/ bid HKD)*S(USD/bid JPY) ? S(USD/ask HKD) ?Or S(2/bid 3) S(1/bid 2) ? S(1/ask 3) where 1=USD, 2=JPY, 3=HKD. 47 with transaction cost Can we arbitrage by reversing the previous strategy? A HKD AB JPY ABC USD S(JPY/bid HKD)=B S(USD/bid JPY)=C S(HKD/bid USD)=A 1 USD A HKD ? ? ? ? ? ? 48 with transaction cost Can we arbitrage by reversing the previous strategy? A HKD AB JPY ABC USD S(JPY/bid USD) ? 1/C 1 USD A HKD S(HKD/bid JPY) ? 1/B S(USD/bid HKD) ? 1/A A=S(HKD/bid USD) C=S(USD/bid JPY) B=S(JPY/bid HKD) 49 We are not sure if we will have a positive arbitrage profit if ? 1/(ABC) 1 。 2 = JPY。 k=. dollars ?S(HK/US)= approximately. 21 S(HKD/USD) vs S(HKD/JPY) S(JPY/USD) ?Suppose no transaction cost ?To get HKD, a holder of USD can use the rate S(HKD/USD) ?Or, he/she can buy JPY at the rate S(JPY/USD) and then use JPY to buy HKD at the rate S(HKD/JPY). In effect he/she is exchanging at a rate of S(HKD/JPY)S(JPY/USD) 22 S(1/3) vs S(1/2) S(2/3) 1 = HKD。 . 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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