FINA0301 Assignment 3

# FINA0301 Assignment 3 - 1 a The ini tial investment equals...

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1) a.The initial investment equals to (-800+75-45=)-770. This position yields \$815 after one year and so the rate of return is 0.05844. b. In a), we have to pay more that the risk-free rate so we are in risk- less position. And the arbitrage implied is that we should first borrow the money at 5% and then buy the position stated by a). As a result, we yield a sure return at 0.68%. c. From the above calculation, the initial investment would be \$775.25 and the yield would be \$815 one year later with the risk-less rate of 5%. So the difference between the call and put prices that would eliminate arbitrage is \$24.748. d. By using the method of c), we can see that for \$780, the difference is \$58.04105; for \$800, it is \$39.01646; for \$820, it is \$19.99187; and for \$840, it is 0.967283. 2) a.By using the put-call parity for the currency options which is: + P (K, T ) = e rf T x 0 + C (K, T ) + e rT K = e 0 .01 0.009 + 0.0006 + e 0 .05 0.009 = 0 .00891045 + 0.0006 +0.00856106 =0.00025 b.The option price is higher than expected, so we sell the put option and create a long put option synthetically to offset the risk perfectly. The following demonstrates the arbitrage process.

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