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27/08/2022
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1 .( 5 pis. ) Find the dollar value today of a 1 – period at- the -money call option on *300, 000 . The spot exchange rateis* 100 = $1. 00 . In the next period , the yen can increase in dollar value by 15 percent or decrease by 15 percent .The risk – free rate in dollars is is = 5%; The risk- free rate in yen is ty = 1%/0 .2 .( 5 pts . ) Find the Black – Scholes price of a six – month call option written on E100 , 000 with a strike price of $1 . 00= $1. 00 . The current exchange rate is $1 . 25 = $1. 00 ; The U.S. risk- free rate is 5 percent over the period and theeuro – zone risk – free rate is 4 percent . The volatility of the underlying asset is 10. 7 percent .3 .( 5 pts . ) Show that in the Black Scholes formula dy = dy – OCT 1 /2 )4 .( 5 pis. ) Draw the tree for a put option on $20 , 000 with a strike price of $10, 000 . The current exchange rate is$1 . 00 = $2.00 and in one period the dollar value of the pound will either double or be cut in half . The currentinterest rates are is = 3% and are if = 2%6.5 .( 5 pts. ) The current spot exchange rate is $1. 55 = $1. 00 and the three – month forward rate is $1 . 60 = $1. 00 .Consider a three – month American call option on $62 , 500 with a strike price of $1. 50 = $1. 00. If you pay andoption premium of $5, 000 to buy this call , at what exchange rate will you break – even ?`6 .( 5 pts . ) From the perspective of the writer of a put option written on E6 2 , 500 . If the strike price is $1. 55 / { , andthe option premium is $1 , 875 , at what exchange rate do you start to lose money ?7 .( 5 pts . ) Suppose you observe the following one – year interest rates , spot exchange rates and futures prices .Futures contracts are available on E10 , 000 . How much risk- free arbitrage profit could you make on one contractat maturity from this mispricing ?So ( S / E )Exchange Rate$1. 45 = $1. 00Interest RateAPRF360 ( S/ E )4%$1. 48 = E1. 008 .( 5 pts . ) Today’s settlement price on a Chicago Mercantile Exchange ( CME ) yen futures contract is$0. 801 1 * *100. Your margin account currently has a balance of $2, 000 . The next three days’ settlement pricesare $0. 8057 / * 100 , $0. 7996 * *100 , and $0. 7985*100 . ( The contractual size of one CME yen contract is* 12 , 500 , 000 ) . If you have a long position in one futures contract , the changes in the margin account from dailymarking – to – market , will result in the balance of the margin account after the third day to be :9 .( 5 pts . ) Yesterday , you entered into a futures contract to buy $6 2 , 500 at $1. 50 per E. Suppose the futures pricecloses today at $1 . 46 . How much have you made / lost ?10 . ( 5 pts. ) Your firm is a U. K. – based exporter of British bicycles . You have sold an order to an Italian firm forE1 , 000, 000 worth of bicycles . Payment from the Italian firm ( in E ) is due in twelve months . Your firm wants tohedge the receivable into pounds . Not dollars . Use the following table for exchange rate data .IN450 – Spring 2019Exam # 3 – Take Home PortionP8 .2180.4+ 1242)
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