作业答案

第四次作业答案1.a) Buy IBX stock in Tokyo and simultaneously sell them in NY, and your arbitrage profit is $2 per share.b) The prices will converge.c) Instead of the prices becoming exactly equal, there can remain a 1% discrepancy between them, roughly $0.35 in this case.2.a) Money market hedge: borrow the dollar now, convert the dollar into the sterling and deposit the sterling. The future dollar cost is fixed.Forward market hedge: buy (long) forward contractb) The one-year forward rate is:c) If the market forward rate is $1.55/, there is an arbitrage opportunity. Assuming the contract size is 1 million, then the arbitrageur should borrow the dollars, convert into the pounds and invest in pounds, and sell them at the market forward rate. The details and cash flows (in millions) of the transactions are as follows:Arbitrage TransactionsCash Flows at t = 0Cash Flows at t = 1Sell forward short0+$1.55 and -1Borrow dollarConvert dollar into poundDeposit pound+103 .See Lecture Notes and Textbook 4.Terminal payoffs:Short PutLong PutXXProfit/Loss:Short PutLong PutXX5.(You may want to convert the interest rate with annual compounding into the one with continuous compounding first)Therefore, The arbitrage involves selling the put option and the underlying share short and buying the call options and lending for six months. The details of transactions and the resulting cash flows are as follows:Arbitrage TransactionsCash Flows at t = 0t = 6 monthsSell the put short0Sell the share shortBuy the call long0Lend +$0.49006.No Arbitrage ValutionAt maturity (two months) the payoff of the call option with strike price of $49 will be either $4 (if the stock price is $53) or $0 (if the stock price is $48).Construct a portfolio consisting of D shares and borrowing or lending. The payoff of the portfolio replicates the payoff the call option, thereforeSolving the above two equations givesThe value of the portfolio today isTo avoid arbitrage, the value of the call option must be $2.235.Risk-neutral ValuationUp factor: Down factor: Risk-neutral probability of an up movement:The value of the put option is given by7.No-arbitrage valuationAt maturity (three months) the payoff of the European put option with strike price of $40 will be either 0 (if the stock price is $45) or $5 (if the stock price is $45). Construct a portfolio consisting of D shares and borrowing or lending. The payoff of the portfolio replicates the payoff the put option, thereforeSolving the equations givesThe value of the portfolio today isTherefore, the value of the put option is $2.0588.Risk-neutral ValuationUp factor: Down factor: Risk-neutral probability of an up movement:The value of the put option is given by8.a)The price of the European call is:b)The initial replicating portfolio consists of (long) shares and borrowing of In this case, the replicating portfolio includes 0.7042 shares and borrowing of $31.56.9.a) The product provides a six-month return equal to max (0, 0.4R), where R is the return on FTSE 100 index. Suppose S0 is the current value of the index and ST is the value of the index in six months.When an amount A is invested, the return received at the end of six months is:This is of the European call options on the index with the strike price of S0.b) With the usual notions, the value of the option offered is:In this case, The value of the call option is 0.0325AInitial investment: A-0.0325A=0.9675AAt six months: ATherefo