Chapter 1 Problems - Chapter 1 Problems Problem 1.22...

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1 Chapter 1 Problems Problem 1.22. Describe the profit from the following portfolio: a long forward contract on an asset and a long European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. The terminal value of the long forward contract is: 0 T SF where T S is the price of the asset at maturity and 0 F is the delivery price, which is the same as the forward price of the asset at the time the portfolio is set up). The terminal value of the put option is: 0 max( 0) T FS The terminal value of the portfolio is therefore 00 0) TT S F F S 0 max(0 ] T This is the same as the terminal value of a European call option with the same maturity as the forward contract and a strike price equal to 0 F . This result is illustrated in the Figure S1.3. The profit equals the terminal value of the call option less the amount paid for the put option. (It does not cost anything to enter into the forward contract. Figure S1.3 Profit from portfolio in Problem 1.22 Problem 1.23. In the 1980s, Bankers Trust developed index currency option notes (ICONs). These are bonds in which the amount received by the holder at maturity varies with a foreign exchange rate. One example was its trade with the Long Term Credit Bank of Japan. The ICON specified that if the yen–U.S. dollar exchange rate, T S , is greater than 169 yen per dollar at maturity (in 1995), the holder of the bond receives $1,000. If it is less than 169 yen per dollar, the amount received by the holder of the bond is
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2 169 1 000 max 0 1 000 1 T S When the exchange rate is below 84.5, nothing is received by the holder at maturity. Show that this ICON is a combination of a regular bond and two options. Suppose that the yen exchange rate (yen per dollar) at maturity of the ICON is T S . The payoff from the ICON is 1 000 if 169 169 1 000 1 000 1 if 84 5 169 0 if 84 5 T T T T S S S S When 84 5 169 T S the payoff can be written 169 000 2 000 T S The payoff from an ICON is the payoff from: (a) A regular bond (b) A short position in call options to buy 169,000 yen with an exercise price of 1/169 (c) A long position in call options to buy 169,000 yen with an exercise price of 1/84.5 This is demonstrated by the following table, which shows the terminal value of the various components of the position Bond Short Calls Long Calls Whole position 169 T S 1000 0 0 1000 84 5 169 T S 1000 11 169 169 000 T S 0 169 000 2000 T S 84 5 T S 1000 169 169 000 T S 84 5 169 000 T S 0 Problem 1.24. On July 1, 2011, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2012. On September 1, 2011, it enters into a forward contract to sell 10 million Japanese yen on January 1, 2012. Describe the payoff from this strategy. Suppose that the forward price for the contract entered into on July 1, 2011 is 1 F and that the forward price for the contract entered into on September 1, 2011 is 2 F with both 1 F and 2 F being measured as dollars per yen. If the value of one Japanese yen (measured in US dollars) is T S on January 1, 2012, then the value of the first contract (in millions of dollars) at that time is 1 10( ) T SF while the value of the second contract (per yen sold) at that time is:
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Chapter 1 Problems - Chapter 1 Problems Problem 1.22...

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