For Exercises 3.25 and 3.26 you should use the following information. The two currency problems below are modelled in a one-step binomial asset pricing model. X (O), X(1,1) and X11,) will refer to USD/CAD exchange rates (directly quotedl), and J0), 7/1,) and J11.1) will refer to JPY/CAD exchange rates (directly quote). JPY is the abbreviation for the Japanese yen. rite Ru (resp., R., R), for the values at t = 1 in CAD (resp., USD, JPY), of one CAD (USD, JPY). The 30-clay annual interest rates for the various currencies are 5.12%, 5.74% and 0.65%, respectively. So Rd = 1 + 1213 1.004267, R 1.004783 and R, 1.000542. Suppose X(0) and J(0) were 1.2195 (about 82 cents), and 0.011377 (about 88 JPY to CAD). Take X11.) = 1.2821 and J(1.1) = 0.012599. We shall take X(1.1) = 1.1905, which corresponds to 84 cents. We shall also use the notation X(1:1) = X(O), X(1,1)= d.X(0). J(1.1) = w;J(O). J(1) = d, J(O). Exercise 3.25 (Call-put parity for currency options). Let P(O) (resp. C(O)) be the present t = 0) value of a put (call) option to sell (resp., buy) I USD for K CAD (exchange rate K) at time t = 1. If the current exchange rate is X(0), slow that COPO) X(0) K (3.33) 1- Ra Ri You can use either a model independent argument or the appropriate pricing formulae from the one-step binomial asset pricing model Find the value (at t = 0) of the call option to buy 1 USD at time i = 1 for 1.2195 CAD. For this you will need the appropriate pricing formula 1,1)+ (1- no ) where 1 = 1, = M. (3.35) ile - Use equation (3.34) to price the corresponding put option to sell 1 USD at time t = 1 for 1.2195 CAD. When you have done this, verify the formula (3.33) 64 3 The Binomial Model for Other Contracts Exercise 3.26. 1. Let pi (the American pi) be given by (3.35), and the Japanese ) be given the same formula but with all a replaces by j. Define the two Arrow-Debren securities for the up and down states at t=1. Give the price at t= 0 of the up Arrow-Debreu security using (a) the American exchange rates and (b) the Japanese exchange rates. Deduce that Ty 2. Use 1. to show that t) 0.011111. 3. Use (assume valid) the interest parity formula to compute the t = 1 forward exchange rates for USD/CAD, JPY/CAD und USD/JPY 1. Canadian Corporation (CC) owns factories in both Japan and in the United States. Today it = 0) the treasurer of CC goes to merchant bank XYZ to buy an option giving her the right to sell 10 million JPY for 93,688 USD At = 1. By this she hopes to transfer cash from Japanese operations to the U.S. at about the forward rate. Show that the value of this option at t= 1 is in CAD) |-10,000,000J(1) + 93,688 X (1) Find the value of this option in CAD at t = 0.