Question

You are given the following information: at t = 0: the price of a 10‐ year zero coupon bond with FV = $5,000 is $3,500; f3,12 = 6%. A bank is offering the following product: for every $1 that you give the bank at t = 10, the bank will give you back $1.5 at t = 15, or for every $1 that you borrow from the bank at t = 10, you will have to pay back $1.5 at t = 15. a) Write down one equation where the only unknown is r0,3. You do not need to solve the equation. b) b) Suppose r0,3 were 1% less than your answer to part a. Call this new value r'0,3 Describe how you would construct an arbitrage where at t = 0 you are simultaneously receiving and investing $1. For each rate, you must specify whether you are using it to borrow or lend, and how much (the "how much" can be expressed as a function of r'0,3). For the bond, you must specify whether you are going long or short, and how many units. For the contract, you must specify whether you are using it to invest or borrow, and how much. i) use r0,3' for borrowing $1 ii) use f3,12 for borrowing (1+r0,3')3 iii) buy 1/3500 units of the bond iv) use product for lending 5,000/3,500

          You are given the following information: at t = 0: the price of a 10‐ year zero coupon bond with FV = $5,000 is $3,500; f3,12 = 6%. A bank is offering the following product: for every $1 that you give the bank at t = 10, the bank will give you back $1.5 at t = 15, or for every $1 that you borrow from the bank at t = 10, you will have to pay back $1.5 at t = 15. a)    Write down one equation where the only unknown is r0,3. You do not need to solve the equation.   b)    b) Suppose r0,3 were 1% less than your answer to part a. Call this new value r'0,3 Describe how you would construct an arbitrage where at t = 0 you are simultaneously receiving and investing $1. For each rate, you must specify whether you are using it to borrow or lend, and how much (the "how much" can be expressed as a function of r'0,3). For the bond, you must specify whether you are going long or short, and how many units. For the contract, you must specify whether you are using it to invest or borrow, and how much.  i)              use r0,3' for borrowing $1 ii)          use f3,12 for borrowing (1+r0,3')3             iii)         buy 1/3500 units of the bond              iv)         use product for lending 5,000/3,500

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