Microsoft has issued a zero-coupon bond. The zero-coupon bond has a price in the market today of 97.5 dollars. The zero-coupon bond pays 100 dollars in exactly one year from now. In the event of default, liquidators would be appointed to sell off Microsoft's assets and then distribute the proceeds to bond-holders. Analysts estimate that Microsoft's assets will generate a payment of $60, per every $100 promised, in one year's time in the event of Microsoft defaulting. Microsoft's bonds trade freely in the market and you can sell them short if you have to (without any extra costs). You can also borrow or lend risk-free at 2% per annum (continuously compounded). There are no transactions costs. You are working as a trader and you get a phone call from a customer who has significant exposure to the risk of Microsoft defaulting. She asks if, today, you will sell her a security to help her hedge her default risk. She wants to buy a security (let us call it a DIGITAL DEFAULT contract) from you today which pays nothing at all if Microsoft does NOT default but will pay her 100 dollars exactly one year from now if Microsoft does default (in essence, she wants to buy a kind of insurance contract) in the intervening time period. The aim of this question is to establish at what price should you sell this DIGITAL DEFAULT contract to your customer. Assume the absence of arbitrage. a) Set up a portfolio consisting of a short position in the DIGITAL DEFAULT contract and a position in the Microsoft's bond which is risk-free to you. I want you to be explicit about this portfolio (long? short? how many?) (4 marks) b) What is the value of this portfolio in dollars in one year's time? c) What is the value of this portfolio in dollars today? d) In the absence of arbitrage, and using your answer to part (c), at what price would you sell the DIGITAL DEFAULT contract to your customer? e) By using the risk-neutral valuation principle, check your calculation in part (d). What is the risk-neutral probability of Microsoft defaulting?