衍生产品市场-课后答案-第二章.pdfVIP

Chapter 2 An Introduction to Forwards and Options Question 2.1 The payoff diagram of the stock is just a graph of the stock price as a function of the stock price: In order to obtain the profit diagram at expiration, we have to incorporate the initial costs of the stock, i.e., how we finance the initial investment. We do this by assuming we borrow $50 at 10% interest. Note that even if we use our own funds to finance the purchase, we want to incorporate the opportunity costs of our investment (i.e., the interest we could have earned). By borrowing $50, after one year we have to pay back: $50 × (1 + 0.1) = $55. The second figure shows the graph of the stock, the $55 we have to pay back, and of the sum of the two positions, which is the profit graph. The arrows show that at a stock price of $55, the profit at expiration is indeed zero. When the stock price is $55, our stock is worth exactly what we owe and, hence, we break even. 10 McDonald • Fundamentals of Derivatives Markets Question 2.2 Since we shorted the stock initially, our payoff at expiration is negative and equal—the stock price. This is the amount we have to spend in order to replace the share of stock we borrowed. Chapter 2 An Introduction to Forwards and Options 11 In order to obtain the profit diagram at expiration, we have to lend out the money we received from the short sale of the stock. We do so by buying a bond for $50. After one year we receive from the investment in the bond: $50 × (1 + 0.1) = $55. The second figure shows the graph of the payoff of the shorted stock, the money we receive from the investment in the bond, and the sum of the two positions, which is the profit graph. The arrows show that at a stock price of $55, the profit at expiration is indeed zero. At $55, the amount of money we receive from our bond investment is exactly offset by the amount of money we need to buy back