This article appeared in The Edge on Dec 3, 2012
We are quite familiar with the recent LIBOR (London Interbank Offered Rate) scandal in the financial markets. The obvious effect of the manipulation of the LIBOR is to mortgage loans and corporate loans. However, there was a bigger concern that LIBOR was integrated into approximately USD350 trillion worth of derivative contracts globally.LIBOR affects derivatives in more that one way. Firstly, interest rate derivatives use LIBOR to determine their payoffs at certain dates. Secondly, all derivative positions are priced using LIBOR, where LIBOR is used as the discounting rate.
我们对金融市场最近的LIBOR（伦敦银行同业拆借利率）丑闻非常熟悉。 操纵LIBOR的明显效果是抵押贷款和公司贷款。 然而，更大的担忧是LIBOR在全球范围内被整合到价值约350万亿美元的衍生品合约中.LIBOR以更多的方式影响衍生品。 首先，利率衍生工具使用LIBOR来确定他们在某些日期的收益。 其次，所有衍生工具头寸均使用LIBOR定价，其中LIBOR用作贴现率。
Interest rate Derivatives
利率衍生品
Interest rate derivatives have payoffs depending on interest rate levels. For example if an investor buys the CME Eurodollar Future, his profit from this derivative will depend on what level the 3-month USD LIBOR is.Other common interest rate derivatives are interest rate forwards (also known as forward rate agreements or FRAs), interest rate swaps, interest rate options and structured rate products. In this 2-part article series, I demonstrate how LIBOR can affect interest rate swaps, interest rate options and structured rate products.
利率衍生品的收益取决于利率水平。 例如，如果投资者购买CME欧洲美元期货，他从该衍生品中获得的利润将取决于3个月美元LIBOR的水平。其他共同利率衍生品是利率远期（也称为远期利率协议或FRA），利息 利率互换，利率期权和结构利率产品。 在这个由两部分组成的系列文章中，我将展示LIBOR如何影响利率掉期，利率期权和结构利率产品。
(i) Interest rate swaps
（i）利率互换协议
Let us say that Company BIG issued a $100m 5% fixed coupon bond to its investors when interest rates in the market were generally high. After a few years, the general interest rates have dropped. To benefit from the lower interest rates, BIG enters into an interest rate swap with its investment bank with the following terms:
让我们说，当市场利率普遍偏高时，BIG公司向其投资者发行了1亿美元的5％固定息票债券。 几年后，总体利率下降了。 为了从较低的利率中受益，BIG与其投资银行进行利率互换，条款如下：
Fixed rate payer: Investment Bank
Fixed rate: 5 percent p.a.
Floating rate payer: Company BIG
Floating rate: 6-month Libor, paid semi-annually
Notional amount: $ 100 million
Maturity: 5 years
固定利率付款人：投资银行
固定利率：5％p.a。
浮动利率付款人：公司大
浮动利率：6个月Libor，每半年支付一次
名义金额：1亿美元
到期日：5年
The swap is shown in Chart 1
互换合约如图表1所示
Chart 1: Interest rate swap
图1：利率互换协议
The investment bank agrees to pay 5.0% of $100 million on an annual basis for the next five years. So, it will pay 5% of $100 million, or $5 million, once a year.Company BIG agrees to pay the 6-month Libor on $100 million on a semi annual basis to the Investment Bank for the next five years.
投资银行同意在未来五年内每年支付1亿美元的5.0％。 因此，它将每年支付1亿美元或500万美元的5％。公司BIG同意在未来五年内每半年向投资银行支付6个月Libor的1亿美元。
That is, the bank will pay the 6-month Libor rate, divided by two and multiplied by the notional amount, two times per year. For example, if the 6-month Libor is 4.2% on a reset date, BIG will be obligated to pay 4.2%/2 = 2.4% of the notional amount, or $2,400,000. (To keep it simple, day count conventions are excluded).The idea is that BIG gets the fixed rate of 5% from the bank and passes it on to its bondholders annually. Then at every 6-month intervals BIG will make floating interest payments to the bank. In this way, on a net basis, BIG is paying floating interest payment on this $100m bond liability and gets to take advantage of the falling interest rates in future.
也就是说，银行将支付6个月的Libor利率，除以2并乘以名义金额，每年两次。 例如，如果6个月Libor在重置日期为4.2％，则BIG将有义务支付4.2％/ 2 = 2.4％的名义金额，或2,400,000美元。 （为了简单起见，不包括日计数惯例。）这个想法是，BIG从银行获得5％的固定利率，并每年将其传递给债券持有人。 然后，每隔6个月，BIG将向银行支付浮动利息。 通过这种方式，在净额基础上，BIG正在支付这笔1亿美元债券负债的浮动利息，并将利用未来的利率下降。
The reader may now wonder about the investment bank. Surely it will make losses as interest rates come down in the market. Well, the bank works it out like this. At the initial of the swap, the banker looks at the forward interest rate curve, to estimate the future 6-month LIBOR it could receive from BIG. Now, there are many ways in which the bank can structure the swap.
读者现在可能想知道投资银行。 当市场利率下降时，它肯定会造成损失。 那么，银行就是这样做的。 在掉期初期，银行家查看远期利率曲线，估计未来可从BIG收到的6个月LIBOR。 现在，银行可以通过多种方式构建掉期交易。
In the first scenario, let us say that BIG is determined to receive a rate of exactly 5% payment from the swap every year. The bank will analyse the future cash flows where it makes a 5% fixed payment and receives floating interest payments in the five years. In a low interest rate forward environment, the net cash flows could very well prove negative for the bank. The bank will have to charge an upfront fee to BIG, as compensation for taking on the interest rate risk.In the second scenario, let us say that BIG is not too keen in paying any upfront fees. The bank analyses its future cash flows again but this time, plays around with the fixed rate until the present value of the net cash flows is almost zero. In a low interest rate forward environment, the fixed rate is likely to be lower than the original 5%. Under this arrangement, BIG will probably only receive, perhaps a fixed rate of 4% and can only partially benefit from the low interest rates in future.So how does LIBOR affect this swap?
在第一种情况下，让我们说BIG决定每年从交换中获得5％的付款利率。银行将分析其5％固定付款的未来现金流量，并在五年内收到浮动利息支付。在低利率远期环境中，净现金流很可能证明对银行不利。银行将不得不向BIG收取预付费用，作为承担利率风险的补偿。在第二种情况下，让我们说BIG不太热衷于支付任何前期费用。银行再次分析其未来现金流量，但这次以固定利率计算，直至净现金流量的现值几乎为零。在低利率远期环境中，固定利率可能低于原来的5％。根据这种安排，BIG可能只会收到4％的固定利率，而且只能部分受益于未来的低利率。那么LIBOR如何影响这种掉期？
Well, at an obvious level, every six months re-set dates, both parties will look at the LIBOR rate that morning to determine the rate that BIG will pay the investment bank for a six- month period. Readers may recall the Barclays case, where the corporate deals side of the bank allegedly asked their money market traders to set the LIBOR rate at a certain date to be not higher (or lower) than a certain rate, for its own benefit.
那么，在一个显而易见的水平上，每六个月重新确定日期，双方将查看当天上午的LIBOR利率，以确定BIG将在六个月内向投资银行支付的利率。 读者可能会回想起巴克莱银行案，该银行的公司交易方据称要求其货币市场交易商将某一日期的LIBOR利率设定为不高于（或低于）特定利率，以换取其自身利益。
Applying this case to our example, let us assume that BIG’s investment bank also contributes to the setting of LIBOR every morning. BIG’s investment bank, being a floating rate receiver in the swap deal, could be tempted to submit a higher LIBOR rate, hoping that a higher LIBOR setting that morning will result in the bank receiving a higher floating rate payment from BIG. Every basis point matters – for this deal, one basis point will results in an additional $10,000 (0.01% * $100million). And the bank has thousand of such deals every day.At a less obvious level, is the pricing of the swap in both counterparties’ books. The bank and BIG will have to record the fair value of the swap in their books. The fair value of the swap is simply the present value of the total cash flows (or payoffs) in the future. For example, let us say that BIG is into the 2nd year of the swap. The fair value of the swap will the be the future fixed $5 million received from the bank at end of Year 2,3,4, and 5, netted with the future semi-annual floating payments to be paid out to the bank in Year 2 to 5. To obtain the present value of these payments, they have to be discounted by a risk-free interest rate. Market players globally have been comfortable with using the LIBOR rate as the discount rate.If LIBOR is artificially higher than it really should be, BIG may have valued its net cash flows lower than it should and could be showing a lower asset or liability in its books.
将此案例应用于我们的示例，让我们假设BIG的投资银行每天早上也为LIBOR的设置做出贡献。 BIG的投资银行，作为掉期交易中的浮动利率接收者，可能会倾向于提交更高的伦敦银行同业拆借利率，希望当天上午LIBOR设置较高将导致银行从BIG获得更高的浮动利率。每个基点都很重要 - 对于这笔交易，一个基点将产生额外的10,000美元（0.01％* 1亿美元）。银行每天都有成千上万的此类交易。在一个不太明显的水平上，交易对手的账本中的交易定价。银行和BIG必须在账面上记录掉期的公允价值。掉期的公允价值仅仅是未来总现金流量（或收益）的现值。例如，让我们说BIG进入交换的第二年。交换的公允价值将是在2,3,4年末从银行收到的未来固定的500万美元，以及将在第2年支付给银行的未来半年度浮动付款的净额要获得这些付款的现值，必须以无风险利率贴现。全球市场参与者已经习惯使用LIBOR利率作为贴现率。如果LIBOR人为地高于实际应有的水平，BIG可能已经估计其净现金流量低于应有的水平，并可能在其中显示较低的资产或负债。图书。
Conclusion
结论
There are millions of interest rate swaps globally, with counterparties wanting to hedge against interest rates such as industries, financial institutions, pension funds, mutual funds, insurance companies, etc. Other than the plain vanilla interest rate swap in the above example, many other popular variations of the interest rate swap like collars, caps, floors, range accruals, etc will be affected by LIBOR in the same way.In the next article, I will illustrate how LIBOR affects the payoffs and pricing of an options and structured rate products.
全球有数百万的利率互换，交易对手希望对冲行业，金融机构，养老基金，共同基金，保险公司等利率。除了上述例子中的普通利率互换，还有很多其他利率互换 LIBOR以同样的方式影响利率互换（如领子，上限，下限，应计利息等）的流行变化。在下一篇文章中，我将说明LIBOR如何影响期权和结构利率产品的收益和定价。
