原創(chuàng) Dorian君 灰?guī)r金融科技 2019-02-23 00:20
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.
我們對金融市場最近的LIBOR（倫敦銀行同業(yè)拆借利率）丑聞非常熟悉。 操縱LIBOR的明顯效果是抵押貸款和公司貸款。 然而，更大的擔(dān)憂是LIBOR在全球范圍內(nèi)被整合到價值約350萬億美元的衍生品合約中.LIBOR以更多的方式影響衍生品。 首先，利率衍生工具使用LIBOR來確定他們在某些日期的收益。 其次，所有衍生工具頭寸均使用LIBOR定價，其中LIBOR用作貼現(xiàn)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決于利率水平。 例如，如果投資者購買CME歐洲美元期貨，他從該衍生品中獲得的利潤將取決于3個月美元LIBOR的水平。其他共同利率衍生品是利率遠期（也稱為遠期利率協(xié)議或FRA），利息 利率互換，利率期權(quán)和結(jié)構(gòu)利率產(chǎn)品。 在這個由兩部分組成的系列文章中，我將展示LIBOR如何影響利率掉期，利率期權(quán)和結(jié)構(gòu)利率產(chǎn)品。
(i) Interest rate swaps
（i）利率互換協(xié)議
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:
讓我們說，當(dāng)市場利率普遍偏高時，BIG公司向其投資者發(fā)行了1億美元的5％固定息票債券。 幾年后，總體利率下降了。 為了從較低的利率中受益，BIG與其投資銀行進行利率互換，條款如下：
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：投資銀行
固定利率：5％p.a。
浮動利率付款人：公司大
浮動利率：6個月Libor，每半年支付一次
名義金額：1億美元
到期日：5年
The swap is shown in Chart 1
互換合約如圖表1所示
Chart 1: Interest rate swap
圖1：利率互換協(xié)議
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.
投資銀行同意在未來五年內(nèi)每年支付1億美元的5.0％。 因此，它將每年支付1億美元或500萬美元的5％。公司BIG同意在未來五年內(nèi)每半年向投資銀行支付6個月Libor的1億美元。
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.
也就是說，銀行將支付6個月的Libor利率，除以2并乘以名義金額，每年兩次。 例如，如果6個月Libor在重置日期為4.2％，則BIG將有義務(wù)支付4.2％/ 2 = 2.4％的名義金額，或2,400,000美元。 （為了簡單起見，不包括日計數(shù)慣例。）這個想法是，BIG從銀行獲得5％的固定利率，并每年將其傳遞給債券持有人。 然后，每隔6個月，BIG將向銀行支付浮動利息。 通過這種方式，在凈額基礎(chǔ)上，BIG正在支付這筆1億美元債券負(fù)債的浮動利息，并將利用未來的利率下降。
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.
讀者現(xiàn)在可能想知道投資銀行。 當(dāng)市場利率下降時，它肯定會造成損失。 那么，銀行就是這樣做的。 在掉期初期，銀行家查看遠期利率曲線，估計未來可從BIG收到的6個月LIBOR。 現(xiàn)在，銀行可以通過多種方式構(gòu)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?
在第一種情況下，讓我們說BIG決定每年從交換中獲得5％的付款利率。銀行將分析其5％固定付款的未來現(xiàn)金流量，并在五年內(nèi)收到浮動利息支付。在低利率遠期環(huán)境中，凈現(xiàn)金流很可能證明對銀行不利。銀行將不得不向BIG收取預(yù)付費用，作為承擔(dān)利率風(fēng)險的補償。在第二種情況下，讓我們說BIG不太熱衷于支付任何前期費用。銀行再次分析其未來現(xiàn)金流量，但這次以固定利率計算，直至凈現(xiàn)金流量的現(xiàn)值幾乎為零。在低利率遠期環(huán)境中，固定利率可能低于原來的5％。根據(jù)這種安排，BIG可能只會收到4％的固定利率，而且只能部分受益于未來的低利率。那么LIBOR如何影響這種掉期？
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，在一個顯而易見的水平上，每六個月重新確定日期，雙方將查看當(dāng)天上午的LIBOR利率，以確定BIG將在六個月內(nèi)向投資銀行支付的利率。 讀者可能會回想起巴克萊銀行案，該銀行的公司交易方據(jù)稱要求其貨幣市場交易商將某一日期的LIBOR利率設(shè)定為不高于（或低于）特定利率，以換取其自身利益。
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.
將此案例應(yīng)用于我們的示例，讓我們假設(shè)BIG的投資銀行每天早上也為LIBOR的設(shè)置做出貢獻。 BIG的投資銀行，作為掉期交易中的浮動利率接收者，可能會傾向于提交更高的倫敦銀行同業(yè)拆借利率，希望當(dāng)天上午LIBOR設(shè)置較高將導(dǎo)致銀行從BIG獲得更高的浮動利率。每個基點都很重要 - 對于這筆交易，一個基點將產(chǎn)生額外的10,000美元（0.01％* 1億美元）。銀行每天都有成千上萬的此類交易。在一個不太明顯的水平上，交易對手的賬本中的交易定價。銀行和BIG必須在賬面上記錄掉期的公允價值。掉期的公允價值僅僅是未來總現(xiàn)金流量（或收益）的現(xiàn)值。例如，讓我們說BIG進入交換的第二年。交換的公允價值將是在2,3,4年末從銀行收到的未來固定的500萬美元，以及將在第2年支付給銀行的未來半年度浮動付款的凈額要獲得這些付款的現(xiàn)值，必須以無風(fēng)險利率貼現(xiàn)。全球市場參與者已經(jīng)習(xí)慣使用LIBOR利率作為貼現(xiàn)率。如果LIBOR人為地高于實際應(yīng)有的水平，BIG可能已經(jīng)估計其凈現(xiàn)金流量低于應(yīng)有的水平，并可能在其中顯示較低的資產(chǎn)或負(fù)債。圖書。
Conclusion
結(jié)論
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.
全球有數(shù)百萬的利率互換，交易對手希望對沖行業(yè)，金融機構(gòu)，養(yǎng)老基金，共同基金，保險公司等利率。除了上述例子中的普通利率互換，還有很多其他利率互換 LIBOR以同樣的方式影響利率互換（如領(lǐng)子，上限，下限，應(yīng)計利息等）的流行變化。在下一篇文章中，我將說明LIBOR如何影響期權(quán)和結(jié)構(gòu)利率產(chǎn)品的收益和定價。
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