Hedging Basics: Swaptions

Interest rate options are excellent tools to use to mitigate interest rate exposure.  One robust structure that is used to reduce exposure to monthly periods of interest rate volatility is the interest rate swaption.  This instrument combines the protection of a swap, with the flexibility of a European style option.

Interest Rate Swap
An interest rate swap is a fixed for floating swap which allows an investor or corporate treasurer to reduce their exposure to interest rates by selling or buying a swap.  A pay fixed swap reduces exposure to climbing interest rates while a pay float swap reduces exposure to declining interest rates.

European Option
A European style option is an option in which the purchaser of the option can only exercise the option on the expiration date.  The option is the right but not the obligation to purchase a financial instrument as a specific date in the future.  The strike price is the price at which the buyer and seller of the option agree to buy/sell the financial product.

Interest Rate Swaption
An interest rate Swaption is the right but not the obligation to purchase an interest rate swap on a specific date.  On the expiration date, the owner of the swaption has the right to purchase the swap at the strike price.  A swaption payout profile is similar to a European option.

Swaps: A basic Q and A

This is part 5 of a 10 part series on currency swaps and interest rate swaps and their role in the global economy. In parts 1 through 4, we discussed the differences between interest rate swaps and currency swaps, as well as the pricing mechanisms for fixed-for-floating, floating-for-floating, and fixed-for-fixed swaps. In part 5, we’ll review the basics before looking at some real world examples in parts 6 and 7.

We’ve fielded some basic questions on interest rate swaps and will provide some clear, succinct answers to make this complex financial instrument a little more understandable.

What is a swap?

A swap is a financial derivative in which two parties (called counterparties) exchange future cash flows of the first party’s financial instrument for the future cash flows of the second party’s financial instruments.

What is the most common type of swap?

The most common type of swap is a plain vanilla swap, or an interest rate swap, and is when one party exchanges its fixed rate obligation with a second party’s floating rate obligation. Currency swaps, sometimes referred to as cross-currency swaps, are also very common, especially in the realm of international financing.

I only recently heard of swaps, how long have they been around for?

The first swap, a currency swap, was a $290 million agreement between the World Bank and IBM, in 1981.

How big is the swap market now?

As the world’s deepest financial derivatives market, the over-the-counter (OTC) swaps market has a notional value of $415.2 trillion as of 2006, according to the Bank of International Settlements (sometimes referred to as the central bank for central banks). At that figure, in 2006 dollars, that would make the swaps market approximately 8.5 times the size of global GDP – combined!

Over-the-counter, what does that mean?

Over-the-counter, or OTC, is off-exchange trading of financial instruments, not just swaps, but stocks, bonds, and commodities as well, directly between parties. While most of the swaps market is OTC, meaning it is without a centralized exchange, interest rate swaps can be standardized contracts regulated by exchanges, like futures.

Who uses swaps?

Swaps are utilized by two groups of people: hedgers and speculators. Bona fide hedgers are using swaps to insulate themselves from future risk, whereas speculators are without hedging need and are in the market for the sake of making money. Under CFTC Regulation 1.3(z), no transactions or position will be classified as bona fide hedging unless their purpose is to offset price risks incidental to commercial cash or spot operations and such positions are established and liquidated in an orderly manner in accordance with sound commercial practices.

So bona fide hedgers come from futures trading?

No! Actually, the first hedge exemption was granted by the CFTC to a swaps dealer for OTC index-based exposure where the swaps dealer writing the swap establishes a futures position to hedge its price exposure on the swap. Sounds complicated, but really, the swaps dealer proved he was protecting his capital rather than using it to speculate on swaps.

I have a fixed rate but I really want a floating rate – what do I do?

If your financing is within your borders and you are using your domestic currency, a domestic fixed-for-floating swap is the type of swap you would initiate with another party. This is known as a plain vanilla swap (see above), and is the most common type of swap.

But I’m not using these funds in my country – I’m funding a project aboard

In this case, this would be a fixed-for-floating currency swap, or a cross-currency swap, and it would require a counterparty in the country in which you’re seeking to finance a project.

I remember where I’ve heard swaps before – didn’t Greece get in trouble with swaps?

This is a complicated subject but we will cover it extensively in part 8 of this series.

In part 6 of 10 of this series, we will lay out simple real world examples of how companies would use swaps to hedge against risk in domestic projects as well as projects abroad.

Floating-for-Floating and Fixed-for-Fixed Swaps: Domestic and Foreign Currency Transactions

This is part 4 of a 10 part series on currency swaps and interest rate swaps and their role in the global economy. In parts 1 and 2, we discussed the beginnings of swaps as well as the differences between interest rate swaps and currency swaps. In part 3, we discussed fixed-for-floating swaps. In part 4, we’ll discuss floating-for-floating and fixed-for-fixed swaps.

In the first 3 parts of this series on interest rate swaps and their role in the global economy, we’ve covered the broader strokes of interest rate swaps and currency swaps, with our most recent discussion focusing on fixed-for-floating swaps, or plain vanilla swaps. While similar, fixed-for-fixed swaps are slightly different from their plain vanilla counterpart.

Floating-for-floating rate swaps can be used to limit risk associated with two indexes fluctuating in value. For example, if company A has a floating rate loan at JPY 1M LIBOR and it has a floating rate investment that yields JPY 1M TIBOR + 60-basis points and currently the JPY 1M TIBOR is equal to JPY 1M LIBOR + 20-basis points. Given these metrics, company A has a current profit of +80-basis points. If company A thinks that JPY 1M TIBOR will decrease relative to the LIBOR rate or that JPY 1M LIBOR is going to increase relative to the TIBOR rate, it would initiate a floating-for-floating swap to hedge against downside risk.

Company A finds company B in a similar situation, each finding a comparable advantage to a floating-for-floating swap. Company A can swap JPY TIBOR + 60-basis points and receive JPY LIBOR + 70-basis points. By doing so, company A has effectively locked in profit of 70-basis points instead of holding +80-basis points unprotected to volatility in the base indexes.

A fixed-for-fixed swap is fairly straight forward. Let’s say an American firm, company C, is able to take out a fixed rate loan in the U.S. at 8%, but needs a loan in Australian Dollars to finance a construction project in Australia. However, the interest rate for company C is 12% in Australia. Simultaneously, an Australian company, company D, can take out a fixed rate loan of 9%, but needs a loan in U.S. dollars to finance a construction project in the U.S., where the interest rate is 13%.

This is where a fixed-for-fixed currency swap comes into play: company C (in the U.S.) can borrow funds at 8% and lend the funds to the Australian company for 8%, while company D (in Australia) can borrow funds at 9% and lend the funds to the U.S. company for 9%. The comparable advantage is equal for both company C and company D: both save 4% they would have otherwise had to have spent without fixed-for-fixed currency swaps.

In part 5 of 10 of this series, we’ve fielded some basic questions on interest rate swaps and will provide some clear, succinct answers to make this complex financial instrument a little more ‘plain vanilla.’

Just what is an interest rate swap?

Aside

One of our team was recently asked to give a simple overview of interest rate swaps and how they work. Below was the explanation we put together, using a comparison between an interest rate swap to a fixed-rate bank loan to illustrate the key characteristics.

We think it is a nice, concise and clear way to explain interest rate swaps so thought we would share it.  Comments welcome.

Bank fixed-rate term loan

Interest rate swap

Bank loan type Separate fixed-rate term loan Borrow floating rate (i.e. 90-day rate resets at market rates plus lending margin). The bank can normally change the lending margin on an annual review of the facilities.
Amount being fixed No flexibility, the full loan amount is fixed. Interest rate swap contract can be entered for any amount, in multiples of $1m. E.g. Borrowing facility of $10m, decide to fix 50% now, therefore enter a $5m swap. Later on the percentage fixed can be increased by doing another swap contract.
Fixing of interest rate Per loan documentation, includes bank lending rate for term (say 5 years) plus bank lending margin = all up fixed interest rate that does not change over the term of the loan Interest rate fixed by entering an “interest rate swap” contract. The borrower pays fixed rate and receives floating rate under the swap contract. The floating interest rate received under the swap for the next 90 days nets off against the 90 day interest rate paid on the physical floating rate loan above. Net result is an all up fixed interest rate, being the fixed swap rate plus the normal bank lending margin on the borrowing facility.
Flexibility Cannot unwind early or unknown penalties applied by the bank for early termination. At any time the swap can be unwound or closed down. If term swap rates subsequently increase, the swap is closed down at a realised cash gain –  being the difference between the contracted swap rate and the higher market swap rate for the term left to run (and vice versa).
Documentation Normal bank loan documents Interest rate swap is a separate legal document under standard “ISDA” bank terms.
Term of fixing Interest rate is fixed for the term of the loan A fixed rate swap can be for any term, does not have to be the same maturity date as the underlying bank loan facility. May be shorter or longer.
Use of bank credit limits Loan principal plus 12 months interest cost usually. Loan principal plus 90 days interest cost, plus credit usage of swap agreement (normally 4% x number of years of swap x principal amount). In addition, if market swap rates subsequently reduce to below the contracted fixed rate of the swap, the bank will add on the unrealised “marked-to-market” revaluation loss onto the total credit usage. The bank normally imposes a a maximum term for swap contracts. They may allow fixing the swap interest rate for 10 years with a “right to break” clause that allows the bank to close down the swap after 5 years if they don’t like the borrower’s credit any more.
Cashflow Interest paid monthly or quarterly. Interest on 90-day physical borrowing paid every 90 days and then the bank calculates the difference between the swap fixed rate and market floating rate every 90 days, with the borrower paying the cash difference between the two interest rates to the bank and vice versa.
Fixing the interest rate in advance of loan drawdown Not really possible. “Forward start” swaps can be entered with the fixed rate commencing from a predetermined date. An option can be purchased to enter a fixed rate swap at a future date as well (“swaption”).

Interest Rate Swap Tutorial, Part 3 of 5, Floating Legs

Interest Rate Swap Example

For our example swap we will be using the following inputs:

  • Notional: $1,000,000 USD
  • Coupon Frequency: Semi-Annual
  • Fixed Coupon Amount: 1.24%
  • Floating Coupon Index: 6 month USD LIBOR
  • Business Day Convention: Modified Following
  • Fixed Coupon Daycount: 30/360
  • Floating Coupon Daycount: Actual/360
  • Effective Date: Nov 14, 2011
  • Termination Date: Nov 14, 2016
  • We will be valuing our swap as of November 10, 2011.
In the previous article we generated our schedule of coupon dates and calculated our fixed coupon amounts.

Calculating Forward Rates

To calculate the amount for each floating coupon we do the following calculation:

Floating Coupon = Forward Rate x Time x Swap Notional Amount

Where:

Forward Rate = The floating rate determined from our zero curve (swap curve)
Time = Year portion that is calculated by the floating coupons daycount method.
Swap Notional = The notional amount set in the swap confirmation.

In the next couple articles we will go through the process of building our zero curve that will be used for the swap pricing. In the meantime we will use the following curve to calculate our forward rates and discount our cashflows.

swap zero curve

The numbers at each date reflect the time value of money principle and reflect what $1 in the future is worth today for each given date.

Let’s look at our first coupon period from Nov 14, 2011 to May 14, 2012. To calculate the forward rate which is expressed as a simple interest rate we use the following formula:
simple interest formula
where:

forward rate discount factor

Solving for R
forward rate formula

In our example we divide the discount factor for May 14, 2012 by the discount factor for Nov 14, 2011 to calculate DF.

0.9966889 / 0.9999843 = 0.9967046

T is calculated using Actual/360. The number of days in our coupon period is 182. 182/360 = 0.505556

R = (1 – 0.9967046) / (0.9967046 x 0.505556) = 0.654%

Our first coupon amount therefore is:

Floating Coupon = Forward Rate x Time x Swap Notional Amount

$ 3,306.33 = 0.654% x 0.505556 x $1,000,000

Below is a table with our forward rate calculations & floating coupon amounts for the rest of our coupons.

swap forward rates

The final step to calculate a fair value for our complete swap is to present value each floating coupon amount and fixed coupon amount using the discount factor for the coupon date.

Present Value of Net Coupon is
(Floating Coupon Amount – Fixed Coupon Amount) x Discount Factor

interest rate swap

Our net fair value of this swap is $ 0.00 as of November 10, 2011.

So far in this tutorial we have gone through basic swap terminology, fixed leg coupon calculations, calculating forward rates for floating leg coupon calculations and discounted our cashflows to value a swap.

Thanks to our sister company Resolution for providing us with this series of posts.

Next Article: Present value of money & bootstrapping a swap curve

Interest Rate Swap Tutorial, Part 5 of 5, building your swap curve

Swap Curve

In the final article in this series, we will continue to build out our discount factor curve using longer datedpar swap ratesPar Swap rates are quoted rates that reflect the fixed coupon for a swap that would have a zero value at inception.

Let look at our zero curve that we have built so far using LIBOR rates.

zero curve

We are now going to build out this curve out to 30 years using par swap rates. These rates are as of Nov 10, 2011, and reflect USD par swap rates for semi-annual LIBOR swaps. The daycount convention is 30/360 ISDA.

par swap rates

Also keep in mind that these rates reflect the settlement conventions, so the one year rate is for an effective date of Nov 14, 2011 and termination of Nov 14, 2012. If we were to price a one year swap from the curve we have built so far, we can derive the 6mo discount factor, but we are currently missing the 1year factor. Since we know the swap should be worth par if we receive the principal at maturity, then the formula for a one year swap is:

1 year par swap rate resized 600

Notice that the T’s would be adjusted for holidays & weekends and are calculated using the appropriate discount factor. We can rearrange our formula to solve for df(1year).

swap bootstrapping

Using our example data:

discount factor par swap

We calculate the missing discount factor as: 0.99422634. But, this for a swap which settles on November 14th, and we are building our curve as of November 10th. So we need to multiple this by the discount factor for November 14th to present value the swap to November 10th. So the discount factor we use in our curve for Nov 14, 2012 is 0.9942107.

We continue by calculating discount factors for all the cashflow dates for our par swap rates. The next step is to calculate the discount factor for May 14, 2013. Our first step is to calculate a par swap rate for this date as it is not an input into our curve. We linear interpolate a rate between our 1 year and 2 year rates.

1.5 year par swap rate = 1 year + (2 year – 1 year)/365 x days

= .58% + (.60%-.58%)/365 x 181 = 0.589918%

We now can solve for the missing discount factor, continuing our bootstrapping through the curve.

zero curve construction

Thanks to our sister company Resolution for providing us with this series of posts.