Trading in Financial Markets
5.5 Plain Vanilla Derivatives
5.5.3 Swaps
trader or broker is not a member of the exchange clearing house, it must arrange to clear trades through a member.
The clearing house requires initial margin and variation margin from its members. The variation margin for a day may be positive or negative and covers the gains and losses during the day. The initial margin is an extra amount held by the exchange that provides protection to the exchange in the event that the member defaults. In addition, the exchange clearing house requires default fund (also known as a guaranty fund) contributions from its members. This provides additional protection to the exchange. If a member defaults and its initial margin and default fund contributions are not enough to cover losses, the default fund contributions of other members can be used.
Exchange clearing house members require margin from brokers and other traders when they agree to clear their trades and brokers require margin from their clients. Typically the relationship between broker and client involves the posting of initial margin (greater than the initial margin applicable to a member). When the balance in the client's margin account (adjusted for daily gains and losses) falls below a maintenance margin level, the client is required to bring the balance back up to the initial margin level.
Whereas a forward contract is equivalent to the exchange of cash flows on just one future date, swaps typically lead to cash flow exchanges taking place on several future dates. The most common swap is a “plain vanilla”
interest rate swap where a fixed rate of interest is exchanged for LIBOR.3 Both interest rates are applied to the same notional principal. (The principal is “notional” because it is used only for the determination of interest
exchanges. The principal itself is not exchanged.) A swap where Company A pays a fixed rate of interest of 3% and receives LIBOR is shown in Figure 5.3. (Note that all rates in this example are semiannually
compounded.) Suppose that in this contract interest rates are reset every six months, the notional principal is $100 million, and the swap lasts for three years. Table 5.4 shows the cash flows to Company A if six‐month LIBOR interest rates prove to be those shown in the second column of the table.
The swap is entered into on March 3, 2019. The six‐month interest rate on that date is 2.2% per year or 1.1% per six months. As a result, the floating‐
rate cash flow received six months later, on September 3, 2019, is 0.011 × 100 or $1.1 million. Similarly, the six‐month interest rate of 2.8% per
annum (or 1.4% per six months) on September 3, 2019, leads to the floating cash flow received six months later (on March 3, 2020) being $1.4 million;
and so on. The fixed‐rate cash flow paid is always $1.5 million (3% of $100 million applied to a six‐month period). Note that the timing of cash flows corresponds to the usual way interest rates such as LIBOR work. The interest is observed at the beginning of the period to which it applies and paid at the end of the period.
Table 5.4 Example of Cash Flows ($ millions) to Company A in Swap in Figure 5.3. Swap lasts three years and has a principal of $100 million.
6‐Month LIBOR Floating Cash Fixed Cash
Net
Date Rate (% per
annum) Flow
Received Flow Paid Cash Flow Mar. 3,
2019
2.20
Sep. 3,
2019 2.80 +1.10 −1.50 −0.40
Mar. 3, 2020
3.30 +1.40 −1.50 −0.10
Sep. 3, 2020
3.50 +1.65 −1.50 +0.15
Mar. 3, 2021
3.60 +1.75 −1.50 +0.25
Sep. 3, 2021
3.90 +1.80 −1.50 +0.30
Mar. 3, 2022
+1.95 −1.50 +0.45
Cash flows do not take account of day count conventions, holiday calendars, and so on. Interest rates are semiannually compounded.
Figure 5.3 A Plain Vanilla Interest Rate Swap
Plain vanilla interest rate swaps are very popular because they can be used for many purposes. For example, the swap in Figure 5.3 could be used by Company A to transform borrowings at a floating rate of LIBOR plus 1% to borrowings at a fixed rate of 4%. The combination of
1. Pay interest at LIBOR plus 1% under loan agreement;
2. Receive LIBOR under swap agreement; and 3. Pay 3% under the swap agreement
nets out to a fixed payment of 4%. It can also be used by Company A to transform an investment earning a fixed rate of 2.5% to an investment earning LIBOR minus 0.5%. The combination of
1. Receive 2.5% on the investment;
2. Receive LIBOR under swap agreement; and 3. Pay 3% under the swap agreement
nets out to a floating income at the rate of LIBOR minus 0.5%.
Example 5.1
Suppose a bank has floating‐rate deposits and five‐year fixed‐rate loans.
As will be discussed in Chapter 9, this exposes the bank to significant risks. If rates rise, the deposits will be rolled over at high rates and the bank's net interest income will contract. The bank can hedge its risks by entering into the interest rate swap in Figure 5.3 (taking the role of Company A). The swap can be viewed as transforming the floating‐rate deposits to fixed‐rate deposits. Alternatively, it can be viewed as
transforming the fixed‐rate loans to floating‐rate loans.
Table 5.5 shows quotes for U.S. dollar swaps that might be posted by the derivatives dealer in Figure 5.3.4 The first row shows that the bank is prepared to enter into a two‐year swap where it pays a fixed rate of 2.55%
and receives LIBOR. It is also prepared to enter into a swap where it
receives 2.58% and pays LIBOR. The bid–offer spread in Table 5.5 is 3 or 4 basis points. The average of the bid and offered fixed rates is known as the swap rate. This is shown in the final column of the table.
Table 5.5 Swap Quotes Made by a Market Maker (percent per annum)
Maturity (years) Bid Offer Swap Rate
2 2.55 2.58 2.565
3 2.97 3.00 2.985
4 3.15 3.19 3.170
5 3.26 3.30 3.280
7 3.40 3.44 3.420
10 3.48 3.52 3.500
The valuation of plain vanilla interest rate swaps is discussed in Appendix D at the end of this book.