Topic 8. Swaps
8.1 Over-the-counter (OTC) Derivatives
8.2 Interest Rate Swap
8.3 Zero Curve
8.4 Forward Curve
8.5 Zero Delta
8.6 Forward Delta
8.7 DV01
1
8.1 OTC Derivatives
2012

Global OTC Derivative Gross Market Value:
-- 25,392 Billion USD
30000

HK GDP:
-- 263 Billion;
-- 96 times of Hong Kong!
25000
20000
15000
10000
5000

0
US GDP:
Hong Kong
United States
GDP
GDP
-- 15,684 Billion;
-- 60% larger than the world largest economy !
Global OTC
Derivatives
2
8.1 OTC Derivatives
http://www.bis.org/statistics/otcder/dt1920a.pdf
3
8.1 OTC Derivatives

The market for swaps has grown enormously, which has raised serious
regulatory concerns regarding credit risk exposures.

Such concerns motivated reforms from global regulators, e.g.,
the Dodd Frank Wall Street Reform Act,
central clearing & collateralizations
18000
16000

OTC swaps in order of mkt value :
-- interest rate: 17,265 billion usd
-- currency:
1,955
-- credit:
1,187
-- commodity:
328
-- equity:
147
14000
12000
10000
8000
6000
4000
2000
0
Rates
FX
Credit
Comm
Equity
4
8.1 Interest Rate Swap
 Swaps are different from most other derivatives
Portfolio of forward contracts
 Marked to market at coupon payment dates
Intermediary should reduce counterparty risk
 Interest rate swap as succession of forwards:
For example, a long position in “payer” means:
-- Swap buyer agrees to pay fixed-rate,
-- Swap seller agrees to pay floating-rate
 Purpose of interest rate swap:
Allows swapping variable-rate income into fixed-rate (or vice versa)
Better match the duration of assets and liabilities -- hedging
5
8.1 Interest Rate Swap
Agreement to exchange fixed for floating interest cash flows
A interest rate swap is quoted by the swap rate
Example: $100m 3.1% 1x10 LIBOR swap
Swap rate 3.1%, every 6m
Bank A
Bank B
3m Libor rate, every 3m
6
8.1 Interest Rate Swap
Ex: $100m 3.1% 1x10 LIBOR swap
Trade level specs:
Notional: 100 million us dollars
Trade date: 2012-Apr-9, today, the date the trade is transacted
Settlement date: 2012-Apr-11, 2bd after the trade date, trade is “live”
Swap effective date: 2013-Apr-11, after 1y, interests start to accrue
Swap expiry date: 2023-Apr-9, after 11y, interests end accruing
7
8.1 Interest Rate Swap
Ex: $100m 3.1% 1x10 LIBOR swap
Floating Leg:
Fixing: 3m USD LIBOR
Pay Freq: quarterly
Reset date: 2 bds before interest accrual period starts
DCT(Day count conventions) : Act/360
BDC(Business day conventions): LON holiday, modified following
8
8.1 Interest Rate Swap
Ex: $100m 3.1% 1x10 LIBOR swap
Fixed leg:
Fixed rate: 3.1% annualized
Pay freq: semiannually
DCT/BDC: 30/360, NY holidays, modified following
9
8.1 Interest Rate Swap
Ex: $100m 3.1% 1x10 LIBOR swap
10
8.1 Interest Rate Swap
Ex: $100m 3.1% 1x10 LIBOR swap
11
8.1 Interest Rate Swap
12
8.1 Interest Rate Swap
Swap Rate – cout.
Discount factor is from the zero curve – RED
Forward LIBOR rate is from the forward curve – Blue
13
8.1 Zero Curve
14
8.1 Zero Curve
15
8.1 Zero Curve
16
8.1 Forward Curve
17
8.1 Forward Curve
18
8.1 Swap Sensitivity – Zero Delta
19
8.1 Swap Sensitivity – Forward Delta
20
8.1 Swap Sensitivity – DV01
21