Floaters and Inverse Floaters
Zvi Wiener
tel: 02-588-3049
Spring-03
mswiener@mscc.huji.ac.il
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Investments
106
Straight bond
6
6
6
6
6
6
Floater
L0
0
Zvi Wiener
1
L1
2
L2
3
100+L6
L5
L3
L4
4
5
Floaters, Inverse Floaters
6
7
slide 2
How to treat Floaters
Floater is similar to a constantly renewed loan
with fixed spread (!).
Thus the yield of a floater is equal to the yield
on the basis plus the spread.
Note that some of the Israeli government bonds
have funny linkage to other bonds.
Zvi Wiener
Floaters, Inverse Floaters
slide 3
Pricing of AA Floaters
Years
Cashflow Price
0
-100
1
L0
2
L1
3
L2
4
L3
5
100+ L4
Zvi Wiener
100+L0
100
100+L1
100
100+L2
100
100+L3
100
100+L4
Floaters, Inverse Floaters
slide 4
Pricing of Floaters
Years
Cashflow
0
-100
Fair loan
Difference
Dd

??
i
1 (1  L  d )
4
1
L0+D
-100
2
L1+D
L1+d
D-d
3
L2+D
L2+d
D-d
4
L3+D
L3+d
D-d
5
100+L4+D
100+L4+d
D-d
Zvi Wiener
Floaters, Inverse Floaters
slide 5
Pricing of Floaters
Years
Cashflow
0
-100
Fair loan
Difference
3
100
-100
  ( D??
 d )e ( Si  d )(i  )
1   L  d  0
1
L0+D
2
L1+D
L1+d
D-d
3
L2+D
L2+d
D-d
4
L3+D
L3+d
D-d
5
100+L4+D
100+L4+d
D-d
Two types of duration: index duration and spread duration.
Zvi Wiener
Floaters, Inverse Floaters
slide 6
Reverse (Inverse) Floater
USD 5 year interest rates are 5%, however short
term interest rates are Libor =2%.
Libor = London Interbank offered rate
on Bloomberg see FWCV + currency
One can construct so-called reverse floater:
Zvi Wiener
Floaters, Inverse Floaters
slide 7
Inverse Floater
Years
bond
loan
bond
Reverse Fl.
0
-100
+100
-100
-100
1
5
-L0
5
8
2
5
-L1
5
10-L1
3
5
-L2
5
10-L2
4
5
-L3
5
10-L3
5
105
-100- L4
105
110- L4
Zvi Wiener
Floaters, Inverse Floaters
slide 8
Duration of inverse floater
Inverse Floater = 2*Bond – Floater
IF = 2*B - F
1 d ( IF )
DIF  
IF dr
1 d (2 B  F )
2 dB
1 dF
DIF  


 2 DB  DF
100
dr
100 dr 100 dr
DIF  2DB  DF  2  4.5  0.5  8.5
Zvi Wiener
Floaters, Inverse Floaters
slide 9
See Fabozzi: “The Handbook of Fixed Income
Securities”, ch. 14, Floating Rate Securities.
Duration of Floaters, see in T. Bjork, “Arbitrage
Theory in Continuous Time”, Ch 15.
Accrual Range, see Accrual Swaps in Hull,
“Options, Futures, and Other Derivatives” Ch. 25
Zvi Wiener
Floaters, Inverse Floaters
slide 10