A PRACTITIONERS GUIDE TO PRICING AND HEDGING CALLABLE
LIBOR EXOTICS IN FORWARD LIBOR MODELS
VLADIMIR V. PITERBARG
Abstract. Callable Libor exotics is a class of single-currency interest-rate contracts that
are Bermuda-style exercisable into underlying con
Fixed Income Securities October 12th
Ch9-11
11.a.Because in history there had been more defaults on foreign
currency-dominated debt. Government could generat more local currency
to meet its local currency debt obligation, but cant do the same with
foreign
Fixed Income Securities September 13th
Ch4-2,4
2.a.Bond A: change yield 1 basis point: 8.01%
C=4, y=0.0801/2=0.04005, n=4
C=C[1-1/(1+r)^n]/r=14.518
M/(1+r)^n=85.464
P=$14.518+$85.464=$99.9819
Price value of a basis point is $100-$99.9819=$0.0181 per $100
Fixed Income Securities
Ch9-8,13
8. The coupon rate could increase, which is referred to as step-up, or
decrease, referred to as step-down over time. Usually rating upgrades
could cause step-downs and rating downgrades could cause step-ups
for some securi
Fixed Income Securities
CH15-5,13
5.A predetermined schedule that prioritized the manner in which
principal and interest generated by the underlying collateral must be
used. At the top of the waterfall is cash flows due to senior bondholders,
then down to
Options & Derivatives October 12th
CH11-27,28
27.a.Value of the managers position in one year is
max(V-D,0), V is the value of the company and D is face value of the debt,
this is payoff for a call option on V with a strike price of D.
b.Debt holders get
Options & Derivatives October 5th
Ch9-12,13
Ch10-24, 26, 28, 29
Ch9-12.
a.R is the 2-year zero rate:
4.2/1.04+104.2/(1+R)^2=100
R=4.204%
R is the 3-year zero rate:
4.4/1.04+4.4/1.04204^2+104.4/(1+R)^3=100
R=4.412%
R is the 4-year zero rate:
4.5/1.04+4.5/1
Options & Derivatives September 28th
Ch7-20,21,23,25
20.a.Pay LIBOR and receive 6.21% for three years. Can exchange loans
at 6.45% into loans at LIBOR+0.24%.
b.Receive LIBOR and pay 6.51% for five years. Can exchange loans at
LIBOR+0.75% for loans at 7.26
Thursday August 25th
Fixed Income Securities Ch2: 3,4,5
3.a.After 4 years:
P4=P0*(1+r)^n=500,000*1.057^4=500,000*1.25=$625,000
After 7 years:
P7=P4*(1+r)^n=625,000*(1.072)^3=625,000*1.23=$768,750
Future value of investment: $768,750
b.After 7 years:
P7=P0
Fixed Income Securities August 31st
Ch3-1,2,5
1.The internal rate of return is y within this expression:
P=CF1/(1+y)+CF2/(1+y)^2+CF3/(1+y)^3+CF4/(1+y)^4
7,704=2000/(1+y)+2000/(1+y)^2+2500/(1+y)^3+4000/(1+y)^4
Using a financial calculator:
Press CF
Input -
Fixed Income Securities September 6th
Ch3-7,10
7.a. When held until maturity, based on cash flows IRR=4.54%, annual
yield-to-maturity is 9.08%.
b.PV of Coupon: C*[1-1/(1+y)^n]/y=55*15.31=$842.05
If called in 13 years PV: M*[1/(1+y)^n]=1000*[1/
(1.043965)^
Fixed Income Securities October 11th
CH7-27, 2,3
27.Recovery ratings were developed by Standard & Poors and Fitch for
the corporate bond market. They were developed in response for
investors need for more information than what credit ratings could
supply.
Fixed Income Securities September 29th
CH6-11,2
11.a.Actual number of days:
In February:15th -28th is 14 days counting February 15th.
In March: 31 days
In April: 1st -8th is 7 days without counting April 8th.
In total the actual number of days is 52 days.
Journal
of Business
Finance
43 Accounfing,
18(4), June 199 1, 0306 686X f2.5b
.
ESTIMATING
THE GILT-EDGED
TERM STRUCTURE:
BASIS SPLINES AND CONFIDENCE
INTERVALS
JAMES
M.
STEELEY*
INTRODUCTION
The term structure
of interest rates defines the array of disco
Swaption skews and convexity adjustments
Fabio Mercurio and Andrea Pallavicini
Product and Business Development Group
Banca IMI
Corso Matteotti, 6
20121 Milano, Italy
July 21, 2006
Abstract
We test both the SABR model [4] and the shifted-lognormal mixture
The Joint Estimation of Term Structures ad Credit Spread&
Patrick Houwelin$
Jaap Hock
Frank Kleibergen
Ra,bobank International and
Robeco Group
University of Amsterdam
Erasmus University Rotterdam
First, version: February. 1999
This version: May 24, 2000
Macro Sales 8: Trading Strats
Markets Post-2008
February 2015
Prepared by a Goldman Sachs sales and trading desk, which may have a position
in the products mentioned that is inconsistent with the views expressed in this
material. In evaluating this materi
c
8
Principal
Components
8. I /NTRODUCTfON
A principal component analysis is concerned with explaining the variance-covariance
structure through a few linear combinations of the original variables. Its general objectives are (1) data reduction, and (2) i
CGMMONFAGTORS
AFFECTING BOND RETURNS
ROBERT LITTERMAN AND jOSlE SCHEINKMAN
).'u,f.
:
ROBERT LITTFRMAN is Vice
President. Fixed Indome Research, at
Goldman Sachs 8c Co. in New York.
Josp. SCHEINKMAN is m: Alvin
Baum Professor of Economics at the
University
New estimates of the UK real and
nominal yield curves
Nicola Anderson
and
John Sleath
The views expressed are those of the authors and do not necessarily reflect those of the Bank of
England. The authors wish to thank Robert Bliss and Dan Waggoner for man
MANAGING SMILE RISK
PATRICK S. HAGAN , DEEP KUMAR , ANDREW S. LESNIEWSKI , AND DIANA E. WOODWARD
Abstract. Market smiles and skews are usually managed by using local volatility models a la Dupire. We discover that
the dynamics of the market smile predicte
Options & Derivatives September 7th
Ch1-31,36,38,39
Ch2-27,29,30,35
31.St is the price of the asset in one year.
Trader A profit: St-1000
Trader B profit: max(St-1000,0)-100
36.Call options have higher risks but can also provide higher returns.
Equally pr
Fixed Income Securities August 30th
Ch2-6,7,8,11
6.Because when the discount rate increases, the present value of the
projected benefits decreases; when the discount rate decreases, the
present value increases. Having an accurate discount rate is importan