The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
2.5 Debt negotiation models and optimal capital structure
The optionbased approach gives the prices of equity and bonds
in a given capital structure. Instead of the static choice of
capital structure, we would like to analyze some possible choices
of dy
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
3.2 Pricing of defaultable claims using the intensity approach
To price any defaultable claim, the recovery mechanism must be
modeled.
recovery of Treasury
( ) = P ( ), P ( ) is the price of Treasury at , 0 < < 1
multiple defaults
In the course of reorg
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
3.4 Copula approach for modeling default dependency
Two aspects of modeling the default times of several obligors
1. Default dynamics of a single obligor.
2. Model the dependence structure of defaults between the obligors.
Question How to specify a joint
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
1.2 Product nature of credit derivatives
Payoff depends on the occurrence of a credit event:
default: any noncompliance with the exact specification of a contract
price or yield change of a bond
credit rating downgrade
In the case of the default of a bon
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
2.6 Default correlations using structural approach
? Estimation of probabilities of multiple defaults is an important
task in credit analysis and risk management of bond portfolios.
? The use of historical default data to estimate default correlations
can
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
2.1 Mertons firm value model
Built upon a stochastic process of the firms value. [This is not
the book value of the assets, but more like the value that the
firm can be sold including good view.]
Aim to provide a link between the prices of equity and al
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
Homework 01 (Due June 23, 2016)
Problem 1
A firm plans to issue a zerocoupon bond with the notional amount of $100 and
maturities of 2year, 5year or 10year. The asset At of the firm evolves according to a
stochastic differential equation
dAt rAt dt At
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
Homework 02 (June 30, 2016)
Problem 1
Consider the pricing of a zerocoupon bond under recovery of face value, such that
T
Q t r ( X v ) dv
t r ( X v ) dv
V e
1 T  t e
1t T  t ,
Assume that hazard rate is deterministic and the riskfree discount curve
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
1.1 Nature of credit risk
Credit risk consists of two components: default risk and spread risk
1. Default risk: any noncompliance with the exact specification of a contract.
2. Spread risk: reduction in market value of the contract / instrument due to ch
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
2.3 Counterparty risks of swaps
Credit risk of defaultable currency swaps
A financial swap is the exchange of cashflows based on an underlying index under some prescribed terms.
Two major sources of risks
rate risk (change in interest rate or exchange
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
3.3 Default correlation binomial models
Desirable properties for a good model of portfolio credit risk modelling
Default dependence produce default correlations of a realistic
magnitude.
Estimation number of parameters should be limited.
Timing risk pr
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
Chapter 9
Affine Term Structure Models
Spring 2013
Lixin Wu
1
Introduction
The basic feature of affine term structure models is that the
short rate is an affine function of some Markov state variables;
the latter can follow diffusion, jumpdiffusion or L
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
MAFS5230 Advanced Credit Risk Models
Part I
SingleName Credit Derivatives
and
Pricing Models
June 4, 2016
Lixin Wu, HKUST
MAFS 5230 Advanced Credit Risk Models,
Part I
1
Objectives of Part I
Through Part I we will learn
Credit markets and products
Pricin
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
The Pricing of Other Credit Instruments
Credit default swaps (CDS)
Asset swaps
Total return swaps (TRS)
Creditlinked notes (CLN)
LixinWu,HKUST
MAFS5230AdvancedCreditRiskModels,PartI
105
Credit Default Swap (CDS)
Fee for protection ().
Reference bond vs.
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
BlackCox Model (1976)
LixinWu,HKUST
MAFS5230AdvancedCreditRiskModels,PartI
56
Default Time
For analytical pricing, we need to find out the
distribution of .
LixinWu,HKUST
MAFS5230AdvancedCreditRiskModels,PartI
57
Cash Flow of A Defaultable Bond
LixinWu,H
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
Market Model for SingleName Credit Derivatives
Lixin Wu
Department of Mathematics
The Hong Kong University of Science and Technology
L. Wu (HKUST)
MAFS5230, Part I
June, 2015
1 / 57
Outline
1
CDS Pricing the old way
2
CDS Pricing the new way
Redefining r
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
1.3 Credit spread and bond pricebased pricing
Markets assessment of the default risk of the obligor (assuming
some form of market efficiency information is aggregated in the
market prices). The sources are
market prices of bonds and other defaultable se
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
2.2 Extensions of the structural approach to the pricing of
risky debts
1. Interest rate uncertainty
Debts are relatively longterm interest rate sensitive instruments.
The assumption of constant interest rate is embarrassing.
2. Jumpdiffusion process of
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
3.1 Mathematical preliminaries for the construction of intensity processes
Default occurs without warning at an exogenous default rate or
intensity. The dynamics of the intensity are specified under the
pricing measure.
Instead of asking why the firm de
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
%
%
This program is about the calculation of bond prices under the Black %
%
Cox model.
%
%
%
Input model parameters
r=0.05; q=0.02; sig=0.3;
D=100; delta=1; gamma=0.0;
C=[0 0 0];
T=[2 5 10];
% Starting pt of default boundary
% Maturities
A0=130;
dt=1/52
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
MATH690 Credit Risk Models
Homework Two
Spring, 2005
Course Instructor: Prof. Y.K. Kwok
1. In the Merton model of risky debt, suppose we define
V ( ; d) =
A V
,
V A
which gives the volatility of the value of the risky debt. Also, we denote the credit spre
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
MAFS 6010H
Fixed Income Class 3
Tom Bain
1
Class 3.0
Introduction
Morning Meeting:
FX, Equities, Commodities,
Bonds
Report:
1.Market
2.Move (in percent)
3.Term
4.Explanation
5.Whats next
3
For example:
S&P500
Up 0.5%
Overnight
GDP data
Further upward
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
MAFS 6010H
Fixed Income Class 2
Pricing, Spot, Forward, YTM
Tom Bain
Class 2.0
Introduction
Morning Meeting:
FX, Equities, Commodities,
Bonds
Report:
1.Market
2.Move (in percent)
3.Term
4.Explanation
5.Whats next
3
For example:
S&P500
Up 0.5%
Overnight
G
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
$3 trillion corporate credit crunch looms as debtors face day of reckoning, says IMF  Telegraph
10/8/15, 8:50 AM
$3 trillion corporate credit crunch looms as debtors face day of reckoning, says
IMF
A poisonous "triad" of global risks is pushing the world
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
China Wants to Make Currency Policy More MarketOriented, PBOCs Yi Says  WSJ
10/8/15, 11:16 AM
This copy is for your personal, noncommercial use only. To order presentationready copies for distribution to your colleagues, clients or customers visit
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The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
Economists See U.S. on Cusp of Full Employment, WSJ Survey Says  WSJ
10/9/15, 7:54 AM
This copy is for your personal, noncommercial use only. To order presentationready copies for distribution to your colleagues, clients or customers visit
http:/www.dj
The Hong Kong University of Science and Technology
Credit risk: Models, pricing and implementation
MATH 685R

Spring 2006
China's Currency Fix Turns Into More Volatility Everywhere Else  Bloomberg Business
10/8/15, 11:31 AM
China's Currency Fix Turns Into More
Volatility Everywhere Else
Lucy Meakin
Liz McCormick
lucy_meakin
mccormickliz
October 8, 2015 7:00 AM HKT
PBOC has