Counterparty risk, collateral and funding across asset classes with arbitrage-free dynamical models

326 Pages·2013·4.57 MB·English

Counterparty risk, collateral and funding
across asset classes
with arbitrage-free dynamical models
London Graduate School in Mathematical Finance - MF6 Course
London, Nov 6,7,13,14, 2012
Prof. Damiano Brigo
Chair and co-Head of the Mathematical Finance Research Group
Dept. of Mathematics
Imperial College, London
Thispresentationreflectssolelytheopinionoftheauthorandnotoftheauthoremployers,presentandpast.
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Imperial College London
Agenda I
1 Course based on the BMP Book
http://www.damianobrigo.it/cvabook.pdf
2 Basic Credit Risk Products and Models
CDS and Defaultable bonds
Market implied default probabilities
CDS and Defaultable Bonds: Intensity Models
Intensity models: Constant Intensity
Intensity models: Deterministic Intensity
Intensity models: Stochastic Intensity
3 Counterparty Credit Risk
Counterparty Credit Risk: Introduction
Credit VaR and CVA
CVA, Model Risk and WWR
Collateral
Netting
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Agenda II
Basel III and CVA Risk
CVA after Collateral: Gap Risk
CVA Restructuring
CVA: Unilateral or Bilateral? DVA
CVA: Closeout
CVA: Payout risk
Funding Costs: FVA?
CCPs
CVA ”Best Practices”: CVA Desk
4 The mechanics of counterparty risk
General formula, Symmetry vs Asymmetry
Unilateral Credit Valuation Adjustment (UCVA)
Unilateral Debit Valuation Adjustment (UDVA)
Bilateral Risk and DVA
DVA Hedging?
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Agenda III
Risk Free Closeout or Substitution Closeout?
Can we neglect first to default risk?
Payoff Risk
5 Our modeling approach
6 4 applications: Rates, Commodities Credit and Equity
Rates
Stressing underlying vols, credit spread vols, and correlations
CVA for Commodities
Credit
Equity
7 Counterparty Credit Risk and Collateral Margining
Collateralization, Gap Risk and Re-Hypothecation
Margining Practice
Close-Out Netting Rules
Risk-Neutral Modelling of Bilateral CVA with Margining
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Agenda IV
8 Funding Costs
9 Funding Costs: Quantitative Analysis and ”FVA”
Risk-Neutral Modelling of Bilateral CVA with Margining
The recursive nature of funding adjusted prices
Funding Costs, CVA Desk and Bank Structure
10 CCPs
11 CVA ”Best Practices”: CVA Desk
12 Restructuring Counterparty Risk
Contingent Credit Default Swap
Basel III and CVA
Floating Margin Lending
Global Valuation
13 Conclusions and References
Conclusions
References
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CoursebasedontheBMPBook http://www.damianobrigo.it/cvabook.pdf
Course based on 2002-13 Research and on Book
(c)2012D.Brigo (www.damianobrigo.it) LGSMF6PhD ImperialCollegeLondon 6/325
CoursebasedontheBMPBook http://www.damianobrigo.it/cvabook.pdf
Check also
I have been working on Credit Risk and CVA since 2002.
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BasicCreditRiskProductsandModels CDSandDefaultablebonds
Intro to Basic Credit Risk Products and Models
Before dealing with the current topical issues of Counterparty Credit
Risk, CVA, DVA and Funding, we need to introduce some basic
elements of Credit Risk Products and Credit Risk Modelling.
We now briefly look at:
Products: Credit Default Swaps (CDS) and Defaultable Bonds
Payoffs and prices of such products
Market implied Q probabilities of default defined by such models
Intensity models and probabilities of defaults as credit spreads
Credit spreads as possibly constant, curved or even stochastic
Credit spread volatility (stochastic credit spreads)
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BasicCreditRiskProductsandModels CDSandDefaultablebonds
Defaultable (corporate) zero coupon bonds
We started this course by defining the zero coupon bond price P(t,T).
Similarly to P(t,T) being one of the possible fundamental quantities
for describing the interest-rate curve, we now consider a defaultable
¯
bond P(t,T) as a possible fundamental variable for describing the
defaultable market.
DEFAULTFREE with DEFAULT
timet time T timet time T :
: ←− : : ←− NODEFAULT:1
P(t,T) 1 P¯(t,T) DEFAULT:0
Whenconsideringdefault,wehavearandomtimeτ representingthetimeat
whichthebondissuerdefaults. τ :Defaulttimeoftheissuer
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BasicCreditRiskProductsandModels CDSandDefaultablebonds
Defaultable (corporate) zero coupon bonds I
The value of a bond issued by the company and promising the
payment of 1 at time T, as seen from time t, is the risk neutral
expectation of the discounted payoff
BondPrice = Expectation[ Discount x Payoff ]
P(t,T) = E{D(t,T) 1 |F }, 1 P¯(t,T) := E{D(t,T)1 |G }
t {τ>t} {τ>T} t
where G represents the flow of information on whether default
t
occurred before t and if so at what time exactly, and on the default free
market variables (like for example the risk free rate r ) up to t. The
t
filtration of default-free market variables is denoted by F . Formally, we
t
assume
G = F ∨σ({τ ≤ u}, 0 ≤ u ≤ t).
t t
D is the stochastic discount factor between two dates, depending on
interest rates, and represents discounting.
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