Structuring and Pricing Complex Credit Assets
with Monte Carlo / @RISK
22.06.2006 – Jörg Günther
EQUITY VS. CREDIT ASSETS
2
Balance Sheet
Assets
E&L
Current
Assests
-
Equity
-
Fixed
Assets
-
Cash Flows
Pricingmodels
CF from Operations
CF from Investing
CF from Financing
Debt
-
(or: what is left for
1. Debt Service
2. Equity Distributions)
Asset Markets
Equity
Stock-Price
Debt
Debt-Price; CDS
EQUITY VS. CREDIT ASSETS - DERIVATIVES
3
Equity Derivatives
Credit Derivatives
1. Vanilla Options
(Call/Put)
1. Credit Default Swaps
(Credit Risk)
2. Complex Options
(Barrier, Basket,
Cliquet, ...)
2. CDO-Tranches
3. other...
Equity and Credit Assets – and their Derivatives - are
structurally different, but are ultimately based on the
same original Cash Flow of an Entity
DIFFERENCES OF EQUITY AND CREDIT ASSETS
4
Equity Assets
Credit Assets
• liquid markets
• Illiquid markets
• abundant empirical
data on
• less empirical data,
different focus
(default/non-default)
• Underlyings
• Options
Sophisticated
Market & Models
Market & Models
„work in progress“
S&Ps RATING METHODOLOGY FOR CDO-TRANCHES
5
Loss Distribution
Cash-Flow-CDO-Application
• Monte-Carlo for
Synthetic CDOStructure
• Scenarios for
• PDs
• Recovery Rates
• Correlation
• Timing of default
• Interest rates
• Loss-Distribution used as
input for cash-flow-model
BASEL II – HOW MONTE CARLO HELPS TO COVER
REGULATORY ISSUES
6
Balance Sheet Bank
Assets
E&L
Loans
Equity
Basel II
Standard
IRB
• in % of loan
non-specific,
i.e. same or
standardized
risk-weight;
on average
more equiy
to be
provided
eg Project
Finance:
• risk-adjusted
Debt
Based on
Monte-Carlo
More specific
Rating;
on average
less equity
PRICING A WIND POWER PROJECT-FINANCE-DEAL
7
Cash Flow Model
Risk-Parameters
Monte-Carlo
• assumptions
• Scenarios (what-if)
• Expected Loss
• Sources / Uses
• Stochastic
Assumptions
• Rating-Class
• Operating Cash Flow
• Financing Cash Flow
Spread-sheet-example:
Wind-Power-Project
STRUCTURING A PORTFOLIO LOAN – THE CASH FLOW
STRUCTURE
8
Cash Flow of Underlyings
Cash Flow of Financing Structure
• Timing Assumptions
• Order of financing and
repayment/distributions
• Stochastic Assumptions
• Asset return
• Volatility
• Correlation
Spread-sheet-example:
PE-blind-pool
• defining loss / recovery rate
STRUCTURING A PORTFOLIO LOAN – APPLYING MONTECARLO FOR THE PRICING
9
Structuring Parameters
Outputs of Analysis
• Size of Equity-Tranche
• Expected Loss
• Order of Distributions
(Cash-Flow-Waterfall)
• Return on Bank‘s Equity
• Interests
• Return on Sponor‘s Equity
• Volatility / Risk of Returns
• Precise Pricing
• Precise Risk-ReturnPackaging
Spread-sheet-example:
PE-blind-pool
FUNCTIONS OF @RISK OFTEN USED
10
Function
Issue / Questions involved
• Distributions
Calculating Risk: Static -> Stochastic
Analysis (Scenario -> Monte-Carlo)
• Correlation Matrix
Quantifying Diversification:
Portfolio-Structures
• Fit to Distribution
Analyzing empirical data
• D-Uniform-Distribution
Bootstrapping