Market Consistent

Economic Scenario Generator
Ricky Power, CERA, Solutions Specialist
[email protected]
Moody’s Analytics Overview – beyond credit ratings
2002
2005
2008
Quantitative
Credit Analysis
Economic
Analysis
ERM
Software
2011
Insurance
Specialist
Research-Led Risk Management Solutions for Financial Institutions
2
2
What is an ESG?
3
What is an Economic Scenario Generator?
» Uses Monte Carlo simulation to generates 1000s of different paths of the economy by
stochastically modelling many different risk drivers
– Interest rates, equity returns, corporate bond returns
20%
20%
15%
15%
10%
x5,000
5%
Short Rates
Short Rate
» A simulation is a collection of many paths (trials)
10%
5%
0%
0%
-5%
-5%
Single path
Distributions of paths
Economic
Scenario
Generator
4
Stochastic Process – Example
» Describe dynamic behaviour of the short rate
– e.g. Vasicek model:
Mean reversion level
Speed of mean reversion
Volatility
Brownian Motion
» Z(t) is a Wiener Process (Brownian motion) in risk-neutral world
» A Brownian motion, W(t) or Z(t), is a process for describing the evolution of a normally
distributed random variable.
» dW(t) or dZ(t) represent the normally distributed increments of a Brownian motion.
– Also referred to as “Shocks”
5
B&H Economic Scenario Generator (ESG)
Equity Returns
Property Returns
Alternative Asset Returns
(eg commodities)
Corporate Bond
Returns
Credit risk model
Initial swap and
government nominal
bonds
Nominal short
rate
Real-economy; GDP
and real wages
Nominal minus
real is inflation
expectations
Index linked
government bonds
Exchange rate
(PPP or Interest
rate parity)
Real short rate
Realised Inflation
and “alternative”
inflation rates (e.g.
Wage, Medical)
Foreign nominal
short rate and
inflation
6
Correlations and Dynamic Behaviours
Inter-economy Correlations
Intra-economy Correlations
7
How the ESG is used?
» Data & Opinions
»Time series
» Market prices
» Expert judgements
Calibrations
Scenarios
ESG
ALM System
»Prophet, Igloo, Moses,
Remetrica etc.
»Delivered by B&H
»Calibration tools
Results
Model
Parameters
»Business Activities
»Decisions
8
Use of the ESG in the insurance sector
Calculation of cost of options and guarantees
(EV, Fair Value, Best Estimate Reserves )
Best Estimate Reserves,
Standard Formula
Economic Capital calculation
Internal models, ORSA
ALM, Asset Allocation, Business Planning
Hedging
Use Test
Pricing and product development
Retail advisory
9
2
Market Consistent vs Real World
10
Market Consistent
» Pre-Solvency II regime: Insurers are to define
discount rates that are appropriate to their
asset and liability exposures.
» Assets could be projected using their own
risky returns
E.g. Solvency II
» Valuation does not converge to Market Value
 Market-consistent frameworks: MCEV and SII
 All assets earn risk-free rate
• No arbitrage condition
• Risk-free discounting and Risk-Neutral
valuation
 Use Market Value wherever possible
11
Using Market Consistent Scenarios
In Solvency II, Market-Consistent scenarios are used to value TVOG.
Can I use the same set of Market-Consistent scenarios to determine the
99.5% percentile of my risk-capital calculation for SCR or ORSA?
» No. You need to use Real-World scenarios where assets earn risk-free rate
PLUS risk-premium
» To project insurance asset-liability forward into the future, whether one-year
(SCR) or through business planning period (ORSA), Real-World simulation is
required NOT Market-Consistent simulation
Solvency II
 [Rule of thumb]
• To Value – Market-Consistent Simulations
• To Project – Real-World Simulations
14
From Market-Consistent Scenarios to Real-World
Scenarios
If I cannot use Market-Consistent scenarios for Real-World projections to
calculate SCR or for ORSA reports, how do I come up with the
appropriate Real-World scenarios?
» Setting Real-World assumptions: A much trickier task than Market-Consistent
!
There is only one market so there is only one unique set of Market-Consistent
scenarios
!
But there are infinitely many Real-Worlds – Real-World is a subjective concept
!
The key to justifying Real-World to regulators/auditors is through clear documentation
» Different Real-World targets based on different use of Real-World stochastic
scenarios
•
Short-term projection (SCR and ORSA)
•
Long-term projection (Run-off planning)
•
Strategic Asset Allocation
15
Definitions of different stochastic simulations
Market-Consistent (MCEV and SII requirements)
• All assets earn risk-free rate (same definition as Risk-Neutral)
• Monte-Carlo simulation replicates market-price
ℚ
• Distribution and statistics are market-implied
Real-World (What you truly expects to happen in the future)
• Risky assets earn risk-free rate PLUS risk-premium
• Distribution and statistics are meaningful. One can set own
assumptions about volatility and distributions of simulated rates.
ℙ
16
3
ESG Calibration
17
Setting Targets and Calibrating the Models
Initial Yield Curve
Swaption Implied Volatilities
𝛼
Market Data
𝛽
𝛾
Option Implied Volatilities
Historic Standard Deviation
Historic Average Returns
Historical
Data
Speed of Convergence
𝑟𝑡
𝜎𝑡
𝜋0 𝜌
Historic Correlations
Long Term Assumptions
Calibration
Targets
Expert
Judgement
Mathematical
Model
Parameters
Note: One can generate both Market-Consistent scenarios and Real-World
scenarios using the same model but with different parameters.
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Incorporating Risk Premiums:
Market Price of Risk
» Risk-neutral world (valuation):
– Risk-neutral mean short rate is
» Real-world (projection)
Shift Brownian motion:
Market price of risk
– Real-world mean short rate is
19
Which is which?
Standard types of calibrations
Market
Consistent
Market
Data
𝑀𝐶 𝑉𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛
Risk Neutral
ALL Assets earn risk-free return
Market
Data
Multi-Year
𝑅𝑢𝑛𝑜𝑓𝑓
One-Year
Time horizon
𝑆𝐶𝑅 … … …
𝑂𝑅𝑆𝐴
Historical
Data
Expert
Judgement
Dynamic
Equilibrium
𝐴𝑠𝑠𝑒𝑡 𝐴𝑙𝑙𝑜𝑐.
Real World
Assets earn risk-free PLUS risk-premium
20
4
MC ESG Validation
21
How Do I Know My Scenarios Are Market-Consistent?
» Do all assets earn risk-free rate on average?
• Check that the average risk-free discounted future price equals to
the current price
• This check is called a Martingale Test
» Do Monte-Carlo option prices equal to Market option prices?
• At different maturities?
• At different strike prices?
• With sophisticated models Monte-Carlo prices converge to Market
option prices if Market Price exists
22
Validation Tests – Market Consistent
» Zero-coupon bond martingale test
This is used to test the validity of the simulated cash behaviour. To do this, the zero
coupon bond prices implied by the cash output, are compared to the prices implied by
the initial yield curve.
23
Asset Martingale Test – Market Consistent
Inputs
» Stochastic model for evolution of
– Asset Total Return Index
– Cash Total Return Index
Calculation
» Obtain N simulations of
and
» Compute the (risk-neutral) expectation:
» Compute standard error:
Test
» Start at
» For each
, check that
within 1.96 s.e.
24
Asset Martingale Test Examples
Fail
1.1
1.15
1.05
1.1
Martingale
Martingale
Pass
1
1.05
0.95
1
0.9
0.95
0
5
10
15
20
25
0
30
5
10
1.15
1.05
1.1
Martingale
Martingale
1.1
1
1
0.9
0.95
10
15
Time (yrs)
25
30
20
25
30
1.05
0.95
5
20
Time (yrs)
Time (yrs)
0
15
20
25
30
0
5
10
15
Time (yrs)
25
Further Validation Tests – Market Consistent
» Option implied volatility test
This test calculates equity option (or swaption) prices/IVs implied by the ESG input. These
can then be compared with market prices.
26
Swaption Implied Volatility Cubes
40%
35%
30%
25%
20%
15%
10%
5%
0%1
» Swaption Cube
•
Maturity
•
Tenor
•
Strike
35%-40%
30%-35%
25%-30%
20%-25%
15%-20%
5
Swap Tenor
10%-15%
9
25
1
2
3
4
5
6
7
8
9
10
15
20
25
20 25
7 10 15
5
4
1 2 3
30
30
5%-10%
0%-5%
Swaption Maturity
1 50% 39% 34% 30% 27% 26% 25% 24% 23% 22% 21% 21% 21% 20%
Swaption Tenor
Swaption Maturity
1
2
3
4
5
1 35% 27% 24% 21% 19%
2 25% 21% 19% 18% 16%
3 20% 17% 16% 15% 14%
4 17% 15% 14% 14% 13%
5 14% 13% 13% 12% 12%
7 12% 11% 11% 11% 10%
10
9%
9%
9%
9%
9%
15 10% 10% 10% 10% 10%
2 36% 30% 27% 25% 23% 22% 22% 21% 20% 20% 19% 19% 19% 19%
3 29% 25% 23% 22% 21% 20% 19% 19%
7
8
9
10
15
20
25
30
4 24% 22% 20% 20% 19% 18% 18% 17%
18% 17% 17% 16% 16% 15% 14% 14% 14%
5 21% 19% 18% 18% 17% 17% 16% 16%
16% 15% 15% 14% 14% 14% 14% 14% 13%
7 17% 16% 16% 15% 15% 15% 14% 14%
14% 14% 13% 13% 13% 12% 13% 13% 12%
10 14% 13% 13% 13% 13% 13% 13% 13%
13% 12% 12% 12% 12% 12% 12% 12% 12%
15 14% 14% 14% 14% 14% 15% 14% 15%
12% 11% 11% 11% 11% 11% 11% 11% 11%
20 15% 15% 15% 15% 15% 15% 15% 15%
10% 10% 10% 10% 10% 10% 10% 10% 10%
25 16% 16% 16% 16% 16% 16% 16% 16%
9% 9% 9% 10% 10% 10% 10% 10% 9%
30 16% 16% 16% 15% 15% 15% 15% 15%
10% 10% 10% 10% 10% 10% 10% 10% 9%
6
20 10% 10% 10% 11% 11% 11% 11% 11% 11% 11% 11% 10% 10%
9%
25 11% 11% 11% 11% 11% 11% 11% 11% 11% 11% 10% 10%
9%
9%
30 11% 11% 11% 11% 11% 11% 11% 11% 10% 10% 10%
8%
8%
9%
18% 18% 18% 18% 18% 18%
17% 17% 17% 17% 17% 17%
16% 16% 16% 16% 16% 16%
14% 14% 15% 15% 15% 14%
14% 14% 14% 14% 14% 14%
15% 15% 15% 15% 14% 13%
15% 15% 15% 14% 14% 13%
16% 16% 15% 14% 13% 12%
15% 15% 14% 13% 12% 12%
27
LMM+ model – Fit to initial market yields
At-The-Money Swaptions IV (10 Year Tenor)
40.00%
40.00%
35.00%
35.00%
30.00%
30.00%
Market
25.00%
Model
20.00%
Market
25.00%
Model
20.00%
15.00%
15.00%
0
10
20
Maturity
LMM+
30
0
10
20
30
Maturity
2FBK
EndJun2013 EUR Swap Calibration: 10 Year Tenor, At-the-money surface
28
LMM+ model – Fit to OTM/ITM Swaption Prices
Out-The-Money Swaptions (Volatility Skew)
50.00%
50.00%
40.00%
40.00%
30.00%
30.00%
Market
20.00%
Model
Model
10.00%
10.00%
0.00%
0.96
Market
20.00%
0.98
1
Strike
LMM+
1.02
1.04
0.00%
0.96
0.98
1
Strike
1.02
1.04
2FBK
EndJun2013 EUR Swap Calibration: 5 Year Maturity, 10 Year Tenor
29
5
RW ESG Validation
31
Sample RW calibration and validation
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30%
20%
Nikkei 225 SVJD
30%
20%
Mar-09
Jun-09
Sep-09
Dec-09
Jun-09
Sep-09
Dec-09
Jun-08
Mar-08
Dec-07
Sep-07
Jun-07
Mar-09
-20%
Dec-08
-20%
Dec-08
-10%
Sep-08
-10%
FTSE 100 Constant Vol
Sep-08
0%
Jun-08
0%
Mar-08
10%
Dec-07
10%
Sep-07
20%
Jun-07
FTSE 100 SVJD
Mar-07
-10%
Dec-06
-10%
Mar-07
30%
Dec-06
0%
Sep-06
0%
Sep-06
10%
Jun-06
10%
Jun-06
Percentile 75 to 95
Percentile 25 to 50
Percentile 1 to 5
Dec-05
20%
Mar-06
20%
Mar-06
Dec-09
Sep-09
Jun-09
Mar-09
Dec-08
Sep-08
Jun-08
Mar-08
Dec-07
Eurostoxx 50 SVJD
Dec-05
Dec-09
Sep-09
Jun-09
Mar-09
Dec-08
Sep-08
Jun-08
Mar-08
Dec-07
Sep-07
Jun-07
Percentile 95 to 99
Percentile 50 to 75
Percentile 5 to 25
Realised
Sep-07
20%
Jun-07
Mar-07
Dec-06
Sep-06
Jun-06
30%
Mar-07
Dec-06
Sep-06
Jun-06
-30%
Mar-06
Dec-05
-20%
Mar-06
Dec-05
Equity Back-test Charts
EndDec2008 1Y-VaR EUR & GBP
Eurostoxx 50 Constant Vol
-20%
-30%
NIKKEI 225 Constant Vol
34
6
Question and Answer
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