2012 Tokyo Ebig Yau
Transcript of 2012 Tokyo Ebig Yau
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Equity-Based Insurance Guarantees Conference
June 18, 2012
Tokyo, Japan
Market Risk Modeling
Eric Yau
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Eric YauConsultant, Barrie & Hibbert Asia
Eric YauConsultant, Barrie & Hibbert Asia
18 June 2012 (1150 1230 hours)18 June 2012 (1150 1230 hours)
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Agenda
+ VA market risk modeling: motivation and building blocks
+ Calibrating to the Japan market
+ Risk factor modeling
Interest rate
Equity
Credit
+ Hedging and hedge projection
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mot i vat i on and bui l d i ng blocks
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Motivation of VA modeling
VA modeling aims to answer a few fundamental questions:
ProductDesign /Pricing
What is the cost of guarantees
embedded in VA?
How do product features impact this
cost?
HedgingValuation
management strategies
affect cashflow profile?
How should we
implement a hedging
What is the right level
of reserve?
How hedging
strategies affect
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strategy and test its
effectiveness?
reserves?
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Building blocks of VA modeling
Economic
Assumption
Model
Assumption
Model
Choice
Market
Data
calibration
Risk Monitoring Reports:
* Asset and liability valuation*
Economic scenarios:
Economic Scenario Generator
* Risk limits and utilization
Base and Sensitivities
Liability
Portfolio ALM SystemAsset
Portfolio
Trading System
Asset Portfolio Optimizer
Generate, for both asset and
liability portfolios:
* Valuation
* Hedge Strategy
* RebalancingRules
* Risk Limits
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Trading
Engine
* Greeks
* Mismatch position
va a e
InstrumentsCalculation
Engine
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VA risk management and modeling
Product design and pricing
- Cost of guarantees
Valuation
- Reserve/capital calculation- ens t v ty ana ys s - eserve pro ect on
Ensure fair and adequate pricing / valuation / capital
Internal hedging
-
Hedge projection
-- Automated calibration
- Variance reduction
Capture key risk exposure of hedging strategy
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Desirable ESG features for VA
+ Integrated modeling
Interest rates, multiple equity indices, credit risks and alternative assets ons stent mar et-cons stent an rea -wor mo e ng
+ Multiple equity modeling choices E.g., Local volatility, Heston with jumps, to support analysis of model risk
Exact fit to starting yield curve (for interest rate models)
Accurate fit to option-implied volatility
And for hedging:
+ Ability to be run on efficient hardware configurations -
+ Fast calibration tools to facilitate re-calibration / sensitivities
+ Automation of scenario production7
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The market
Bond / Interest rate market+ Longest available swap / JGB up to 40 years
+ Swap liquid tenors up to ~10 years
Derivative implied volatilities+ E.g. Nikkei 225 options up to ~10 years
What happens if we need to discount long term liabilities?
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Linkage to liability valuation
+ This generally apply to a number of areas
Interest rate volatility
Equity volatility10
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Simple extrapolation: interest rate
12%USD government forward
8%
9%
10%
11%
strate
rates assuming constant
rate beyond 30 years
for1985-2007
5%
6%
7%
Forwardin
ter
Very conservative and willgenerate very high
volatility in the MTM value
of ultra long-term cash
2%
3%
0 10 20 30 40 50 60 70 80 90 100
Maturity(years)
.
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Macroeconomic extrapolation
Three questions:
latility
Limiting, unconditionalforwardrate/IVassumption1) What is the longest
market interest rate that
we can observe?
ate/Option
V
Marketforwards
2) What is an appropriateassumption for the very
long-term
unconditional or
InterestRorwar ra e
3) What path should beset between the longest
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0 10 20 30 40 50 60 70 80 90 100 110 120
Term(years)mar e ra e an e
unconditional forward
rate?
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Extrapolation of interest rate
A common approach
+ Fitting to available market data+ Setting a target for the ultra long-term forward rate
+ Developing an economically sensible functional form
11%
12% 11%
6%
7%
8%
9%
10%
ardinterestrate
5%
6%
7%
8%
9%
ardinterestrate
2%
3%
4%
5%
0 10 20 30 40 50 60 70 80 90 100
For
Maturity(years)1%
2%
3%
4%
0 10 20 30 40 50 60 70 80 90 100
For
Maturity (years)
+ Unconditional anchor: stability in mark-to-model valuations
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Extrapolation of derivative implied vol
+ A perfect fit to market data? + Economically robust, stable
+ How should we extrapolate?
extrapolation lead to stable,
sensible valuation
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Example: equity implied vol
+ One possible extrapolation approach:
Real-world volatility estimate as the limit of extrapolation... ... Adjusted for empirical option implied volatility / real-world volatility bias
How fast do we revert to this long-term position?
N225Im liedVolatilitiesandExtra olation
30%
35%
40%
45%
latilities
10%
15%
20%
25%
EquityImpliedV
Q42007
Q42008
Q42009
Q42010
15
0%
5%
0 5 10 15 20 25 30 35 40 45 50
Term(years)
Q42011
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What makes VA modeling difficult?
Embedded derivative nature
+ Path-dependent payoff+ Multiple assets, multiple time periods
Uncertainty
+ Insurance risks
+ Management actions
+ Policyholder options
ut are po cy o ers pr ce-sens t ve or u y rat ona
Complex exposure to various financial risk factors
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- , - , -
for a realistic estimation of risk exposure and valuation
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Sample ESG model structure
Property returnsAlternative asset returns
(e.g. commodities)
Credit risk model
Corporate bond returnsEquity returns
Initial swap and
government nominal
bonds
Nominal short rate
Real-economy; GDP
and real wages
Exchange rate
(PPP or IRP)
Inflation
expectations
Real short rateIndex linked
government bonds
Realised Inflation and
alternative inflation
Foreign nominal
short rate and
inflation
o n s r u on
Correlation relationships between the shocks to different models
Economically rational structure 18
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Real-world vs Market-consistent
A clarification of terminology
- -
Question to answer: What is the probability
distribution of future asset
prices?
What is the current
market-consistent value of
future cashflows?
Usage: Financial projections for
ALM, cashflow testing,probability of ruin analysis
Fair valuation of liabilities
(and Greeks)
Calibration: Calibrated to best-estimate Calibrated to market
arge s op on- mp e vo a es
Risk premium: Y N
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The section below focuses on market-consistent modeling
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n eres ra e mo e s
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Key consideration
+ Provide good fit to market option-implied volatility surface
+ Take yield curve as input+ Flexibility in volatility factor specification and modeling
From a modeling perspective it generally means
+ A number of popular yield curve choices for MC modelling
Hull-White
ox- ngerso - oss
Heath-Jarrow-Morton
+
In particular LIBOR Market Model is a market standard for rate derivatives trading+ Fast robust calibration tools should be available for fre uent re-
calibrations
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Low interest environment
+ Negative interest rate issues with
Gaussian models like HW Lognormal models with displacement
+ Theoretically acceptable, but in practice
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Model choice matters
Hull-White /
Vasicek
Black-
Karasinski
LMM DDLMM + SV
Fit to initial
yield curve
Depends on
implementation
Depends on
implementation
Fit to swaption
pr ces
Calibrationefficiency
Negative
interest rate
Yes No No Yes
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qu y mo e s
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Black-Scholes model as a starting point
+ Model assumption affects fair valuation / pricing of liability
+ Among other assumption: Returns are normally distributed
Volatility is constant
Constant volatilit assum tion
0.7%
0.8%
0.9%
1.0%
y
Historic (20th Century)
Stochastic Vol Model
Normal Distribution
35.00%
40.00%
0.2%
0.3%
0.4%
0.5%
0.6%
Frequenc
10.00%
15.00%
20.00%
25.00%
30.00%
25
0.0%
0.1%
-30% -25% -20% -15% -10%
Equity returns in excess of ri sk-free rates
0.
25 0
.5
0.
75
1
2
34
57 1
0
0.00%
5.00%
Maturity
Strike
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Key consideration
+ Provide good fit to market option-implied volatility surface
+ Support fast and frequent re-calibration+ Provide simultaneous fit to multiple equity indices vol surfaces
From a modeling perspective it generally means
+ Going beyond Black-Scholes (constant volatility), e.g.
Stochastic volatility
orre a on e ween re urn an vo a y
Mean reverting volatility and volatility clustering
+ But still provide (semi-) analytical calculation
Technology infrastructure for daily recalibration
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Market-consistent valuation
+ Model should first fit to market prices of derivativesMarket Volality Sur face Model Volality Surface
35.00%
40.00%
35.00%-40.00%
30.00%-35.00%
25.00%-30.00%
20.00%-25.00% 30.00%
35.00%
40.00%
35.00%-40.00%
30.00%-35.00%
25.00%-30.00%
20.00%-25.00%
5.00%
10.00%
15.00%
20.00%
25.00%
.
15.00%-20.00%
10.00%-15.00%
5.00%-10.00%
0.00%-5.00% 5.00%
10.00%
15.00%
20.00%
25.00% 15.00%-20.00%
10.00%-15.00%
5.00%-10.00%
0.00%-5.00%
0.2
5 0.
50.
75
1
2
3
45
7 10
0.00%
Maturity
Strike
0.
25 0
.5
0.
75
1
2
3
4
5
7 10
.
Maturity
Strike
s mp e ac - c o es mo e canno a vo a y sur ace - u
market implies one
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What is SVJD?
+ The SVJD model is a combination of two well known models of
quantitative finance
The Heston Stochastic Volatility Model
er on s ump us on o e
+ Benefits:
Fairly realistic but parsimonious model
Generally provides a good fit to volatility surface at both long and short maturities
Semi-analytic (i.e. fast) valuation formulae for vanilla option prices
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Technical specification
+ Two parts:
Stochastic volatility part, Heston model (red) Jump diffusion part, Merton model (blue)
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Example simulationSimulation of the SVJD Model
Example Simulation
45%200.00
10 Year Total Return Index
Index No Jumps Index Jumps Only Index Stochastic Volatility
30%
35%
40%
120.00
140.00
160.00
.
ility
ex
15%
20%
25%
60.00
80.00
100.00
Stochastic
Volati
TotalReturn
In
0%
5%
10%
0.00
20.00
40.00
30
Month
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Calibrating to implied vol surface
Market Feature Model Component Key Parameters
Implied volatility term
structure
Stochastic variance Initial variance, mean
reversion level, andspeed of mean reversion
Lon term skew/smile Stochastic Variance Return-variance
correlation and volatility
of variance
Short term skew/smile Jump Diffusion Jump parameters
+ Realistic description of underlying dynamics is key
volatility surface
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re mo e s
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Impact of credit models
+ The impact of credit risky bonds can be highly significant
On both guarantee costs / pricing
And required hedge portfolio
2.60%
2.80%
3.00%
)
2.00%
2.20%
2.40%
'tees(%
InitialFund
premium GMAB & GMDB for a 45year-old male for 20 years 50%
invested in equities and 50% in a
1.40%
1.60%
.
Costof-yr on un ...
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1.00%
.
Govt AA BBB
AssumedBondStrategy
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Credit Modelling: Key Features
A good credit risk model should be
+ Arbitrage-free
+ Stochastic credit rating migrations and defaults+ Stochastic variations in credit spreads
+ Integrated with other market risks (e.g. equities and interest rates)
o e ynam c ers or eren app ca ons:
+ Real world modelling Pricing matrix more severe than underlying transition matrix
=>
+ Risk neutral modelling
Pricing matrix as severe as underlying transition matrix
=> risk neutral
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hedge projection
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Projection of hedging strategies
+ Real-world model capturing hedging strategys key risk exposures
Vega: Increases in option-implied volatility levels
- -
+ Integrated modelling of equity total returns and changes in the level
of equity option-implied volatilities
25%
30%
35%
40%
45%
50%
gVolatility
0.5
0.6
0.7
0.8
0.9
1.0
Correlation
UK Volatility (LHS)
US Volatility (LHS)
UK vs US Correlation (RHS)
0%
5%
10%
15%
20%
-63
-68
-73
-78
-83
-88
-93
-98
-03
5Y
Rolli
0.0
0.1
0.2
0.3
0.4
5Y
Rollin
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De
De
De
De
De
De
De
De
De
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Long-term Hedging P/L Analysis
+ Long-term profitability of delta hedging strategy driven by how
realized volatility behaves relative to implied volatility levels
Expected real-world volatility vs option-implied volatility
Variability of real-world volatility
15.0%1.50%
-2.5%
0.0%
2.5%
5.0%
7.5%
10.0%
12.5%
-0.25%
0.00%
0.25%
0.50%
0.75%
1.00%
1.25%
PriceChane(%
)
edgingLosses
rlyinhgfund)
CumulativeDeltaHedgingP/L
-17.5%-15.0%
-12.5%
-10.0%
-7.5%
-5.0%
-1.75%-1.50%
-1.25%
-1.00%
-0.75%
-0.50%
DailyS&P500
Cumulative
(%ofunde
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- .- .
1 3 5 7 9 1113151719212325272931333537
TradingDay(October1st November20th'08)
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Variance reduction for risk assessment
+ Hedge projection requires Greeks projection
Estimation of Greeks at each point in each real-world simulation requires
stochastic-on-stochastic (theoretically)
+ Variance reduction for Greeks calculation
E.g. Least Squares Monte Carlo to efficiently capture future liability valuation
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Example LSMC for projected Greeks
+ Simple Black-Scholes example
projection of 10-year vanilla put option
+ 10,000 outer scenarios and 2 inners per outer
Higher numbers of inner sims can be used to increase accuracy
+ Fit cubic function and differentiate to estimate delta
0.4
0.5
True value (Black-Scholes)
I-0.2
-0.1
0
0.5 1 1.5 2 2.5
Value (after 1 year) Delta (after 1 year)
y = -0.1367x3 + 0.74x2 - 1.4881x + 1.1539
0.1
0.2
0.3
OptionValue@Year1 In a -scenaro es mae
Regression estimate
Differentiate
fitted polynomial
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
ption
Delta@Year1
True delta (Black-Scholes)
Regression estimate
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0
0.5 1 1.5 2 2.5
Put
Equity Price @ Year 1
-1
-0.9
Put
Equity Price @ Year 1
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Concluding remarks
+ Market risk modeling impacts
Fair and adequate pricing / valuation / capital
Design / risk exposure of hedging strategy
+ Model choice and calibration, among others, have significant impact
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Copyright 2012 Barrie & Hibbert Limited. All rights reserved. Reproduction in whole or in part is
prohibited except by prior written permission of Barrie & Hibbert Limited (SC157210) registered in
Scotland at 7 Exchange Crescent, Conference Square, Edinburgh EH3 8RD.
.
estimates included in this document constitute our judgment as of the date indicated and are subject
to change without notice. Any opinions expressed do not constitute any form of advice (includinglegal, tax and/or investment advice). This document is intended for information purposes only and is
not intended as an offer or recommendation to buy or sell securities. The Barrie & Hibbert group
excludes all liabilit howsoever arisin other than liabilit which ma not be limited or excluded at
law) to any party for any loss resulting from any action taken as a result of the information provided in
this document. The Barrie & Hibbert group, its clients and officers may have a position or engage in
transactions in any of the securities mentioned.
Barrie & Hibbert Inc. and Barrie & Hibbert Asia Limited (company number 1240846) are both wholly
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owne su s ar es o arr e ert m te .
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