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© 2014 Deloitte MCS Limited. All rights reserved.
Testing and
validating stochastic
economic scenarios
Shaun Lazzari
29 Ma...
© 2014 Deloitte MCS Limited. All rights reserved.
Agenda
• Using ESGs
‒ Purpose
‒ Process (providers, groups and business ...
© 2014 Deloitte MCS Limited. All rights reserved.3
Using ESGs
© 2014 Deloitte MCS Limited. All rights reserved.
Using ESGs
What do ESGs do?
• Generate many scenarios for future economi...
© 2014 Deloitte MCS Limited. All rights reserved.
Using ESGs
Purposes
• Two key types of ESG model:
• Application: Monte C...
© 2014 Deloitte MCS Limited. All rights reserved.
Using ESGs
Stochastic modelling for valuation
Liability values found as ...
© 2014 Deloitte MCS Limited. All rights reserved.
Using ESGs
Market consistency
• Risk-neutral ESG models are calibrated t...
© 2014 Deloitte MCS Limited. All rights reserved.
Using ESGs
Provision of scenarios: a typical process
8
ESG
provider
Grou...
© 2014 Deloitte MCS Limited. All rights reserved.
Using ESGs
Provision of scenarios - challenges
• For example:
‒ Ownershi...
© 2014 Deloitte MCS Limited. All rights reserved.
Using ESGs
Solvency II
Article 126
“The use of a model or data obtained ...
© 2014 Deloitte MCS Limited. All rights reserved.11
Formulating calibration assumptions
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Required assumptions
• Aim wherever ...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Required assumptions
• Ideally:
+ in...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Data challenges
Ideally, we would ca...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Important features of an assumption-...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Solutions
1 – Use of historic data
•...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Solutions
2 – Use of proxy data seri...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Solutions
3 – Third party guidance
•...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Example – Czech/CEE equity
• Only sh...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Example – Czech/CEE equity
Historic ...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Example – Czech/CEE equity
Higher mo...
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptions
Example – Czech/CEE equity
• Lot of ...
© 2014 Deloitte MCS Limited. All rights reserved.23
Validating scenario sets
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Aims
• Having made a set of scenarios, must ade...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – no arbitrage/leakage
Test both raw o...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – market consistency
Compare market pr...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – market consistency
Compare market pr...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – market consistency
• Monte Carlo pri...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – convergence
• Are we convinced enoug...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – out of sample testing
• Wish to veri...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – distributional features
• Out-of-sam...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – distributional features
• Out-of-sam...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Analyses – calibration stability
• For a given ...
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario sets
Doing all this analysis
• Some of this is one-o...
© 2014 Deloitte MCS Limited. All rights reserved.35
Future challenges
© 2014 Deloitte MCS Limited. All rights reserved.
Future challenges
Immediate issues
• ESGs models have reached a mature s...
© 2014 Deloitte MCS Limited. All rights reserved.
Future challenges
Longer term
• Emerging standards, including Solvency I...
© 2014 Deloitte MCS Limited. All rights reserved.
Future challenges
Longer term
• Banks have adopted adjustments to counte...
© 2014 Deloitte MCS Limited. All rights reserved.
Future challenges
Longer term
• Real-world modelling has itself advanced...
© 2014 Deloitte MCS Limited. All rights reserved.
Deloitte refers to one or more of Deloitte Touche Tohmatsu Limited (“DTT...
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20140528 - ESGs (Czech Society of Actuaries) - Shaun Lazzari

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20140528 - ESGs (Czech Society of Actuaries) - Shaun Lazzari

  1. 1. © 2014 Deloitte MCS Limited. All rights reserved. Testing and validating stochastic economic scenarios Shaun Lazzari 29 May 2014
  2. 2. © 2014 Deloitte MCS Limited. All rights reserved. Agenda • Using ESGs ‒ Purpose ‒ Process (providers, groups and business units) ‒ Solvency II requirements • Formulating calibration assumptions ‒ Required assumptions ‒ Data challenges ‒ Potential solutions • Validating scenario sets ‒ Aims ‒ Analyses • Future challenges 2
  3. 3. © 2014 Deloitte MCS Limited. All rights reserved.3 Using ESGs
  4. 4. © 2014 Deloitte MCS Limited. All rights reserved. Using ESGs What do ESGs do? • Generate many scenarios for future economic variables • Asset classes: ‒ Nominal rates ‒ Real rates ‒ Inflation ‒ Equities ‒ Property ‒ Credit spreads / default probabilities ‒ Alternatives ‒ Exchange rates 4 0 5 10 15 20 25 30 35 Time (y)
  5. 5. © 2014 Deloitte MCS Limited. All rights reserved. Using ESGs Purposes • Two key types of ESG model: • Application: Monte Carlo approach especially useful for valuation when liabilities involve non-linear cashflows: ‒ Options/guarantees ‒ Path-dependence ‒ Management actions 5 • Market-consistent valuation (for reporting) • HedgingRisk neutral • Risk/return quantification • Regulatory/economic capital calculation • Investment strategy setting • Pricing Real world (Deflator-based models incorporate features of both types of model)
  6. 6. © 2014 Deloitte MCS Limited. All rights reserved. Using ESGs Stochastic modelling for valuation Liability values found as expected value of discounted projected cashflows: • Risk-neutral means no arbitrage opportunities: ‒ Expected PV of any investment strategy is equal to amount invested today ‒ In contrast to real-world simulation, where risk premiums may be used 6 ESG Discount factors Other outputs Liability info Projected cashflows (Market) value average
  7. 7. © 2014 Deloitte MCS Limited. All rights reserved. Using ESGs Market consistency • Risk-neutral ESG models are calibrated to market data • Calculated values of liabilities (which are complex financial contracts) can be thought of as being a “market price”7 Calibration targets (market prices) Calibration Model parameters Scenario generation Economic scenarios Pricing Scenario- calculated prices ESG
  8. 8. © 2014 Deloitte MCS Limited. All rights reserved. Using ESGs Provision of scenarios: a typical process 8 ESG provider Group office Business unit • Software • Calibrations • Assumptions/insights • Scenario files • Software? • Calibrations? • Scenario files • Business-unit specific assumptions and file requirements • Company-specific assumptions and file requirements Data Data Data
  9. 9. © 2014 Deloitte MCS Limited. All rights reserved. Using ESGs Provision of scenarios - challenges • For example: ‒ Ownership of assumptions ‒ Adequate validation/challenge of assumptions ‒ Meeting ad-hoc requirements • Often Business Units do not have access to software / provider contact themselves, perhaps due to: ‒ Cost ‒ Resource/expertise requirements • We are seeing reliance on third party providers and/or group centralisation increasing over time ‒ For software and resources… but not assumptions! • For CEE calibrations (e.g. Czech Koruna), lack of market data can make calibration difficult 9
  10. 10. © 2014 Deloitte MCS Limited. All rights reserved. Using ESGs Solvency II Article 126 “The use of a model or data obtained from a third-party shall not be considered to be a justification for exemption from any of the requirements for the internal model set out in Articles 120 to 125.” • Use test • Statistical quality standards • Calibration standards • Profit & loss attribution • Validation • Documentation As an ESG provider, we find we get many more questions and challenges now than we used to – this is good! 10
  11. 11. © 2014 Deloitte MCS Limited. All rights reserved.11 Formulating calibration assumptions
  12. 12. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Required assumptions • Aim wherever possible to calibrate to today’s market price data • Projected behaviour based upon these prices: 12 3 6 9 15 30 0% 20% 40% 60% 1 3 5 7 9 12 20 30 Option term (y)Swap term (y) Market implied vol (ATM) 40%-60% 20%-40% 0%-20% Drift • Linear payoffs – bonds, forward contracts Volatility, skew, autocorrelation etc. • Non-linear payoffs - options + other derivatives 0% 1% 2% 3% 4% 0 10 20 30 40 SpotRate Term (y) Initial yield curve
  13. 13. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Required assumptions • Ideally: + inter-asset class correlation assumptions! 13 Nominal rates • Initial yield curve • Swaption prices/implied vols Real rates/inflation • Initial yield curve • Volatility & mean reversion levels Equities & other indices • Option prices/implied vols • Forward dividends • Dividend volatility & mean reversion Credit • Initial credit spread curves • Spread volatility FX • FX option prices/implied vols
  14. 14. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Data challenges Ideally, we would calibrate using targets solely sourced from market prices. In practice, many reasons why not possible: 14 • Swaption prices based on swap rates – inconsistency if using government curveNominal rates • Few economies issue inflation-linked bonds • Derivatives on these bonds are even rarerReal rates • Insurers generally interested in long term implied volatilities – very scarce data • For property etc., no liquid derivative markets Equities & other indices • Data very fragmented as multiple issuers – some indices do exist for major economies • Few derivatives Credit • Few liquid cross-asset class derivativesCorrelations
  15. 15. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Important features of an assumption-setting approach The issues described have long existed and many workarounds can be used. In a Solvency II world, these must be well-justified! • Informed by relevant data • Limited and well-validated use of expert judgement • Stability over time 15
  16. 16. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Solutions 1 – Use of historic data • Common approach for several targets ‒ Volatility – property, inflation, credit… ‒ Correlations • Note implied volatility ≠ volatility ‒ Bias ‒ Observed volatility says nothing about forward-looking term structure, skew 16 0 20 40 60 80 1990 1993 1995 1998 2001 2004 2006 2009 2012 IV/vhistoricvol(%) Time VIX implied 60D vol Average 3.5% difference
  17. 17. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Solutions 2 – Use of proxy data series • Asset class may be approximated by a related, more established class for which data exists • Substitute assumption should be well-validated: ‒ Statistically ‒ Analysis of underlying drivers • May seek to make appropriate adjustments to proxy data 17 1998 2001 2004 2007 2009 2012 CECE CTX
  18. 18. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Solutions 3 – Third party guidance • Calibration assumptions are, ultimately, prices of simple financial contracts ‒ Request quotes from banks – they are the market makers! ‒ Seek assistance from data provider ‒ Inspect regulatory returns • With Solvency II, insurer still required to take ownership of assumptions 18
  19. 19. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Example – Czech/CEE equity • Only short-term options traded for CECE ‒ Would like a full surface • Could we use a major EUR index like the Eurostoxx or DAX as a proxy? Historic behaviour: 19 1998 2001 2004 2007 2009 2012 CECE Eurostoxx 50 DAX
  20. 20. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Example – Czech/CEE equity Historic volatility: Short term ATM implied volatilities: 20 CECE Eurostoxx 50 DAX 27.2% 23.1% 24.44% 0 5 10 15 20 25 30 May-14 Oct-15 Feb-17 Jun-18 ATMIV(%) Expiry date CECE DAX Eurostoxx 50 Unusual downward slope!
  21. 21. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Example – Czech/CEE equity Higher moments: 21 Density Historic log returns (annualised) CECE Eurostoxx 50 CECE Eurostoxx 50 Skewness -0.7 -0.8 Kurtosis 6.2 5.9
  22. 22. © 2014 Deloitte MCS Limited. All rights reserved. Formulating calibration assumptions Example – Czech/CEE equity • Lot of choice as to how incorporate these observations into assumptions ‒ But this analysis provides us with evidence to back-up approach • Approach should be robust – i.e. stable over time 22 Calibration assumptions Short-term market data Difference in historical volatility Similar higher moments, hence skew
  23. 23. © 2014 Deloitte MCS Limited. All rights reserved.23 Validating scenario sets
  24. 24. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Aims • Having made a set of scenarios, must adequately validate them • Seek to verify: • Ideally in as automated and judgement-free way as possible 24 Arbitrage- freeness Market consistency / fit to calibration targets Model stability Compatibility with cashflow model
  25. 25. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – no arbitrage/leakage Test both raw outputs and more complex (dynamic?) strategies: • Means of quantifying error: ‒ Maximal error ‒ Confidence intervals ‒ Terminal leakage 25 0.8 0.9 1 1.1 1.2 0 10 20 30 40 Time (y) Govt. CMI Term 15 0.8 0.9 1 1.1 1.2 0 10 20 30 40 Time (y) Equity TRI Undervaluation of guarantees
  26. 26. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – market consistency Compare market prices against those found through pricing using scenarios: 26
  27. 27. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – market consistency Compare market prices against those found through pricing using scenarios: 27 0% 1% 2% 3% 4% 5% 0 5 10 15 20 25 30 35 40 Spotrate Term (y) Average deflator Yield curve 95% confidence interval
  28. 28. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – market consistency • Monte Carlo prices are an average → can use similar pass/fail criteria used for no-arbitrage tests • Can break down error into two parts: • Significance of sampling error best quantified through comparing prices, not vols etc. 28 Fitting error Sampling error Market consistency error Targets - Fitted Fitted - Generated
  29. 29. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – convergence • Are we convinced enough simulations have been used? • In more volatile environments, more scenarios required 29 10% 15% 20% 25% 0 1,000 2,000 3,000 4,000 5,000 10x10swaptionImpliedvol # simulations Simulations Model
  30. 30. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – out of sample testing • Wish to verify model is not over-fitted, but instead has some predictive power ‒ If it doesn’t, ESG is pointless! Do not always have excess data available, but sometimes we do! 30 10% 15% 20% 0 5 10 15 Impliedvolatility Term (y) Simulated Market Fitting o Bond prices o Swaption cube points o Interest rate caps o Intermediate points on implied vol term structure
  31. 31. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – distributional features • Out-of-sample contracts most likely to be mispriced if output distributions are “not sensible” • Extreme distributions may also impact ALM model compatibility • Additionally, consider changes in distributional statistics over time – are these consistent with changes in calibration assumptions? 31 -80% -60% -40% -20% 0% 20% 40% 60% 80% Log-return SVJD Black-Scholes
  32. 32. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – distributional features • Out-of-sample contracts most likely to be mispriced if output distributions are “not sensible” • Extreme distributions may also impact ALM model compatibility • Additionally, consider changes in distributional statistics over time – are these consistent with changes in calibration assumptions? • Aside: have seen other European regulators asking firms to test multiple models 32 -4% 0% 4% 8% 12% 16% 20% 24% 28% 0 5 10 15 20 25 30 35 40 Spotrate Time (y) Hull-White -4% 0% 4% 8% 12% 16% 20% 24% 28% 0 5 10 15 20 25 30 35 40 Spotrate Time (y) LMM -4% 0% 4% 8% 12% 16% 20% 24% 28% 0 5 10 15 20 25 30 35 40 Spotrate Time (y) LMM-DDSV
  33. 33. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Analyses – calibration stability • For a given model, finding optimal parameter set is a hard problem 1) Test optimisation routine ‒ Generate targets from the model ‒ Fit to these targets – should be able to achieve exact fit, and ideally same parameters as used to generate targets 2) Test goodness-of-fit over time ‒ Fit to historic targets ‒ Asses fit in range of market conditions, and stability over time 3) Test parameter stability ‒ Make small adjustments to initial guess – should have small impact on outcome 33
  34. 34. © 2014 Deloitte MCS Limited. All rights reserved. Validating scenario sets Doing all this analysis • Some of this is one-off work (validating optimisation routine etc.) • Model is not particularly firm-specific – provider may be best to validate ‒ Firm need only demonstrate evidence and understanding • If Business Unit is reliant on Group for scenarios, must seek to request sufficient information to calibrate ‒ e.g. to accurately price swaption, many outputs required • Much of regular validation process can be automated 34
  35. 35. © 2014 Deloitte MCS Limited. All rights reserved.35 Future challenges
  36. 36. © 2014 Deloitte MCS Limited. All rights reserved. Future challenges Immediate issues • ESGs models have reached a mature stage where most calibration targets can be achieved: ‒ Initial yield curves ‒ Option surfaces ‒ Volatility cubes • Some advances can still be made with regards to credit modelling • Automation an area of focus as volume of ESG file required increases ‒ Quicker delivery ‒ Sensitivities ‒ Nested stochastic etc. 36
  37. 37. © 2014 Deloitte MCS Limited. All rights reserved. Future challenges Longer term • Emerging standards, including Solvency II and IFRS, continue to emphasize market consistency - generally a good thing. • Insurance definition is based on classical option pricing theory (replicating portfolios); many assumptions: • Limitations highlighted post-2008! 37 Forbidden • Bid-ask spreads • Market impact of trades • Information asymmetries • Taxes • Solvency capital requirements and costs of holding these. • Collateral posting requirements • Risk of default on derivatives • Illiquidity premiums or other non-cash- flow valuation effects Required • Investment and unlimited borrowing at a single risk free rate. • Unlimited and infinitely-divisible supply of underlying assets. • Continuous-time trading (24/7) • Buying and selling with no impact on the market price. • Consensus on possible price moves in the underlying asset.
  38. 38. © 2014 Deloitte MCS Limited. All rights reserved. Future challenges Longer term • Banks have adopted adjustments to counter weaknesses in theory: • These innovations may hit insurers first via IFRS rather than Solvency II 38 Credit valuation adjustment CVA Debit valuation adjustment DVA Funding valuation adjustment FVA Allowance for possible default by derivative counterparties Reduce stated liabilities with an allowance for own default. Allowance for funding of derivative position (borrowing over the risk free rate, stock lending, collateral posting).
  39. 39. © 2014 Deloitte MCS Limited. All rights reserved. Future challenges Longer term • Real-world modelling has itself advanced greatly in recent years due to Solvency II ‒ Diverged from risk-neutral approach • Incorporating these “real-world” features into market-consistent modelling will bring these two types of modelling closer together • Working towards a Grand Unified Model! 39
  40. 40. © 2014 Deloitte MCS Limited. All rights reserved. Deloitte refers to one or more of Deloitte Touche Tohmatsu Limited (“DTTL”), a UK private company limited by guarantee, and its network of member firms, each of which is a legally separate and independent entity. Please see www.deloitte.co.uk/about for a detailed description of the legal structure of DTTL and its member firms. Deloitte MCS Limited is a subsidiary of Deloitte LLP, the United Kingdom member firm of DTTL. This publication has been written in general terms and therefore cannot be relied on to cover specific situations; application of the principles set out will depend upon the particular circumstances involved and we recommend that you obtain professional advice before acting or refraining from acting on any of the contents of this publication. Deloitte MCS Limited would be pleased to advise readers on how to apply the principles set out in this publication to their specific circumstances. Deloitte MCS Limited accepts no duty of care or liability for any loss occasioned to any person acting or refraining from action as a result of any material in this publication. Registered office: Hill House, 1 Little New Street, London EC4A 3TR, United Kingdom. Registered in England No 3311052. © 2014 Deloitte MCS Limited. All rights reserved.

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