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ORSA and Multi-Year Capital Projection

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This presentation offers an overview of ORSA and the quantitative modelling requirements needed. Topics include: Least Squares Monte Carlo (LSMC); LSMC as an important component of a firm’s ORSA in …

This presentation offers an overview of ORSA and the quantitative modelling requirements needed. Topics include: Least Squares Monte Carlo (LSMC); LSMC as an important component of a firm’s ORSA in the context of solvency capital projection; Projecting capital in the future, over multiple time-steps to facilitate stress and scenario testing.

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  • 1. ORSA and multi-year capital projection
  • 2. 2 Own Risk and Solvency Assessment (ORSA) » ORSA is emerging as a global regulatory standard » Pillar II of Solvency II » US and Canada have each proposed ORSA frameworks for 2014 implementation » Core part of International Association of Insurance Supervisors (IAIS) Common Framework » ORSA implementation approaches may have local differences, but in all cases they require insurance firms to make assessments of their current and future solvency capital requirements
  • 3. 3 Quantitative modelling requirements of ORSA Modelling requirements of ORSA could be considered in three categories: » Backward-looking Analysis of annual change in Pillar 1 regulatory reserves » Current-looking Real-time monitoring of Pillar 1 regulatory capital requirements Own assessment of current solvency capital requirements » Forward-looking Multi-timestep forward projection of solvency capital requirements (regulatory capital and / or economic capital)
  • 4. 4 Capital & Solvency Projection (ORSA)
  • 5. 5 Calculating solvency capital along the path Multi time-step projection is orders of magnitude more calculation intensive than a capital calculation Capital calculation Multi-timestep capital projection
  • 6. 6 LSMC: From One Year to Multiple Years One year LSMC Multi-year LSMC
  • 7. 7 ‘Local’ vs ‘Global’ fitting 1. ‘Local’ fitting Separately calibrate different proxy functions for each time t: Market-consistent value(t) = ft (risk factors) A potential drawback with this fitting method is that certain coefficients in the polynomial may vary widely over time. 2. ‘Global’ fitting Include time as an additional variable and calibrate once: Market-consistent value(t) = fglobal(time, risk factors) Equivalent to assuming that the coefficients of the ‘local’ polynomials ft are themselves polynomials.
  • 8. 8 Multi-Year Fitting Example
  • 9. 9 Product Example » Annual return credited to policyholder is calculated as • Credited return (t) = max (Fund return (t) – 1.5%, 2%) • i.e. Policy Account (t) = Policy Account (t-1) * { 1+ credited return (t) } • Policy Account (0) = Asset Portfolio Value (0) • Product pay-out at time 10 is Policy Account (10) » Asset fund invested in diversified portfolio of investment-grade corporate bonds • 70% A-rated • 30% BBB-rated • Term of 8 years • Re-balanced annually » No allowance for taxes, expenses, lapses, mortality
  • 10. 10 Market-consistent liability valuation » The policy pay-out is path-dependent, i.e. it is a function of the 10 annual returns, not the 10-year return • Market-consistent simulation required to produce the time-0 valuation » Market-consistent liability value at time 0 was calculated to be 119% of the starting fund value in end-2012 market conditions • Calculated using market-consistent scenario set for interest rates and corporate bond returns » How will this market-consistent liability value behave over the 10-year lifetime of the product?
  • 11. 11 Proxy Function Fitting » Proxy functions produced using 5 risk factor variables • Two risk-free yield curve factors • Interest rate volatility factor • Credit return factor • Policy account value (i.e. roll-up of credited returns) » Proxy functions produced for valuation at each time-step using the ‘global’ and ‘local’ methods described earlier • Functions fitted to quadratic term in individual risk factors and cross-terms • Fitted local functions had around 10 statistically significant parameters • Global function had 32 statistically significant parameters
  • 12. 12 Validation Results – Year 1 1.1 1.15 1.2 1.25 1.3 1.1 1.15 1.2 1.25 1.3 Proxy Actual 'Local' fit Adverse scenarios Random scenarios 1.1 1.15 1.2 1.25 1.3 1.1 1.15 1.2 1.25 1.3Proxy Actual 'Global' fit Adverse scenarios Random scenarios
  • 13. 13 Validation Results – Year 5 1 1.1 1.2 1.3 1.4 1.5 1 1.1 1.2 1.3 1.4 1.5 Proxy Actual 'Local' fit Adverse scenarios Random scenarios 1 1.1 1.2 1.3 1.4 1.5 1 1.1 1.2 1.3 1.4 1.5Proxy Actual 'Global' fit Adverse scenarios Random scenarios
  • 14. 14 Validation Results – Year 9 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 Proxy Actual 'Local' fit Adverse scenarios Random scenarios 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1Proxy Actual 'Global' fit Adverse scenarios Random scenarios
  • 15. 15 Multi-Year Proxy Function Applications: 1. Stochastic Projections 2. Reverse Stress Testing 3. Scenario Testing
  • 16. 16 Multi-Year Stochastic Projections: Liability Value 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 0 1 2 3 4 5 6 7 8 9 10 Market-consistentliabilityvalue Time (years) Percentiles 95% to99% Percentiles 75% to95% Percentiles 50% to75% Percentiles 25% to50% Percentiles 5%to 25% Percentiles 1%to 5% Average » Time 0 valuation produced by set of market-consistent scenarios » Time 10 valuation is simply the product payout in the real-world scenario » Proxy function used to estimate market-consistent values in years 1-9
  • 17. 17 Multi-Year Stochastic Projections: Liability Value – Asset Portfolio Value -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0 1 2 3 4 5 6 7 8 9 10 Market-consistentliabilityvalue -fundvalue Time (years) Percentiles 95% to99% Percentiles 75% to95% Percentiles 50% to75% Percentiles 25% to50% Percentiles 5%to 25% Percentiles 1%to 5% Average » M-C deficit is expected to reduce over time due to risk premium in asset fund » c30% probability of product pay-out being less than final asset portfolio value
  • 18. 18 Multi-Year Stochastic Projections: Liability Value – Asset Portfolio Value in Year 5 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 Liabilityvalue-fundvalue@year5 Credit spread @ year 5 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.02 0.04 0.06 0.08 0.1 0.12 Liabilityvalue-fundvalue@year5 10-year Treasury rate @ year 5 High risk-free rates also bad for shareholder in this product But not so significant as high rates also reduce liability value Strong exposure to credit spread behaviour
  • 19. 19 Reverse Stress Test: Economic scenario path for worst ranking simulation 0% 1% 2% 3% 4% 5% 6% 7% 2012 2013 2014 2015 2016 2017 1-yr Treasury rate 10-yr Treasury rate 10-yr BBB corporate spread 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 2012 2013 2014 2015 2016 2017 Fund value Policy account M-C liability value • Rank year 5 real-world scenarios by market-consistent deficit • This scenario has the biggest deficit at year 5 • The economic scenario is consistent with previous scatterplots • M-C deficit at year 5 is 0.60 (99th percentile in earlier chart was 0.30)
  • 20. 20 Scenario Testing: Apply 7 macro-economic stress tests 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 2011 2012 2013 2014 2015 2017 Policyvalue-fundvalue Baseline forecast Stronger Near-Term Rebound Slower Near-Term Growth Double-Dip Recession Protracted Slump Below-Trend Long- Term Growth Oil Price Increase, Dollar Crash Inflation » 7 macro-economic, multi-year stress tests specified by Moody Analytics ECCA team » Proxy function used to project liability valuations through these scenarios » What is happening in the oil price scenario?!
  • 21. 21 Oil Shock Scenario 0% 1% 2% 3% 4% 5% 6% 7% 2011 2012 2013 2014 2015 2016 1-yr Treasury rate 10-yr Treasury rate 10-yr BBB corporate spread 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2011 2012 2013 2014 2015 2016 Fund value Policy account M-C liability value • Very significant yield curve increases in the early years of the product. Asset fund value falls by 40% after two years • Followed by very strong bond returns in later years • This down-then-up path is very bad for the product (shareholders) • Early poor returns clearly hurt due to 2% minimum guarantee • Later strong returns also hurt as they are applied to the policy account value, which is much greater than the asset portfolio value
  • 22. 22 Conclusions » LSMC extendable to multi-timestep proxy function fitting » In the case study we have produced proxy functions for a path- dependent, complex guaranteed product, and the proxies perform very well in out-of-sample validation testing at all time horizons » These functions enable a wide variety of projection analytics such as stochastic projection, reverse stress testing and stress and scenario testing » This is extremely useful for firms who need to consider the medium-term behaviour of their solvency requirements as part of ORSA

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