Session 70 PD, Model Efficiency - Part II. Moderator: Anthony Dardis, FSA, CERA, FIA, MAAA

Transcription

1 Session 70 PD, Model Efficiency - Part II Moderator: Anthony Dardis, FSA, CERA, FIA, MAAA Presenters: Anthony Dardis, FSA, CERA, FIA, MAAA Ronald J. Harasym, FSA, CERA, FCIA, MAAA Andrew Ching Ng, FSA, MAAA

2 Model Efficiency Part 2: The Program Moderator & Panelist: Tony Dardis (Milliman) Panelists: Ron Harasym & Andrew Ng (New York Life) The presenters at this session will discuss several model efficiency techniques from real-life case studies. These case studies will illustrate how companies are actually using model efficiency techniques in practice. The panel will consist of experts who can speak from experience regarding methods that have worked well and share lessons learned in the process. At the conclusion of the session, attendees will be able to describe benefits and applications of model efficiency. 1

3 The Family of Proxy Modeling Methodologies: Case Studies Tony Dardis 2016 Life & Annuity Symposium Tuesday May 17, 2016

4 3

5 What is a Proxy Model? Think of a proxy model as a formula you link your modeled metric to its underlying risk drivers E.g., L = f (i, e, v, ) Use your heavy model to establish what your fitting and validation points are Not to be confused with Replicating Portfolio (which is a model efficiency technique in its own right)

6 Proxy Modeling Case Study 1: Curve Fitting Used initially by some companies in Europe for initial SII work Calculates a sample of accurate values and then fit a curve to these sample values May not fit at all well to non-sampled areas of the distribution, quickly falls apart for complex functions such as VA GLBs

7 Proxy Modeling Case Study 1: Curve Fitting

8 Proxy Modeling Case Study 2: Least Squares Monte Carlo Now quite widely used in Europe for SII purposes Some traction in North America Intention is to fit a function to the entire risk space Requires fitting to many (inaccurate) values. If estimates are unbiased and independent, then the errors will come out in the wash, and the resulting curve will be a very good fit. Can become problematic for very complex multi-dimensional functions (needs neural networks)

9 Proxy Modeling Case Study 2: Least Squares Monte Carlo

10 Proxy Modeling Case Study 3: Radial Basis Functions Not yet widely used in the industry but gaining increasing attention as an alternative to LSMC for more complex functions such as projected AG 43 / C3 P2. See presentation by Ivan Parker (Jackson National), Using a Proxy Model to Lighten your Load at 2016 ERM Symposium, April , DC - Usage of RBFs for recalculating required capital for what-if analysis, stress & scenario testing, risk limits, continuous reporting. Establish a series of accurately calculated values, and consider all values when fitting the function (or interpolating) - enables us to accurately capture the shape of very complex underlying functions. An RBF s value at any given point depends only on its distance from a central point..

11 Proxy Modeling Case Study 3: Radial Basis Functions

12 Thank you

13 Forecasting Stochastic Required Capital Ron Harasym Vice President & Actuary Andrew Ng Corporate Vice President & Actuary 2016 SOA Life & Annuity Symposium Session 70 PD Model Efficiency Part II May 17, 2016 Nashville, TN

14 Agenda Background: Stochastic Required Capital Valuation Forecasting Stochastic Required Capital SOA Life & Annuity Symposium May 17,

15 The Metric Stochastic Required Capital (SRC) is the average, over the least favorable stochastic asset liability simulations, of the projected maximum present value of balance sheet deficiency Projections are based on portfolio run-off asset/liability simulations Based on statutory accounting, instead of GAAP or market value balance sheet Conditional tail expectation, a CTE measure, is used to reflect downside risk of loss Can define internal required statutory-based capital 2016 SOA Life & Annuity Symposium May 17,

16 Scenario Size & Initial Market Conditions Matter The above analysis is based on SRC valuation of a large block of life business with recent market conditions. The convergence profile varies by initial market condition. A more stressed initial environment will likely have wider ranges and slower convergence SOA Life & Annuity Symposium May 17,

17 Challenges of Stochastic Capital Modeling A reliable stochastic capital measure often needs to be reflective of a large set of scenarios, with the size of scenario set driven by: the portfolio s sensitivity to risk drivers, run-off horizon, and the CTE level Tolerance of any repetitive manual process is substantially Needs to deal with large set of super size files and limited storage space Process time can grow exponentially as size of scenario set increases Applications for normal scale production often no longer work lower 2016 SOA Life & Annuity Symposium May 17,

18 Agenda Background: Stochastic Required Capital Valuation Forecasting Stochastic Required Capital SOA Life & Annuity Symposium May 17,

19 A Real Life Case Study Develop fast stochastic required capital forecasting capability LOB Forecast Horizon Market Dynamics SRC Metric Covers $90Bn+ B/S of L&A One year beyond in-force date Interest rates, equities, credits CTE on run-off projection Enable very fast valuation of SRC at the forecast date reflecting a wide range of market movements since the in-force date * All analysis ignores impact due to new business acquired over the 1-year forecasting horizon 2016 SOA Life & Annuity Symposium May 17,

20 Forecasted Stochastic Required Capital Sample Forecast SRC Analytics Dynamics of Risk Drivers over Forecasting Horizon Above illustration is based on capital data points of a large block of life business SOA Life & Annuity Symposium May 17,

21 Risk Driver #1 Sample Forecast SRC Analytics Risk Driver #2 Dynamics of Risk Drivers over Forecasting Horizon Forecasted Stochastic Required Capital Above illustration is based on capital data points of a large block of life business SOA Life & Annuity Symposium May 17,

22 Mission (Im)Possible Forecasting SRC necessitates very fast development of hundreds of thousands of CTE valuations over a range of future initial market conditions CTE measures need more simulations as only the tail scenarios matters Stochastic metrics require large simulation set to be reliable and useful Conventional brute force simulation approach is neither practical nor cost justifiable for stochastic capital metrics 2016 SOA Life & Annuity Symposium May 17,

23 Forecasting SRC Modeling: Value Added Strengthen a company s capital management program Enable better understanding of profile and dynamics of risk and capital Facilitate development of capital sensitivity measures (i.e., Greeks ) Allow robust capital planning to address impact due to volatile market Answer management s What If capital questions effectively 2016 SOA Life & Annuity Symposium May 17,

24 Making It Possible Real time forecasting of SRC is a scenario intensive exercises Creative development and usage of efficiency techniques make it possible with nearly a 1000:1 scenario reduction Extension of LSMC Property (5:1) Scenario Stratification (8:1) Stress Scenario Selection (4:1) LSMC Proxy Fitting (6:1) 50,000 scenarios: reliable SRC valuation 1,200 scenarios 322 scenarios Process starts with 10K scenarios (per fitting point) 54 simulations: for each SRC valuation 2016 SOA Life & Annuity Symposium May 17,

25 Making It Possible: The Use of Proxy Function The only way of discovering the limits of the possible is to venture a little way past them into the impossible. - Sir Arthur C. Clarke s Second Law Define Proxy Function Assume SRC at time T n can be expressed as a closed form function of SRC at T 0 and the dynamics of risk variables between T 0 and T n Parameterize Proxy Function Pick fitting points and perform brute force SRC valuations Identify the optimal proxy fitting function through regression Validate proxy function with extensive out-of-sample testing Re-evaluate Proxy Function Set up the closed form proxy function calculation Define sets of market dynamics for future SRC evaluation Re-evaluate proxy to derive all SRC valuations real time 2016 SOA Life & Annuity Symposium May 17,

26 Making It Possible: Least Square Monte Carlo Least Square Monte Carlo (LSMC) proxy fitting offers more credible results Traditional Proxy Fitting ( Curve Fitting ) Fitting with Least Squares Monte Carlo 2016 SOA Life & Annuity Symposium May 17,

27 The Magic of Ultra Deep Model Efficiency Any sufficiently advanced technology is indistinguishable from magic. - Sir Arthur C. Clarke s Third Law 2016 SOA Life & Annuity Symposium May 17,

28 The Magic of Ultra Deep Model Efficiency Reliability of forecasted stochastic required capital proxy can be better than a level suggested by fitting point scenarios utilized! A fitting point forecasted SRC valuation utilizes only 54 balance sheet simulations based on a set of 10,000 scenarios, partly benefited from stress scenario selection Comparing to forecasted SRC using 50,000 brute force balance sheet simulations: errors of forecasted SRC proxy typically stay within 5% errors of forecasted SRC using 10,000 brute force simulations can easily be as high as 15% 2016 SOA Life & Annuity Symposium May 17,

29 Making It Possible: Modular Apps! Stress Scenario Picker LSMC Scenario Selector Model Point Cluster Scenario Xformer Scenario Stratifier Model Data Extractor Nested Scenario Creator SRC Calculator Principal Component Analyzer Sobel Sequence Seeker Apps were developed for every key step with large scale processing capability LSMC Proxy Fitter SRC Forecaster 2016 SOA Life & Annuity Symposium May 17,

30 Key Success Factors Small Dynamic Team Individuals with diversified talent Be compact and agile to minimize overhead and communication challenge Customized Techniques Valid stress scenario selection & scenario stratification methods reflective of portfolio s attributes Effective Collaboration Internal modeling, technology External platform vendors Thought Leadership Courageous to challenge status quo and be innovative to deal with challenges Robust Project Design Smart planning for maximum efficiency and embrace flexibility to deal with unknowns Efficient Execution Emphasize efficient process automation, be agile, and be relentless on execution Keep It Simple Follow principle of parsimony, be pragmatic, and no unnecessary complexity 2016 SOA Life & Annuity Symposium May 17,

31 Q & A 2016 SOA Life & Annuity Symposium May 17,