The Actuarial Society of Hong Kong Modelling market risk in extremely low interest rate environment

Transcription

1 The Actuarial Society of Hong Kong Modelling market risk in extremely low interest rate environment Eric Yau Consultant, Barrie & Hibbert Asia 12 th Appointed Actuaries Symposium, 7 November 2012

2 Agenda Low interest rate but can it go even lower? Monitor your portfolio Technical modeling aspects Constructing the current yield curve: key assumptions and impact Projecting interest rate: stylized facts to consider 1

3 Can rates go even lower? 2

4 Nominal rates German EUR curve at end of last year 3

5 How low can it go Traditional axiom of nominal interest rate modelling: interest rates are bounded below at zero Closely related to approaches that model shocks as proportional to rate levels However, US short term rates have gone negative at some points since 2008 End 2008, March 26th 2009, January 27th 2010, August 4th 2011 Swiss and German yields have also gone negative Two views: 1) Very short rates can move to be effectively zero, we might want to model a point probability of rates hitting zero 2) Negative rates are a potential future CB policy (?), therefore we would want to model a significant probability of negative yield curves 4

6 Impact of interest rate on balance sheet 5

7 Nature of interest rate risk Market risk is now highly related to Central Bank / Government actions Quantitative easing, Operation Twist are distorting market dynamics Nice-to-have: A crystal ball The next best: 1) A real time estimation of valuation/capital metrics based on latest market conditions 2) Understanding of impact if rates go further down / eventually go back up 6

8 Monitoring your portfolio Suppose long term rates are down and swaption implied vols are up, how do these changing market conditions affect your portfolio? 7

9 Quick revaluation of liabilities when markets move A number of ways to achieve this: Rerun your models every day / week Impractical for most Ask what-if questions ( stress testing ) Need to ask the right questions! Imagine your liabilities behave like assets ( replicating asset ) Good replicating assets are hard to find Describe your liabilities using a function ( curve fitting / LSMC ) Curve fitting, Least Square Monte Carlo are sometimes hard to understand initially 8

10 Illustration of quantitative approaches 9 9

11 MCEV Explaining liabilities as function of risk factors using LSMC Express liability value as a function of 2 interest rate principal components An example using LSMC approach [another topic on its own] Read from liability function using updated interest rate factors 10

12 Real time value Example of an insurance portfolio - the market consistent embedded value calculated using real time market info As well as the MCEV, we can also track liability valuation, risk exposure, etc in real time 11

13 Constructing the initial yield curve 12

14 Bond Yield Why does it matter? Interpolation Discrete bond prices from data vendor / brokers Methodology needed to construct a full yield curve Extrapolation 1.8% 1.6% 1.4% 1.2% 1.0% 0.8% 0.6% 0.4% 0.2% 0.0% Yield from Fwd Spline Market Maturity Liquid trading for HKD Government bonds only up to years Some limited freedom in constructing yield curve beyond this last liquid point More significant for firms with medium/long term products and low lapse rates 13

15 Forward interest rate Simple extrapolation for interest rate USD government forward rates assuming constant rate beyond 30 years for : 12% 11% 10% 9% 8% 7% 6% 5% 4% 3% 2% Maturity (years) Very conservative and will generate very high volatility in the MTM value of ultra long-term cash flows. E.g. for HKD it would be at low levels for all maturities as of Sep

16 Unconditional forward rate an anchor Unconditional anchor : stability in mark-to-model valuations 15

17 Forward Rate Extrapolating the HKD curve Two key assumptions in yield curve extrapolation Ultimate forward rate (UFR): long term forward rate target Speed of mean reversion: how quickly long term rates reach UFR 7% 6% 5% 4% 3% 2% 1% 0% Maturity Base Curve Shocked UFR Shocked Mean Reversion Speed 16

18 HKD Millions Exploring the impact on liability valuation A typical example cashflow profile, assuming no options and guranatees Cashflow

19 Forward Rate Sensitivities to assumptions Comparison: Discounted cashflow / GPV (HKD Million) Base (232) Stressed down UFR 1,526 Stressed up mean reversion speed (5,922) 7% 6% 5% 4% 3% 2% 1% Rate level might have impact on cost of option. Not included here. Liquidity premium / matching adjustment also an important input 0% Maturity Base Curve Shocked UFR Shocked Mean Reversion Speed 18

20 Modeling future interest rate movement 19

21 Some stylized facts Interest rates are mean reverting Justification for using mean reverting model Long term expectations are stable Useful for setting ultimate forward rate target (UFR) Volatilities are proportional to rates level, but not 1:1 Vols determine how wide the ranges are and hence VaR Cost of guarantee driven by both level of rates and vols 20

22 (1) Interest rates are mean reverting Fundamental assumption in rates modeling backed by historical observation: 21

23 (2) Long term expectations are stable A rational individual does not make frequent changes to his/her interest rate expectations more than 30 years in the future Some related evidence in inflation expectation 22

24 (3) Volatilities are proportional to rates level 23

25 (3) but it is not 1:1 proportional 24

26 Some common models Hull-White / Vasicek Black- Karasinski LMM DDLMM + SV Fit to initial yield curve Depends on implementation Depends on implementation Fit to swaption prices Calibration efficiency Volatilities Typically fixed Proportional Proportional Proportional + fixed Distribution Normal Lognormal Lognormal Varies Negative interest rate Yes No No Yes 25

27 Modeling negative interest rates? Negative interest rates with Gaussian models like Hull-White Lognormal models with displacement A few things to consider: Theoretically acceptable for market consistent valuation Is this in line with your house view for real world projection? Can your ALM system / asset value projection handle it? 26

28 Concluding remarks Prediction vs probability distribution Observing stylized facts in the markets and reflecting them in the models Understanding sensitivities of your liabilities 27

29 Thank you! 28

30 Technical appendix

31 Calibration 30

32 Real-world vs market-consistent A clarification of terminology Real-world Market-consistent Question to answer Usage What is the probability distribution of future asset prices? Financial projections for ALM, cashflow testing, probability of ruin What is the current fair value of future cashflows? Fair valuation of liabilities (and Greeks) Example (SII) Solvency Capital Requirement (SCR) Technical Provision (TP) Calibration approach Through-thecycle Point-in-time Market-consistent Horizon Medium to long Short (e.g.1-year) All Methodology Calibrated to best-estimate long term targets Calibrated to bestestimate short term targets Calibrated to market option-implied volatilities 31

33 Challenges in risk factor modelling Consistency of calibration approach across diverse range of risk factors Different types of model processes, different data availability Documentation and validation, especially in areas of expert judgement Limitations of volume and relevance of historical data for calibration and validation of 1-year 99.5 th percentile Definition of the 1-year risk measure: Through-the-Cycle and Point-in-Time probability definitions e.g. If calibrating the Internal Model today: How much mean-reversion is it reasonable to assume will, on average, occur to interest rates over next 12 months? More than implied by current forward rates? Should 1-year equity volatility assumption reflect unusual economic environment and the current high levels of market volatility? 32

34 Calibration and validation Assumptions about the relevance of different historical data periods / data will be key, and mainly a matter of expert judgement Back-testing of calibration method can provide insight into robustness of performance But will generally not be sufficient historical data to produce statistically useful validation results for a 1-in-200 year percentile estimate 33

35 Economic balance sheet 34

36 Economic balance sheet: recap Mark-to-market (or mark-to-model) for both assets and liabilities Economic Balance Sheet A L Market value MCEV Adjustment Marketconsistent value Assets Liabilities A better reflection of the true economics of the firm MVL / MCEV calculation typically requires stochastic projection Liability = complex non-linear function of multiple risk factors Options and guarantees require stochastic quantification 35

37 What LSMC is Aim to proxy liability value as a function of changing market conditions Technique used in pricing American options Fit a regression (least squares) through inner simulations Application in insurance ALM context is analogous to curve fitting Instead of calculating specific points on the unknown function calculate random points around the function Example: How does the average top speed of all cars vary by engine size? Method 1: Calculate very accurately the average top speed of all 1 litre and 2 litre cars and interpolate Method 2: Find a random sample of cars and do a regression through the results Regression efficiency leads to greater accuracy, especially in multiple risk dimensions 36

38 How LSMC works Instead of doing full nested simulation, only do a few inner simulations - this gives very inaccurate liability valuation Use regression through inaccurate valuations to get function which approximates true nested stochastic valuation 37

39 Comparing to full nested stochastic LSMC approach converges to nested stochastic when number of scenario increases 38

40 Liability Value (Millions) Liability Value (Millions) Short Rate Liability Value (Millions) Process for LSMC Four main steps to derive the LSMC proxy function Identify risk and generate fitting points Use Least Squares regression to fit PVs Step 1 Step 2 10% 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% Equity Return Equity Return Step 3 Step Approximate Valuations LSMC fit Approximate Valuations Accuarte Validation Points LSMC fit Equity Return Equity Return Calculate liability PV for each fitting point Validate proxy function using accurate valuations 39

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