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Practical Issues in Stochastic Modelling. September 2004 Nigel Knowles (Standard Life) Michael Payne (Scottish Widows). Agenda. Overview of realistic balance sheets The liability model Model points Asset model calibration Modelling assumptions Dynamic behaviour Dynamic decisions

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practical issues in stochastic modelling

Practical Issues in Stochastic Modelling

September 2004

Nigel Knowles (Standard Life)

Michael Payne (Scottish Widows)

  • Overview of realistic balance sheets
  • The liability model
    • Model points
    • Asset model calibration
  • Modelling assumptions
    • Dynamic behaviour
    • Dynamic decisions
  • Systems and controls
  • Communication
  • Current Topics
  • Summary
overview of realistic balance sheets
Overview of realistic balance sheets
  • With-profits portfolios contains many complex liabilities that look similar to put options
  • The aim of the Regulations is to place a realistic (market consistent) value on the contingent claims embedded in the with-profits portfolios of major UK life offices
    • Hedging costs (the office does the replication itself)
    • The cost of purchasing hedging instruments
  • Actuaries need to learn a little about financial economics
the liability model
The liability model
  • Model points
  • Asset model calibration
the liability model1
The liability model
  • Closed form Black-Scholes is one possible method of assessing option costs
  • Monte Carlo simulation is an alternative
    • Already have projection engines for the model office (Financial condition reports)
    • Add ESG
    • Dynamic decisions
    • Future premiums
the complexity of these models is unparalleled for many insurers
The complexity of these models is unparalleled for many insurers
  • Long projection periods
    • Monthly for 30+ years
  • Large numbers of model points
  • Lengthy run times
  • The requirement to warehouse large volumes of data
  • Better buy shares in Compaq?
model points
Model points
  • We cannot project 5m policies or premium tranches monthly for 40 years in a stochastic environment.
    • Use model points instead
    • “Reasonably” heterogeneous clusters of policies
  • How should we create a set of model points that is representative of the portfolio?
    • First principles degrees of freedom “moneyness” (asset share, term outstanding, term in-force) and contract type
    • Model point budgets (dynamic decisions might have reference to all the portfolio at once so cannot look at just one half).
model points1
Model points
  • Sparse data (can we drop small data items or distant ones where the intrinsic value tiny?)
  • Smoothing needs a lot less clumping to be meaningful.
  • What if you cannot (or don’t want to) model everything?
    • Scaling (approximately modelled – small contracts?)
    • Scaling to statutory reserve versus WPBR
asset model choice calibration
Asset model choice/calibration
  • What does market consistency mean?

7.4.168 R The market-consistent asset model in PRU 7.4.167R(1):

(1) means a model that delivers prices for assets and liabilities that can be directly verified from the market; and

(2) must be calibrated to deliver market-consistent prices for those assets that reflect the nature and term of the with-profits insurance liabilities of the with-profits fund.

asset model choice calibration1
Asset model choice/calibration
  • What does market consistency mean?
    • Are we replicating options (including the expenses of setting up trading strategies) Or
    • Are we buying options (estimate price charged by third parties)?
asset model choice calibration2
Asset model choice/calibration
  • Price is not defined by a single model so any calibrated model is unlikely to fit all observable data.
  • There are few instruments of the right term and duration that look like an insurer’s portfolio
  • Extrapolation from short-term over 40 years is a “Herculean” assumption.
    • Is it spurious to worry about “moneyness” structures over 40 years?
    • Constant volatility often assumed even though we know it isn’t
    • Data suggests stability over the long-term.
figure 1 short term versus long term implied volatility
Figure 1. Short-term versus long-term implied volatility
  • In the absence of anything else assume market rates up to 5 years and a stable forward rate thereafter?
asset model choice calibration3
Asset model choice/calibration
  • Calibrate models to prices versus properties of instruments such as implied volatility – is this market consistent?
  • Unlikely to reproduce closely the prices of swaps if calibrate to Gilt-edged securities and vice versa.
asset model choice calibration4
Asset model choice/calibration
  • Crucial point is to sensitivity test the outcome;
    • If deduce that it is not quite as sensitive to equity volatility anyway if we have 50-60% equity backing ratios – getting it “wrong” by 20 basis points is not material
asset model choice calibration5
Asset model choice/calibration
  • Crucial point is to sensitivity test the outcome;
  • Separate model features from real world features;
    • Consols process in 2 factor model will tend to dominate long bond volatilities
    • Lognormal models are skew
  • Get the basics right first;
    • Not very sensitive to interest rate model choice of fixed interest if matched by duration
asset model choice calibration6
Asset model choice/calibration
  • Crucial point is to sensitivity test the outcome;
  • Separate model features from real world features;
  • Get the basics right first;
  • Remember that assumptions about payments on surrender or other management actions may have a far more significant impact.
asset model choice calibration7
Asset model choice/calibration
  • Cannot avoid the maths and delegate responsibility for completeness and appropriateness
    • Martingale tests for all asset classes
  • How many simulations should be used?
    • Central limit theorem/standard errors
    • How big an unexplained item do you want in your analysis of surplus?
    • How big are you prepared “unexpected” movements to be?
  • Modelling assumptions
    • Dynamic behaviour
    • Dynamic decisions
modelling assumptions
Modelling assumptions
  • Models should allow for policyholder behaviour
  • 7.4.57 R Policyholder actions refer to the foreseeable actions that would be taken by the firm’s policyholders, taking into account:

(1) the experience of the firm in the past; and

(2) the changes that may occur in the future if options and guarantees become more valuable to policyholders than in the past.

policyholder behaviour
Policyholder behaviour
  • Realism sought
  • Eliminate artificial releases of surplus arising from lapses
  • Allow for likely option take-up rates
    • WP Bonds spot guarantee dates at key policy anniversaries
    • Tax-free cash in GAOs
    • Pensions contracts and endowment assurances may have material guaranteed surrender values/early retirement options
  • Irrational policyholders vs. American options
    • American options cost more
    • Limited data in extreme conditions
    • Contradictory data
  • WP PVIF value offsets in some instances
modelling assumptions1
Modelling assumptions
  • Dynamic management actions are available to mitigate risk
    • 7.4.50 R In calculating the risk capital margin for a with-profits fund, a firm may reflect, in its projections of the value of assets and liabilities under the scenarios in PRU 7.4.42R, the firm’s prospective management actions (see PRU 7.4.51R).
  • But assumptions need to be reasonable

7.4.51 R Prospective management actions refer to the foreseeable actions that would be taken by the firm’s management, taking into account:

(1) an appropriately realistic period of time for the management actions to take effect; and

(2) the firm’s PPFM and its regulatory duty to treat its customers fairly.

dynamic management actions
Dynamic management actions
  • Why do we want to the model to make dynamic decisions?
    • Complex office behaviour needs replicated by model if it’s to be realistic
    • More useful if it’s realistic
    • Capital requirements based on the output of these models
      • Unnecessary prudence undesirable
investment decisions
Investment Decisions
  • Manage exposure to risky assets
  • Explicit stress test of the balance sheet in line with RCM (-20% equity and/or –100bps gilt yields)
    • Run times
    • Complexity
    • Closed fund projections
  • Implicitly through proxy based on FTSE
    • Simple
regular bonus decisions
Regular Bonus Decisions
  • Projected affordability/sustainability
  • Smoothing of changes from one year to the next
  • Portfolio-wide costs can be estimated
systems and controls
Systems and controls
  • Testing and checking
  • Model controls
  • Output analysis
testing and checking
Testing and checking
  • Start deterministic
    • Then scenarios
    • Then percentiles from stochastic
  • Worth the effort on
    • Accurate specifications
    • Detailed test plans
    • Extensive testing
    • Enlist the help of expert in their owe areas
  • Extreme returns break code
    • “Div almost zero” errors
    • Burst out of top of arrays
    • Taylor’s theorem relies on small interest rate deltas
  • Third parties can add value in reviewing
  • Simulation walkthrough
model controls
Model controls
  • It’s important as drives balance sheet (through WPICC)
    • Unit admin, quotation/projection and valuation systems all rolled into one!
  • Complexity means that it is infeasible to audit?
    • Sign off of the initial model
    • Ongoing audit trails and controls
      • Sign-off of master model for all purposes based on full stochastic run
    • Sign off of the model following a model update
      • Test grouped model points remain appropriate
      • Recalibrate and check again the economic scenario files
output analysis
Output analysis
  • Analyses of change
    • BSM instructive
    • Crude deltas and other Greeks
  • Explanation of results from one period to the next
  • Changes in model
  • Changes to management actions
  • Changes in intrinsic component
  • Changes in time value component
  • Explaining the results is tricky!
  • Who is the audience ?
    • Actuarial / Technical
    • Executive
    • Regulator
  • What message are we trying to get across ?
    • What is the purpose of the results
  • What are the key messages from the results
  • What action should I take (if any) given this information
  • How should the results be presented ?
    • Single point estimate
    • Confidence Intervals
    • Percentile Graphs
current topic fred 34
Current Topic – FRED 34
  • Results currently required to go to FSA within 3 months (of year end)
    • Many companies are completing within 6 – 8 weeks
  • Shareholder reporting means that results likely to be required within around 2 weeks
  • Results rolled forward
    • Risk of actual being significantly different than expected
    • Risk of R&A differing from FSA submission
  • Models and methodology still being developed
    • Many companies currently going through audits of RBS
    • Will auditors be happy to sign off on working day 10 “estimates”
  • Useful tool to understand dynamics of complex liabilities
  • Still in its infancy
    • Keeping things understandable is important
    • Thousands of model inputs and outputs
  • Complex models requires extensive testing
  • Strong auditable controls around master model developments
  • Tailor the output to the user
  • The key challenge is to develop a well controlled process that produces explainable results in time to meet tight shareholder (or other) reporting deadlines