The Investment Section Presents 

Economic Scenario Generation for the Practitioner May 6, 2018 | Baltimore Marriott Waterfront | Baltimore, MD 

Presenters: Christian Curran, FIA Alasdair Johnston 

Hal Warren Pedersen, ASA Daniel Mark Schobel, ASA 

Suhrid Swaminarayan, FSA, FIA  

SOA Antitrust Compliance Guidelines SOA Presentation Disclaimer

Economic Scenario Generation for the Practitioner Seminar

DANIEL MARK SCHOBEL, ASA 

CHRISTIAN CURRAN

ALASDAIR JOHNSTON

HAL WARREN PEDERSEN, ASASunday May 6, 2018   1:00‐5:00 PM

PRESENTED BY THE INVESTMENT SECTION

SOCIETY OF ACTUARIESAntitrust Compliance Guidelines

Active participation in the Society of Actuaries is an important aspect of membership.  While the positive contributions of professional societies and associations are well‐recognized and encouraged, association activities are vulnerable to close antitrust scrutiny.  By their very nature, associations bring together industry competitors and other market participants.  

The United States antitrust laws aim to protect consumers by preserving the free economy and prohibiting anti‐competitive business practices; they promote competition.  There are both state and federal antitrust laws, although state antitrust laws closely follow federal law.  The Sherman Act, is the primary U.S. antitrust law pertaining to association activities.   The Sherman Act prohibits every contract, combination or conspiracy that places an unreasonable restraint on trade.  There are, however, some activities that are illegal under all circumstances, such as price fixing, market allocation and collusive bidding.  

There is no safe harbor under the antitrust law for professional association activities.  Therefore, association meeting participants should refrain from discussing any activity that could potentially be construed as having an anti‐competitive effect. Discussions relating to product or service pricing, market allocations, membership restrictions, product standardization or other conditions on trade could arguably be perceived as a restraint on trade and may expose the SOA and its members to antitrust enforcement procedures.

While participating in all SOA in person meetings, webinars, teleconferences or side discussions, you should avoid discussing competitively sensitive information with competitors and follow these guidelines:

• Do not discuss prices for services or products or anything else that might affect prices

• Do not discuss what you or other entities plan to do in a particular geographic or product markets or with particular customers.

• Do not speak on behalf of the SOA or any of its committees unless specifically authorized to do so.

• Do leave a meeting where any anticompetitive pricing or market allocation discussion occurs.

• Do alert SOA staff and/or legal counsel to any concerning discussions

• Do consult with legal counsel before raising any matter or making a statement that may involve competitively sensitive information.

Adherence to these guidelines involves not only avoidance of antitrust violations, but avoidance of behavior which might be so construed.  These guidelines only provide an overview of prohibited activities.  SOA legal counsel reviews meeting agenda and materials as deemed appropriate and any discussion that departs from the formal agenda should be scrutinized carefully.  Antitrust compliance is everyone’s responsibility; however, please seek legal counsel if you have any questions or concerns.

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Presentation Disclaimer

Presentations are intended for educational purposes only and do not replace independent professional judgment. Statements of fact and opinions expressed are those of the participants individually and, unless expressly stated to the contrary, are not the opinion or position of the Society of Actuaries, its cosponsors or its committees. The Society of Actuaries does not endorse or approve, and assumes no responsibility for, the content, accuracy or completeness of the information presented. Attendees should note that the sessions are audio‐recorded and may be published in various media, including print, audio and video formats without further notice.

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• Introduction• Let’s introduce each other

• Economic Scenario Generator (ESG) Foundational Concepts

• Daniel Mark Schobel, ASA• Risk Neutral Modeling

• Daniel Mark Schobel, ASA• Real World Scenario Generation

• Christian Curran; Alasdair Johnston• Expert Judgement in Calibration and Pitfalls

• Hal Warren Petersen, ASA

4

Agenda

• Show of hands:• Level of ESG expertise• Large vs. Small company• Pricing, Valuation, Modeling role

• Speakers• Dan Schobel• Christian Curran• Alasdair Johnston• Hal Warren Pedersen

• Moderator• David Schraub, FSA

5

Introduction

VP & Actuary, Insurance Product Manager, Client Solutions GroupNumerix

Mr. Schobel works with clients around the globe to develop economic scenario generators to meet regulatory requirements and risk management goals, utilizing actuarial experience and Numerix Analytics. He is active in client implementations and in the development of new features and new methodologies within the Numerix Economic Scenario Generator. He is an Associate of the Society of Actuaries with more than 5 years of experience developing scenario generators.

6

Daniel Mark Schobel, ASA

DirectorMoody’s Analytics

Christian is a Fellow of the Institute and Faculty of Actuaries and leads the North America advisory team for Moody’s Economic Scenario Generator. He joined Moody’s in 2012 and is responsible for working with Insurers and Asset Managers to implement and support their ESG product. Prior to joining Moody’s, he worked at Aon Hewitt advising Defined Benefit Pension Plans. Following his undergraduate studies in Mathematics at the University of Edinburgh and UC Berkeley he completed an MSc in Finance at Imperial College London.

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Christian Curran, FIA, CERA

Associate DirectorMoody’s Analytics

Alasdair works as part of the Moody’s Analytics Advisory Services team based in New York and is focused on supporting Insurance and Asset Management clients with implementation, support and bespoke calibration of the Moody’s Analytics Scenario Generator. Alasdair has been with Moody’s since 2012 working with clients across EMEA, North America and APAC. Alasdair holds an MA in Mathematics and Economics, MSc in Financial Mathematics and is student member of the IFoA.

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Alasdair Johnston

Managing Director, Risk SolutionsConning

Dr. Hal W. Pedersen is one of the principal architects of GEMS, Conning’s economic and capital market scenario generator. He is the senior leader in the Quantitative Finance team where he directs the application of Conning’s ESG technology to risk management, business analytics, and innovative client focused solutions. He is an Associate of the Society of Actuaries and has more than 20 years academic and industry experience in the application of financial economics to insurance. He was L.A.H. Warren professor of actuarial science at the University of Manitoba from 2003 through 2011 and served on the actuarial faculty at Georgia State University from 1996 through 2001. He is a member of the Society of Actuaries Investment Section council.

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Hal Petersen, ASA

Staff FellowSOA

David Schraub is the Staff Fellow for Risk Management and Investment at the Society of Actuaries (SOA) working to develop and support better risk management and investment effort of the actuaries, directing volunteer activities in these two areas. In addition, he provides risk expertise to the SOA’s education (including both basic and continuing education programs) and research functions. He also serves as a liaison between the SOA and other organizations in the risk arena and works to facilitate the intellectual capital development of actuaries in risk management.

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David Schraub, FSA

DateDaniel SchobelVP & Actuary, Insurance Product Manager, NumerixMay 6th, 2018

Economic Scenario Generators

What is it?What is it?

An Economic Scenario Generator (ESG) is a tool that helps firms generate stochastic risk‐neutral and real world scenarios to meet regulatory requirements and risk management goals.

Importance of the Use CaseImportance of the Use Case

Example use cases for ESGs include:• Economic Capital• Pricing• Valuation• Hedging• Asset Valuation & Asset Management• Risk Management

Use cases may vary with respect to:• Projection Horizon• Covered Risk Factors• Availability of Market Data• Calibration Requirements (may be prescribed)

DateDaniel SchobelVP & Actuary, Insurance Product Manager, NumerixMay 6th, 2018

Risk-Neutral Economic Scenario Generation

AgendaAgenda

• Risk‐Neutral Review

• Typical ESG Workflow and Common Challenges

• Model Selection and Calibration– Model Flexibility and Speed– Validation

• Example Demo

• Takeaways

AgendaAgenda

• Risk‐Neutral Review

• Typical ESG Workflow and Common Challenges

• Model Selection and Calibration– Model Flexibility and Speed– Validation

• Example Demo

• Takeaways

Background – Why use a RN ESG?Background – Why use a RN ESG?

• Regulation– Market Consistent Embedded Value (MCEV)– Fair Value (FASB 133/157, IFRS 4/9/17)– Solvency II– GAAP, other accounting frameworks

• Product Offering– Hedging of Variable Annuity Guarantees (GMxBs)– Measuring Greek exposures– P&L analysis– Attribution analysis

• Asset/Liability Management– Duration/Convexity analysis

Two Frameworks: Real World vs. Risk‐NeutralTwo Frameworks: Real World vs. Risk‐Neutral

Real World

Probabilistic Statements

Risk Premia

Dynamics must represent the true 

world

Risk‐Neutral

Pricing/Valuation

Assets grow at the risk‐free rate

Dynamics do not need to represent the true world

Risk‐Neutral BasicsRisk‐Neutral Basics

• Arbitrage‐free– All assets grow at the risk‐free rate– Martingales

• Objective calibration criteria– Validation by comparison to known market prices of assets

• Based on risk‐neutral probabilities– Example: Price a contract on the weather

Payoff = 1

Payoff = 0

Price = ?

AgendaAgenda

• Risk‐Neutral Review

• Typical ESG Workflow and Common Challenges

• Model Selection and Calibration– Model Flexibility and Speed– Validation

• Example Demo

• Takeaways

Typical ESG WorkflowTypical ESG Workflow

• Quotes• Curves• Surfaces

Market Data

• Hull-White• Black-Scholes• Etc.

Models• Treasury Yield• Swap Rate• Equity Return• FX Rate• Etc.

Scenarios

Common ChallengesCommon Challenges

• Market & Historical Data– What market data should be used?– Is the market data of high enough quality (deep, liquid, transparent markets, 

and covers the required projection horizon)?– Extrapolation and interpolation?

• Models– What model should be used for a particular asset class?– How many factors are needed?– How should my model be calibrated for a given use case?– How should I check/validate my model calibration?

• Scenarios– Are the scenarios converging?– Do the scenarios pass validation tests (e.g. Martingale test)?

AgendaAgenda

• Risk‐Neutral Review

• Typical ESG Workflow and Common Challenges

• Model Selection and Calibration– Model Flexibility and Speed– Validation

• Example Demo

• Takeaways

Model Flexibility and SpeedModel Flexibility and Speed

• Challenges and Considerations:– Time‐varying parameters

• Are parameters flexible enough to fit calibration targets?

– Affine models• Is the model affine allowing for fast simulation?

– Simulation• Does the model produce appropriate dynamics?

– Black-Scholes vs. Heston vs. Bates» Stochastic Volatility» Jumps

– Hull-White vs. CIR vs. Black-Karasinski» Normal vs. Lognormal» Constant elasticity of variance

– Complexity and Convergence• Will scenarios converge for desired metric given the model complexity?

– Regime switching models

Variance Reduction – Random Number GenerationVariance Reduction – Random Number Generation

Quasi Pseudo

Source: https://en.wikipedia.org/wiki/Low-discrepancy_sequence

Variance Reduction – Random Number GenerationVariance Reduction – Random Number Generation

• Convergence: Price of a 1‐Year European Call Option– Test 1000 Random Seeds– Note the range of values for the option PV under the different RNGs

7.8

7.85

7.9

7.95

8

8.05

8.1

0 1000 2000 3000 4000 5000 6000 7000

PV

paths

1‐yr Call (Quasi)

avg 95% perc 5% perc analytic price

6.8

7.3

7.8

8.3

8.8

0 1000 2000 3000 4000 5000 6000 7000

PV

paths

1‐yr Call (Pseudo)

avg 95% perc 5% perc analytic price

AgendaAgenda

• Risk‐Neutral Review

• Typical ESG Workflow and Common Challenges

• Model Selection and Calibration– Model Flexibility and Speed– Validation

• Example Demo

• Takeaways

Validation: Model Calibration ReportsValidation: Model Calibration Reports

Detailed analysis of the fit to market data performed by the ESG

Validation: Martingale Tests for Risk‐Neutral ESGValidation: Martingale Tests for Risk‐Neutral ESG

Comparing scenarios against market data used for calibration

AgendaAgenda

• Risk‐Neutral Review

• Typical ESG Workflow and Common Challenges

• Model Selection and Calibration– Model Flexibility and Speed– Validation

• Example Demo

• Takeaways

ExampleExample

• Excel ESG Sample Implementation– 1‐Factor Vasicek– 1‐Factor CIR

AgendaAgenda

• Risk‐Neutral Review

• Typical ESG Workflow and Common Challenges

• Model Selection and Calibration– Model Flexibility and Speed– Validation

• Example Demo

• Takeaways

TakeawaysTakeaways

• Risk‐Neutral Calibration is objective– Compare against observable market prices of assets

• Model selection and calibration is clearly important, but the best choices depend heavily on the specific use case

– One‐size fits all is rarely appropriate– Required time horizon & market data

• All assets grow at a risk‐free rate, so there is no risk premium to be earned

• Framework primarily for pricing/valuation• Variance reduction may be achieved through more efficient random number generation

Q&AQ&A

Thank You

www.numerix.com

Real World ESG

May, 2018Christian Curran, Alasdair Johnston

ESG, May 2018 37

1. Summary of Real World ESG Usage2. Example Real World ESG Capital Calculation3. Transitioning from Risk Neutral to Real World 4. Example Interest Rate and Equity Simulation5. Model Drawbacks

Agenda

ESG, May 2018 38

• Reserves and Capital• Accounting for UL• CF Testing• Hedge Effectiveness• Pricing• Economic Capital• Strategic Asset Allocation

Real World

• Accounting for VA• Market Consistent Embedded Value• Hedging• Economic Capital

Risk Neutral

Summary of Uses of an ESG

ESG, May 2018 39

• What is needed to meet emerging policy holder liabilities as they fall due?

• Long-term real world scenarios

• Rank order the discounted surplus

• CTE 70 – Reserves

• CTE 90 – Capital

Example of reserve or capital calculation

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0 1 2 3 4 5

ESG, May 2018 40

d α θ σ

• r(t) – short rate

• θ(t) – long term mean (time-dependent)

• α – speed of mean reversion

• σ – volatility

• - brownian motion

Model functional form

1 Factor Hull-White Model

ESG, May 2018 41

d α θ σ

• Generate full yield curve from short rate by taking expectation of above formula. Analytic function of model parameters

• Normally distributed interest rates

• Time-dependent theta – can fit initial yield curve exactly

• Perfectly correlated movements in rates across the yield curve

• Analytical formulae for prices of vanilla IR derivatives

Model features

1 Factor Hull-White Model

ESG, May 2018 42

d σ

• S(t) – stock price

• – cash/risk-free return

• σ – volatility

• - brownian motion

Model functional form

Equity

ESG, May 2018 43

d σ

• Constant mean return

• Constant volatility

• Log returns are normally distributed

• No relationship between return and volatility

• Large negative equity returns occur with low probability

Risk Neutral Model functional form

Equity

ESG, May 2018 44

Risk Neutral to Real World• One way can price liabilities using risk neutral valuation methods.

– A convenient mathematical technique where we adjust the probability measure so that all assets earn the risk-free rate.

– Investors are indifferent (or neutral) to risk and do not demand a premium for investing in risky assets.

– Under the risk neutral probability measure, all assets, when discounted at the cash rollup, are martingales.

• Value of a future cash flow X (liability) at time T is:

where C is the cash roll-up and the expectation is calculated under the “risk-neutral” probability measure ℚ.

• Models are typically calibrated to replicate market prices.

• Distributions of interest rates, equity etc. won’t necessarily be “realistic”.

ESG, May 2018 45

Risk Neutral to Real World• For certain applications we are interested in projecting cashflows that are contingent on a range of market

and economic variables

• We aren’t however looking to place a price/value on these cashflows today but look at how they may evolve in the future under a range of different scenarios

• For this we require our models to produce a set of “realistic” or scenarios reflecting the Real World

• In the Risk-Neutral world we implied that expected returns on all assets was equal to the risk-free rate. Investors, however, are likely to demand a risk premium for taking on risk of certain assets.

• That is, in the Real World:

Eℙ 1 Eℙ 1

• We can achieve this through a change of measure which we discuss in the following slides.

ESG, May 2018 46

• Introduce term-premia, to move from Risk Neutral to Real World

d α θ σ

α θσα σ

• Under the RW dynamics the short rate reverts to a different average level than implied by the initial yield curve

• Introduces term premia on longer date bonds – expected returns on longer dated bonds can be higher or lower than shorter date bond

Model features

1 Factor Hull-White Model

ESG, May 2018 47

Example Simulation

1 Factor Hull-White Model

ESG, May 2018 48

• Introduce risk-premia, to move from Risk Neutral to Real World

d σσ σ

• Under the RW dynamics there is a risk premium of σin excess of cash.

• Investors are rewarded for taking additional risk of holding equity

Model features

Black-Scholes Equity Model

ESG, May 2018 49

Example Simulation

Black-Scholes Equity Model

ESG, May 2018 50

Holding capital against a put option

Simple Capital Calculation

• Ignore stochastic interest rates – assume 4% flat yield curve, r = 4%, for discounting

• 5 Year Maturity Put Option on the S&P Index

• Initial Equity Index, S0 = 2700

• Strike of Option, K = 3500

1. Project Equity return index, S(t), over 5 years using Black-Scholes Model• Total returns, σ 8%

• Volatility, σ 20%

• 10000 Trials

2. Calculate Put Option Pay off in each trial (S5 – K).

3. Rank the payoffs in order and take the average of the 30% of highest pay-offs.

ESG, May 2018 51

Simple Capital & Reserving Calculation

CTE 90 = -2090

CTE 70 = -1624

ESG, May 2018 52

• In a Real World context the main aim is to produce realistic distributions for risk-factors and asset returns.

• Typically seek to calibrate the models to a range of assumptions for the distributions which may include but is not limited to:

• Expected Values

• Volatilities

• Correlation between risk factors

• Key questions• What time horizon are we interested in? Which aspects of the distribution will have the most impact on my results? Is

there a relationship between the parameters/assumptions?

• There is also a need to inform a suitable starting point for the projection – e.g. initialize interest rate models at today’s yield curve

Target Setting

ESG, May 2018 53

• What data can we look to leverage?- Market data e.g. yield curves, equity volatility

- Historical data – long term interest rates, historical equity returns

- Economic Forecasts

- Internal House Views

• May use a combination of the above but there may be some challenges in combining these consistently

• Historical data can be of varying lengths

• Historical realizations may not provide a reasonable view of the future

• Economic Forecasts or Internal House Views may be biased towards particular economic conditions.

Data

ESG, May 2018 54

• There are a number of different approaches that you can take to calibration:• Maximum Likelihood

• Least Squares Regression

• Kalman Filter

• Minimizing sum of squared difference between model and target values

• Each of these will likely produce different parameters for the model even if the data used is similar.

• There is a need to validate calibrations to ensure not only that targets are met but the model produces sensible dynamics

• It’s possible to utilize a mix of these approaches as well

• An example calibration of the 1-Factor HW model is provided on the next slide

Approaches to Calibration

Model calibration

ESG, May 2018 55

• The following targets for the short-rate have been set or derived from market data:• December 31st 2017 Treasury Yield Curve

• Expected Value for the Short Rate in 10 years – 3%

• Volatility (St. Dev of Changes) of the Short Rate in 10 years – 1.5%

• Dispersion (St. Dev of Levels) of the Short Rate in 10 years – 2.8%

• To calibrate the model we adjust the α, σ and γ parameters of the Hull-White model to minimize the difference between values produced by the Hull-White model and the targets above

Example Calibration

Model calibration

Target Model

Expected Value 3% 3.00%

Dispersion 2.8% 2.79%

Volatility 1.5% 1.51%

Parameter

Alpha 0.147876

Sigma 0.014892

Gamma -0.0912

ESG, May 2018 56

- Perfect correlation in movements in the yield curve- Can capture tits, twists, inversions of the yield curve

- Unable to target volatility, dispersion of multiple rate maturities

- Rate distributions produced are normal- No control over size of possible negative rates produced by the model

- Interest rate volatility is absolute- Volatility of rates doesn’t change with a change in the rate level

- May not be consistent with historically observed rate behavior

1FHW Challenges

ESG, May 2018 57

- Constant volatility- Historical returns across equity markets exhibit periods of high and low volatility

- Constant return

- Return/volatility relationships

- Large negative shocks, tail correlations

Black-Scholes Equity Challenges

Q&A

ESG, May 2018 59

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www.conning.com | © 2018 Conning, Inc.

Economic Scenario Generation for the Practitioner:

Expert Judgement in Calibration and Pitfalls

Hal Pedersen, Conning

Society of Life & Annuity Symposium 2018

Baltimore

10:00-11:15

May 8, 2018

Concept of an ESG

An Economic Scenario Generator (ESG) is a computer-based model of an economic environment that is used to produce simulations of the joint behavior of financial market values and economic variables.

An ESG should:

• produce simulation results that reflect a relevant view

• produce some extreme but plausible results

• generate scenarios that embed realistic market dynamics

Obtaining sufficient dispersion by way of a collection of future economic possibilities is an essential requirement for capturing market risk. The operational meaning of “sufficient dispersion” depends on some expert judgment.

ESGs can be applied in “real world” and “risk-neutral” applications.

• The simulation of interest rates and portfolio investment strategy testing are examples of real-world simulation.

• The pricing of guarantees and management of derivatives overlays is an example of risk-neutral simulation.

There are two common applications that are driving the increased utilization of ESGs:

• Market consistent valuation work for pricing complex financial derivatives and insurance contracts with embedded options. This application is mostly concerned with mathematical relationships within and among financial instruments and less concerned with forward–looking expectations of economic variables.

• Real world models for risk management work in calculating regulatory capital and rating agency requirements. Concerned with forward-looking potential paths of economic variables and their potential influence on capital and solvency.

1

Concept of an ESG

Market consistent valuation applications require ESGs to be capable of reproducing the observable prices of traded derivative instruments in order to determine comparable prices for derivative instruments and insurance contracts with embedded options that are not traded, but that require market valuation. ESGs that are used for these purposes need to adhere to strict mathematical properties such as risk neutral and arbitrage-free conditions.

Because the market consistent model calibration process is designed to reproduce the prices of traded derivatives, the ultimate calibration is dependent on both the pricing date and the set of traded derivatives used to calibrate the model.

The validation associated with the model calibration is based on how well the model reproduces the market values of the universe of traded derivatives used to calibrate the model.

In contrast to risk-neutral, the purpose of a real-world simulation is to capture market dynamics, risks, and returns in a way that an insurance company or other financial institution will experience them.

Because real world parameterizations are forward-looking, they require explicit views as to how the economy will develop in the future and, as such, they require a significant amount of expert judgment to determine the veracity of the scenarios thatresult from the parameterization process.

In practice, real world calibrations are often parameterized to be consistent with historical dynamics of economic variables,although the long-term steady state levels (expected means) associated with these parameterizations can differ from long-term historical averages in favor of current consensus expectations or specific user views. An example would be applying expert judgement to reflect a prolonged low interest rate environment as a result of central bank activities during the post-2008 environment.

Real-world simulations enable the “what if” questions by management as it tries to gauge the likelihood of future events and the business impact.

2

Concept of an ESG

The manner in which the “what if” questions are posed and the scope of the analysis that follows continue to evolve. It seems probable that this aspect of risk management will be more integrated into ERM in the coming years.

Users of an ESG should have a good understanding of the scope of applications they need to address and whether these applications require real-world scenarios, risk-neutral scenarios, or both.

Parameterizations of real world ESG models require the user to think about the future economic environment that they want to reflect in their risk analysis work. Some of the key steps involved in parameterizing a real world model include:

• Selecting the appropriate steady state levels.

• Determining the appropriate values for the initial conditions.

• Identifying key parameterization targets for the application (stylized facts).

• Controlling the expected mean reversion path.

One might consider a broad process for ESG management to consist of:

• Model selection

• Target setting

• Calibration

• Validation

Model selection is informed by an understanding of both the application and the stylised facts for the markets that are beingmodelled.

Risk-neutral (RN) and real world (RW) share the basic approach but have different aspects to each component.

3

Three Components of the ESG Process

4

Models

Calibration Validation

These components interact to determine the performance of an ESG

Three Components of the ESG Process

The calibration brings the model performance alive.

Calibration is the process of setting the parameters of the equations within an ESG model to produce the distributions and dynamics (e.g. volatility, correlations, tail characteristics) of economic and financial variables that are required by the application for which they are being used.

The choice of calibration targets reflects a view.

To distinguish real world calibrations from market consistent calibrations, we will refer to the real world calibration process as "model parameterization."

5

REAL WORLD PARAMETERIZATION PROCESS

Three Components of the ESG Process

The robustness of the scenarios depends on achieving calibration objectives, obtaining a range of

scenarios that encapsulate historical experience, and generating some extreme but plausible

scenarios.

The natural steps in preparing ESG scenarios are to calibrate the models and run a validation

check.

Validation ensures that the estimation of an ESG’s parameters result in simulated behavior that is a

good representation of the variable or market under consideration.

Benchmarks may be based upon historical data, internal views, regulator demands or a

combination of these factors.

If validation raises issues then a recalibration may be required.

It may also happen than the limitations of the model dynamics are such that there is no calibration

that will achieve all validation objectives. In such cases, alternative ESG models may be needed.

These three components of an ESG: models, calibration and validation interact in the maintenance

of an ESG.

6

RN Calibration Considerations

Accurate match to initial yield curves.

Fit to benchmark derivatives with liquid price quotes. Often using equity derivatives and swaptions

to benchmark the model calibration.

RN simulated financial variables such as interest rates may look quite unrealistic if compared

against empirical data. The basic validation test is the ability to reproduce the market prices of

derivatives.

RN models may also be audited using a martingale test to check that the calibration and model

dynamics conform to basic theoretical arbitrage-free restrictions.

Correlations are important.

The evolution of the swaption vol surface might also be checked to ensure that the model dynamics

are producing robust pricing scenarios as the simulation moves away from its initial calibration

point.

Some complications can exist when RN scenarios produce values for financial variables that lie

outside normal empirical ranges. For example, if one is using RN scenarios for pricing insurance

products there can be challenges in mapping 40% interest rates into policyholder behaviour.

7

RW Calibration Considerations

Accurate match to initial yield curves.

RW calibrations are typically validated against statistical targets (mean, volatility), possible at

various simulation horizons.

The characteristics of the simulated distributions are carefully examined. One often compares the

simulated with the historical distributions.

Tail behaviour is a focus. The idea that a good calibration meets or exceeds history and produces

extreme but plausible outcomes is a typical guiding principle.

Of course, one does not mean all history. Such a comparison is done for a carefully chosen

historical window or a view based on a composite of historical experience.

For those variables that exhibit mean reversion, the rate of mean reversion is usually considered.

Correlations are important.

8

RN Calibration (Black Volatility)

9

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration (Black Volatility)

10

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Equity Options

11

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Equity Options

12

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Swaption Volatilities Change Over Time

13

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Some Issues in the Model Calibration

14

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – A Successful Model Calibration

15

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Initial Yield Curve Fit (30 Year Tenor)

16

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Initial Yield Curve Fit (10 Year Tenor)

17

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Initial Yield Curve Fit (1 Year Tenor)

18

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Martingale Test Theory

Constructing a martingale asset test begins with the choice of a horizon T > 0 and the expression

which is valid for self-financing trading strategies and for which it is assumed that all traded assets

have risk-neutral parameterizations so that the expectation is a risk-neutral expectation.

As a simple example, if one selects the self-financing strategy of purchasing an asset with ex-dividend

price process Xt and reinvesting the dividends into that asset, then the martingale test at horizon T

takes the form

Where QT denotes the accumulated units of the asset that are held at time T as a result of the

reinvestment of dividends.

19

RN Calibration – Martingale Test Theory

In order to apply the martingale test, one must determine QT. In cases of practical interest, QT is

usually a deterministic function of a dividend rate or payment schedule and the horizon T. To apply

the martingale test, a risk-neutral scenario set consisting of the values for XT and BT must be given

and one then computes the average

which should be close to X0. We denote the number of scenarios in the risk-neutral scenario as M.

The martingale test is often set up as a “1 = 1” test. This is nothing more than normalizing both sides

of the second equation on the previous slide by X0, resulting in the test expression

20

RN Calibration – Martingale Test Theory

A total return index may be constructed from traded assets according to the simple weighted formula

Where Ri(t, t + s) is the total return on asset i over the investment period beginning at time t and

ending at time t + s (i.e., over the interval [t, t + s]) and ωi is the portfolio weight of asset i. The

corresponding total return index is now constructed recursively starting with I(0) = 1 and proceeding

as

It can now be shown, using the martingale property of each of the constituent assets, that

at horizon T. This expression is a generic but easy-to-apply martingale test for total return indices. In

order to perform the martingale test, one must have available a risk-neutral scenario set of the total

return series for the index.

21

RN Calibration – Martingale Test 1

22

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RN Calibration – Martingale Test 2

23

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RW Calibration

“What if” risk management focus.

RW calibrations are typically validated against historical norms.

Flexibility of calibrations can be important so that a range of views and investment strategies can be

analyzed.

One needs targets and a sense of what the market is like.

One needs a robust suite of tools to recalibrate.

Alternative modeling techniques might enter into the ESG if validations fail due to material change

in market norms.

24

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

RW Model Building & Stylized Facts – Treasury Term Structure

A casual review of this chart suggests that yields for longer maturities tend to be greater than yields for shorter maturities. The chart also shows that the very short end of the yield curve has been close to zero since 2008.

One-factor models are quite limiting – only one curve per rate level per tenor.

25

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0 5 10 15 20 25 30

Yie

ld t

o M

atu

rity

Maturity

US Treasury Constant Maturity Yield Curves

Dec-04

Dec-06

Dec-08

Dec-10

Dec-12

Dec-14

U.S. TREASURY YIELD CURVES 2004-2014

Sources: Bloomberg, L.P., and Conning, Inc.

US Interest Rates – Monthly Changes in 1Yr and 10Yr Yields

It is not surprising that when the 1 year rate is pinned at zero it hardly moves. It is notable that the 10 year rate is changing a lot in recent years despite being at a low level, and that those movements are comparable to what was observed in the 1990s.

26

Prepared by Conning, Inc. Source: ©1926-2016 Bloomberg, L.P.

Stylized Facts – Corporate AAA Yield Spreads

27

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

Stylized Facts – Corporate BBB Yield Spreads

28

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

US Corporate Bond Spreads and Treasury Yield Changes

29

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

Emerging Markets Corporate Bond Spreads (Malaysia)

30

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

US 3m Treasury Yield – Months into Great Depression/Recession

31

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

US 3m Treasury Yield – Months into Great Depression/Recession

32

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

US 10yr Treasury Yield – Months into Great Depression/Recession

33

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

US 10yr Treasury Yield – Months into Great Depression/Recession

34

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

Model Building & Stylized Facts

Certain stylized facts are generally adopted as guiding principles in the selection of ESG model components. Models that areselected should be capable of being parameterized to capture these stylized facts.

Examples

• Yields for longer maturity bonds tend to be greater than yields for shorter maturity bonds.

• Monthly fluctuations in short maturity yields tend to be larger than monthly fluctuations in longer maturity yields.

• When short maturity yields are low, longer maturity yields are normally higher than the shorter maturity yields (a normal shaped yield curve).

• When short maturity yields are high, longer maturity yields are often lower than shorter maturity yields (an inverted yield curve).

• Interest rates can be negative.

• Corporate credit spreads are wider for lower credit quality instruments.

• There is a tendency for corporate credit spreads to fluctuate more during recessionary periods.

• The probabilities of default will fluctuate with general economic conditions and firm or industry specific conditions.

• Equity returns exhibit both higher expected returns and higher volatility than fixed income returns.

• The volatility of equity returns fluctuates significantly.

35

Calibration Targets

Statistical analysis of historical data provides offers no definitive methodology for setting long-term calibration targets.

Some element of expert judgement is unavoidable.

36

Prepared by Conning, Inc. Source: ©1926-2016 Bloomberg, L.P.

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

0.065

0.070

0.075

0.080

0.085

0.090

0.095

0.100

0.105

0.110

Rolling 10 Year Averages Ending July 2015

US 1yr Rolling Avg US 10yr Rolling Avg

ROLLING 10 YEAR AVERAGES FOR THE U.S. 1-YEAR AND U.S. 10-YEAR TREASURY YIELDS

Sources: Ibbotson, Bloomberg, L.P., and Conning, Inc.

Steady State US Treasury (Long Term Calibration Targets)

37

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

US Inflation – Has It Settled Down for Good?

Ongoing trends create difficulties in assessing long-term inflation levels.

38

Prepared by Conning, Inc. Source: ©1975-2016 Bloomberg, L.P.

UK Interest Rates – Long Run History (2.5% Consol Yield)

Avoid letting recent experience dominate the way a longer-term calibration view is

formed

“‘The rate of interest has fallen.’ ‘The rate of interest is falling.’ ‘The rate of interest will probably

continue to fall.’ These sentences, and others of a similar nature, we have read so often, that I fear

it is quite possible ‘familiarity’ may, to some extent, have had its usual effect. The fact remains,

however that any further fall in the interest yield is of vital importance to insurance companies with

large funds to invest, and bound by contracts, the fulfillment of which depends, to a large extent, on

the rate of interest obtainable.”

There is nothing surprising about the stress that very low interest rates can have on insurance

company operations. However, what may be surprising is that these words are the opening words

of the article by Joseph Burn in Some Considerations in Reference to the Fall in the Rate of Interest

Experienced in the Past, and the Probability of its Continuance, published in the Journal of the

Institute of Actuaries in April 1899 (Vol. 34, pp. 474-509).

According to the U.K. Debt Management Office, the interest rate experience at that time looked like

the following chart….

39

UK Interest Rates – Long Run History (2.5% Consol Yield)

40

Source: U.K. Debt Management Office.

UK Gilt Market 2.5% Consolidated Stock Average Yield (1727–1899)

UK Interest Rates – Long Run History (2.5% Consol Yield)

With the benefit of more than 100 years of additional data, we can put this chart in a longer-term perspective.

41

Source: U.K. Debt Management Office.

UK Gilt Market 2.5% Consolidated Stock Average Yield (1727–2012)

UK Interest Rates – Long Run History (2.5% Consol Yield)

Low for the series is 2.25% in 1897.

42

Source: U.K. Debt Management Office.

UK Interest Rates – Long Run History (2.5% Consol Yield)

While the observations of Mr. Burn are understandable, it is instructive that they were made very

near to the 300-year bottom of British interest rates.

The lesson for the user of an ESG is that while an ESG must produce extreme but plausible

scenarios, one cannot permit the concerns of the day to unduly influence the behavior of the

simulated scenarios if these scenarios are to be used for long-term risk management.

A good ESG in 1899 would have had the capability of producing the record low interest rates that

were observed at that time while also producing scenarios in line with longer-term historical levels.

The imposed calibration view for such a good ESG would have generated some rate scenarios that

stayed low, returned to more normal levels, and moved to even higher levels.

43

Calibration Targets

Correlation between asset classes fluctuate over time.

It is difficult to discern the cause for these fluctuations. It is particularly difficult to establish modelling triggers for these fluctuations.

44

Prepared by Conning, Inc. Source: ©1926-2016 Bloomberg, L.P.

-80.0%

-60.0%

-40.0%

-20.0%

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

De

c-98

Ma

y-9

9

Oct

-99

Ma

r-00

Au

g-0

0

Jan

-01

Jun

-01

No

v-0

1

Ap

r-0

2

Sep

-02

Feb

-03

Jul-

03

De

c-03

Ma

y-0

4

Oct

-04

Ma

r-05

Au

g-0

5

Jan

-06

Jun

-06

No

v-0

6

Ap

r-0

7

Sep

-07

Feb

-08

Jul-

08

De

c-08

Ma

y-0

9

Oct

-09

Ma

r-10

Au

g-1

0

Jan

-11

10 Year Rolling Correlation for 1yr+ Data with Treas 1yr+ TR

Inv Grd 1yr+

AAA

AA

A

BBB

HY

CORRELATIONS BETWEEN CORPORATE BONDS AND TREASURY BONDS OVER TIME

Sources: Bloomberg, L.P. and Conning, Inc.

Steady State – Putting It Together (Risk-Return Check)

45

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

Targeting Shorter Term (1yr Example)

Some RW simulations are focused on shorter term behaviour.

1yr calibrations are often used for regulatory purposes.

Capital modelling horizons might be in the range of 3yr–5yr, requiring hitting calibration targets over

that intermediate time frame.

46

Illustrative example.

One-Year Targets

Target Avg. (1yr) Target StDev (1yr)

1 0.00704 0.01357

10 0.02513 0.00809

30 0.03067 0.00701

Targeting Shorter Term (1yr Example)

47

Prepared by Conning, Inc. Source: GEMS® Economic Scenario Generator scenario.

Targeting Shorter Term (1yr Example)

48

Prepared by Conning, Inc. Source: GEMS® Economic Scenario Generator scenario.

Targeting Shorter Term (1yr Example)

49

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

Base Reversion Rate Calibration

50

Prepared by Conning, Inc..

Adjusted Reversion Rate Calibration

51

Prepared by Conning, Inc.

Measuring Effect of Mean Reversion (Treasury Portfolio Returns)

52

Prepared by Conning, Inc.

Measuring Effect of Mean Reversion (Treasury Portfolio Returns)

53

Prepared by Conning, Inc.

Measuring Effect of Mean Reversion (Treasury Portfolio Returns)

54

Prepared by Conning, Inc.

Measuring Effect of Mean Reversion (Treasury Portfolio Returns)

55

Prepared by Conning, Inc.

Measuring Effect of Mean Reversion (Treasury Portfolio Returns)

56

Prepared by Conning, Inc. Source: GEMS® Economic Scenario Generator scenario.

Measuring Effect of Mean Reversion (Treasury Portfolio Returns)

57

Prepared by Conning, Inc. Source: GEMS® Economic Scenario Generator scenario.

“Wrong” Models – Black-Scholes

58

Prepared by Conning, Inc.

“Wrong” Models – Black-Scholes

S&P 500 Daily returns

59

Prepared by Conning, Inc. Source: ©2018 Bloomberg, L.P.

“Wrong” Models – Black-Scholes

Daily simulation under Black-Scholes model

60

Prepared by Conning, Inc.

“Wrong” Models – Stochastic Volatility Only

Daily simulation under Illustrative Stochastic Volatility Structure

61

Prepared by Conning, Inc.

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All investment performance information included within this material is historical. Past performance is not indicative of future results. Any tax related information contained

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