Reserving for Investment Guarantees The Stochastic Modelling Approach Wai-Sum Chan, Ph.D., F.S.A., C.Stat. ASHK 6th Appointed Actuaries Symposium November 15, 2006 Reserving for Investment Guarantees – p. 1/47
What is Stochastic Modelling? A random variable — X Reserving for Investment Guarantees – p. 2/47
What is Stochastic Modelling? A random variable — X A stochastic process — X t — A system that evolves in time according to probabilistic equations, that is, the behavior of the system is determined by one or more time-dependent random variables. Reserving for Investment Guarantees – p. 2/47
What is Stochastic Modelling? A random variable — X A stochastic process — X t — A system that evolves in time according to probabilistic equations, that is, the behavior of the system is determined by one or more time-dependent random variables. Stochastic modelling is to build an empirical model to “best” describe the underlying stochastic process (say, interest-rate process, share return process, ..., etc.). Reserving for Investment Guarantees – p. 2/47
Actuarial Applications Valuation of assets and liabilities: • valuation of assets or portfolio of assets • valuation of libabilities • pricing and reserving actual products: VAs, EIAs, SFs Reserving for Investment Guarantees – p. 3/47
Actuarial Applications Valuation of assets and liabilities: • valuation of assets or portfolio of assets • valuation of libabilities • pricing and reserving actual products: VAs, EIAs, SFs Enterprise Risk Management & ALM • VaR, earnings at risk, embedded value at risk,... • Canadian Asset Liability Method (CALM) Reserving for Investment Guarantees – p. 3/47
Actuarial Applications Valuation of assets and liabilities: • valuation of assets or portfolio of assets • valuation of libabilities • pricing and reserving actual products: VAs, EIAs, SFs Enterprise Risk Management & ALM • VaR, earnings at risk, embedded value at risk,... • Canadian Asset Liability Method (CALM) Credit Risk Management Reserving for Investment Guarantees – p. 3/47
Major Types of Stochastic Models (A) P -Measure versus Q -Measure Q -Measure Concept of Arbitrage-Free — It is often referred to as no free lunch (NFL). NFL requires that on the basis of publicly available information, no investor can make a positive riskless return with no new investment. Reserving for Investment Guarantees – p. 4/47
Major Types of Stochastic Models (A) P -Measure versus Q -Measure Q -Measure Concept of Arbitrage-Free — It is often referred to as no free lunch (NFL). NFL requires that on the basis of publicly available information, no investor can make a positive riskless return with no new investment. The important point to understand here is how the martingale property of a stochastic process relates to the idea of the absence of arbitrage. Reserving for Investment Guarantees – p. 4/47
Major Types of Stochastic Models Q -Measure Informally, the Martingale Representation Theorem (an important theorem in Statistics) says that in equilibrium prices represented as the present (discounted) value of future payoffs from the asset must satisfy a martingale under a given probability measure Q . This Q -measure is often called the risk neutral measure. Reserving for Investment Guarantees – p. 5/47
Major Types of Stochastic Models Q -Measure Informally, the Martingale Representation Theorem (an important theorem in Statistics) says that in equilibrium prices represented as the present (discounted) value of future payoffs from the asset must satisfy a martingale under a given probability measure Q . This Q -measure is often called the risk neutral measure. Why do I care about MRT? If our chosen stochastic models have the above characteristic, they are “guaranteed” arbitrage-free (or called no-arbitrage) models. Reserving for Investment Guarantees – p. 5/47
Major Types of Stochastic Models P -Measure Informally, P -measure (the physcial measure) models only look at historical data (information). Reserving for Investment Guarantees – p. 6/47
Major Types of Stochastic Models P -Measure Informally, P -measure (the physcial measure) models only look at historical data (information). P -measure stochastic models do not “guaranteed” arbitrage-free. Reserving for Investment Guarantees – p. 6/47
Actuarial Stochastic Models Stochastic Liability Models • Life & Health • P&C (non-life) Reserving for Investment Guarantees – p. 7/47
Actuarial Stochastic Models Stochastic Liability Models • Life & Health • P&C (non-life) Stochastic Asset (Investment) Models • Equity Return Models • Interest-Rate Models • Composite (Multivariate) Models Reserving for Investment Guarantees – p. 7/47
Part I: Equity Return Models Reserving for Investment Guarantees – p. 8/47
Introduction Sharp decline and high volatility observed in stock markets around the world over the past few years Performance of World Stock Markets, 2000-2002 Country Market Index Jan 2000 Dec 2002 Change(%) Australia All Ordinaries Stock Index 3096 2976 -3.89% Canada TSE 300 Stock Index 8481 6615 -22.01% France CAC 40 Stock Index 5660 3064 -45.87% Hong Kong Hang Seng Stock Index 15532 9321 -39.99% Japan Nikkei 225 Stock Index 19540 8579 -56.09% United Kingdom FTSE 100 Stock Index 6269 3940 -37.14% United States S&P 500 Stock Index 1394 880 -36.91% Reserving for Investment Guarantees – p. 9/47
Introduction Many actuaries are now being asked to employ stochastic models to measure solvency risk created by insurance products with equity-linked guarantees Reserving for Investment Guarantees – p. 10/47
Introduction Many actuaries are now being asked to employ stochastic models to measure solvency risk created by insurance products with equity-linked guarantees The March 2002 final report of the Canadian Institute of Actuaries (CIA) Task Force on Segregated Fund Investment Guarantees (TFSFIG) provides useful guidance for appointed actuaries applying stochastic techniques to value segregated fund guarantees in a Canadian GAAP valuation environment. Reserving for Investment Guarantees – p. 10/47
Introduction In the United States, the Life Capital Adequacy Subcommittee (LCAS) of the American Academy of Actuaries issued the C-3 Phase II Risk-Based Capital (RBC) report in June 2005. Reserving for Investment Guarantees – p. 11/47
Introduction In the United States, the Life Capital Adequacy Subcommittee (LCAS) of the American Academy of Actuaries issued the C-3 Phase II Risk-Based Capital (RBC) report in June 2005. In addition to the interest rate risk for interest-sensitive products, the C-3 Phase II report also addresses the equity risk exposure inherent in variable products with guarantees, such as (1) guaranteed minimum death benefits (GMDBs); (2) guaranteed minimum income benefits (GMIBs); and (3) guaranteed minimum accumulation benefits (GMABs). Reserving for Investment Guarantees – p. 11/47
Introduction In the United States, the Life Capital Adequacy Subcommittee (LCAS) of the American Academy of Actuaries issued the C-3 Phase II Risk-Based Capital (RBC) report in June 2005. In addition to the interest rate risk for interest-sensitive products, the C-3 Phase II report also addresses the equity risk exposure inherent in variable products with guarantees, such as (1) guaranteed minimum death benefits (GMDBs); (2) guaranteed minimum income benefits (GMIBs); and (3) guaranteed minimum accumulation benefits (GMABs). Reserving for Investment Guarantees – p. 11/47
Introduction In Hong Kong, the Office of the Commissioner of Insurance issued the GN7: Guidance Note 7 on Reserving Standards for Investment Guarantees • Class G insurance policies • 99% level of confidence • scenario testing based on a stochastic model Reserving for Investment Guarantees – p. 12/47
Introduction In Hong Kong, the Office of the Commissioner of Insurance issued the GN7: Guidance Note 7 on Reserving Standards for Investment Guarantees • Class G insurance policies • 99% level of confidence • scenario testing based on a stochastic model ASHK issued AGN8: Process for determining liabilities under the Guidance Note 7 Reserving for Investment Guarantees – p. 12/47
Introduction There are a large number of potential stochastic models for equity returns. Regulators normally do not restrict the use of any model that reasonably fits the historical data. Reserving for Investment Guarantees – p. 13/47
Introduction There are a large number of potential stochastic models for equity returns. Regulators normally do not restrict the use of any model that reasonably fits the historical data. Reasonable = ⇒ pass a calibration test Reserving for Investment Guarantees – p. 13/47
Introduction There are a large number of potential stochastic models for equity returns. Regulators normally do not restrict the use of any model that reasonably fits the historical data. Reasonable = ⇒ pass a calibration test The emphasis of the calibration process remains at the tails of the equity return distribution (percentiles) over different holding periods (1- 5- and 10-year periods). Reserving for Investment Guarantees – p. 13/47
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