(cid:7637)(cid:7637)(cid:21399)(cid:15289)(cid:9907)(cid:19558)(cid:19263)(cid:11040)(cid:13995)(cid:18364)(cid:22966)(cid:13995) AIRC Seminar (cid:11690)(cid:10204)(cid:26704)(cid:26194)(cid:14793)(cid:10035) Market Risk Modeling (cid:11938)(cid:20246)(cid:20911)(cid:12657)(cid:17616) - An Introduction Eric Yau Consultant, Barrie & Hibbert Asia [email protected] December 2012 Agenda + Introduction to market risk modeling – What we are trying to do here – Common applications – Components of ESG model + The devil is in the details (part 1) – Constructing the initial yield curve – Liquidity premium – Mark-to-model in the absence of market prices + Workshop! P.1 2 Introducing market risk modeling 3 What we are trying to do here + What is the fair valuation of embedded financial derivatives on my liability book? – Liability is not tradable + What are the risk exposures of my net assets, and how should I measure them? – Risk exposure is multi-asset, multi-currency, multi-time period + What would my balance sheet look like in a probabilistic world? E.g. what is the chance of having NAV less than X billion? – Developing a view above the future state (or distribution) of the world is a subjective matter + How should I manage my asset-liability in light of such risks? – Requires thorough understanding of the risk nature of assets and liabilities on your book P.2 4 Model components Risk Modeling Engine: Economic Model Model Market Economic Scenario Generator Assumption Assumption Choice Data calibration Economic Scenario Generator Economic scenarios: Base and Sensitivities Projection Engine: ALM System Liability Asset ALM System Portfolio Portfolio 100 Millions 80 HKD 60 40 20 Generate analysis for both asset 0 1 3 5 7 9 1113151719212325272931333537394143454749 and liability portfolios: -20 -40 * Valuation -60 * Risk / Capital measures -80 -100 * Mismatch position -120 5 What is ESG? – Monte Carlo Simulation + Produce economically coherent joint distributions of financial and economic factors. + Generated using sophisticated models that capture the dynamics of financial markets – dependency, tail risk etc. Example output for interest rates Typical variables being modeled - + Interest rates + Inflation + Credit + Equity + Alternative investment + Option implied volatility + FX P.3 6 Common applications 7 Economic balance sheet + Mark-to-market (or mark-to-model) for both assets and liabilities Economic Balance Sheet A MCEV Adjustment L Market value Market- consistent 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 P.4 8 Stochastic vs deterministic + We live in a probabilistic world + Example: interest rate Guaranteed rate Pricing / valuation interest rate (deterministic) Consideration + distributional assumption + parameters (e.g. volatility) + multi-asset Expected + multi-time period Profit + etc Actual interest rate (random) How should we price in such an event? 9 Liability valuation / pricing + ESG model selection and calibration has to be appropriate for liabilities – Model choice - simple vs complex – Expert judgement must be prudent, reliable and justifiable + Using a richer model will make this easy to deliver in practice… P.5 10 Equity volatility – simple models ESG Generated IV Surface from a Market Implied Volatility Surface simple model (TVDV) 40% 40% 35% 35% 30% 30% V V I 25% 35%-40% I 25% 35%-40% 20% 30%-35% 20% 30%-35% 15% 25%-30% 15% 25%-30% 6 6 0. 8 20%-25% 0. 8 20%-25% 0. 1 15%-20% 0. 0 15%-20% 1. Strike 1.2 3 5 Matur10 ity Strike 1.2 3 5 10 1 1.4 1 1.4 Maturity + Simple model only appropriate for limited range of liability valuations – eg all ATM + If not all, need to segment book… – Dependencies between policies ? + … or hard-to-justify ‘averaging’ assumption? 11 Equity volatility – richer model ESG Generated IV Surface from Market Implied Volatility Surface sophisticated model (SVJD) 40% 40% 35% 35% V 30% V 30% I 25% 35%-40% I 25% 35%-40% 20% 30%-35% 20% 30%-35% 15% 0.6 0.8 1 221505%%%---322050%%% 15% 0.6 0.8 1 221505%%%---322050%%% Strike 1.2 1 1.4 3 5 Matur10 ity Strike 1.2 1 1.4 3 5 Matur10 ity + Richer model provides simpler, easier to justify solution P.6 12 ESG Economy Model Structure Alternative Asset Returns (eg Corporate Bond Equity Returns Property Returns Excess commodities) Returns returns (if any) Credit risk model Real-economy; GDP Initial swap and and real wages government nominal Nominal short rate bonds Nominal minus Exchange rate real is inflation (PPP or Interest expectations rate parity) Index linked Real short rate government bonds Realised Inflation and Foreign nominal “alternative” inflation short rate and rates (i.e Medical) inflation Macro economic + variables Joint distribution – Correlation assumptions ensure plausible economic relationship across asset classes 13 Risk factor distribution + Use joint distribution of financial risk factors to deduce income statement and balance sheet distribution Example: Credit/Equity risk + E.g. asset price falls should be associated with negative credit shocks P.7 14 Global equity modeling example “Global” Risk Risk Risk Risk Risk Risk Factor Factor Factor Factor Factor Factor 1 2 3 4 5 6 HK US Japan Equities Equities Equities + Indices have exposure in different risk factors + Volatility of equities moves up and down together – When vol goes up, correlation goes up too 15 Sources of risk… Interest rate & Equity Alternative Interaction of risk factors inflation risk risk investments 90 6 80 5 m) m) 70 £ aR (£ 60 4 mium ( V s re u 50 P rpl 3 sk Su 40 Ri e in 30 2 cted g e n p a x h 20 E C 1 10 0 0 Nominal Int. Rates Real Int. Rates Experienced Inflation Credit Domestic Equities OverseasEquities SourPropertyces of RAlternativesisk Currency Active Risk Mortality Total diversification All Risks P.8 16 Applications + Specific consideration to applications What it is for Consideration Calibration (1) Liability valuation / pricing Estimate fair value of (cid:2) Valuation of options / (cid:3)MC liability guarantees (2) Economic capital Assess level of resources (cid:2) Tail risk modeling (cid:3)MC required to withstand (cid:3)RW adverse scenarios (3) Risk factor distribution Understand impact of (cid:2) Relationship between (cid:3)RW market movements on each risk factor company financials (4) Strategic asset allocation Determine optimal asset (cid:2) Realistic assumption / (cid:3)RW strategies based on distribution asset/liability portfolio (cid:2) Alignment with risk metrics 17 Components of ESG model P.9 18 Core components of ESG + Mathematical modelling: ESG Software – Research, develop, and maintain state of the art mathematical models – Deliver these in an efficient, flexible, and user friendly format + Financial economic expertise and research: Model Calibration – Market Consistent: Set up models to replicate observable market prices – Real World: Set up models so that they produce realistic asset return behaviour + Documentation – Communications and validation of results are important too! 19 Typical ESG modeling process Calibration Content ESG - Calculation Engine Output scenarios Mathematical models Generate model parameters ESG/WSG specific to £65m application and market Market or conditions (cid:4)r (cid:7)(cid:9)(cid:2)m(cid:6)r(t)(cid:3)(cid:4)t(cid:5)(cid:8)(cid:4)Z (t) 1 1 1 historical A series of mathematical models data implemented in software (cid:4)r (cid:7)(cid:9)(cid:2)m(cid:6)r(t)(cid:3)(cid:4)t(cid:5)(cid:8)(cid:4)Z (t) 1 1 1 Documentation covering the whole process P.10 20