Modeling Partial Greeks of Variable Annuities with Dependence
|
|
- Percival Montgomery
- 5 years ago
- Views:
Transcription
1 Modeling Partial Greeks of Variable Annuities with Dependence Emiliano A. Valdez joint work with Guojun Gan University of Connecticut Recent Developments in Dependence Modeling with Applications in Finance and Insurance The Island of Aegina, Greece 12 May 2017 Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
2 Outline of work This presentation is based on a collection of work: G. Gan and E.A. Valdez, Regression Modeling for the Valuation of Large Variable Annuity Portfolios, 2016, submitted to North American Actuarial Journal G. Gan and E.A. Valdez, An Empirical Comparison of Some Experimental Designs for the Valuation of Large Variable Annuity Portfolios, 2016, Dependence Modeling G. Gan and E.A. Valdez, Modeling Partial Greeks of Variable Annuities with Dependence, 2017, submitted in Insurance: Mathematics and Economics This collection of work tackles the issues related to efficient valuation of large variable annuity portfolios: valuation of VA products present some computational challenges Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
3 What is a variable annuity? A variable annuity is a retirement product, offered by an insurance company, that gives you the option to select from a variety of investment funds and then pays you retirement income, the amount of which will depend on the investment performance of funds you choose. Premiums Policyholder Guarantee Payments Separate Account Charges Withdrawals/ Payments General Account Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
4 Variable annuities come with guarantees GMxB GMDB GMLB GMIB GMMB GMWB Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
5 Insurance companies have to make guarantee payments under bad market conditions Example (An immediate variable annuity with GMWB) Total investment and initial benefits base: $100,000 Maximum annual withdrawal: $8,000 Policy Year INV Return Fund Before WD Annual WD Fund After WD Remaining Benefit Guarantee CF 1-10% 90,000 8,000 82,000 92, % 90,200 8,000 82,200 84, % 57,540 8,000 49,540 76, % 34,678 8,000 26,678 68, % 24,010 8,000 16,010 60, % 14,409 8,000 6,409 52, % 7,050 8, , r 0 8, ,000 8, r 0 8, ,000 8, r 0 4, ,000 Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
6 Dynamic hedging Dynamic hedging is a popular approach to mitigate the financial risk, but Dynamic hedging requires calculating the dollar Deltas of a portfolio of variable annuity policies within a short time interval The value of the guarantees cannot be determined by closed-form formula The Monte Carlo simulation model is time-consuming Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
7 Use of Monte Carlo method Using the Monte Carlo method to value large variable annuity portfolios is time-consuming: Example (Valuing a portfolio of 100,000 policies) 1,000 risk neutral scenarios 360 monthly time steps 100, 000 1, = ! projections = 50 hours! 200, 000 projections/second Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
8 A portfolio of synthetic variable annuity policies Feature Value Policyholder birth date [1/1/1950, 1/1/1980] Issue date [1/1/2000, 1/1/2014] Valuation date 1/1/2014 Maturity [15, 30] years Account value [50000, ] Female percent 40% Product type DBRP, DBRU, WB, WBSU, MB (20% of each type) Fund fee 30, 50, 60, 80, 10, 38, 45, 55, 57, 46bps for Funds 1 to 10, respectively Base fee Rider fee Number of funds invested [1, 10] 200 bps 20, 50, 60, 50, 50bps for DBRP, DBRU, WB, WBSU, MB, respectively Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
9 Summary statistics of selected variables Categorical Variables Category Count gender Female 4071 Male 5929 prodtype DBRP 2028 DBRU 2018 MB 1959 WB 1991 WBSU 2004 Continuous Variables Minimum Mean Maximum gmdbamt gmwbamt gmwbbalance gmmbamt withdrawal FundValue FundValue FundValue FundValue FundValue FundValue FundValue FundValue FundValue FundValue age ttm Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
10 Metamodeling A metamodel, also a surrogate model, is a model of another model. Metamodeling has been applied to address the computational problems arising from valuation of variable annuity portfolios: a number of work published by co-author G. Gan. It involves four steps: Select representative VA policies Value representative VA policies Build a metamodel Use the metamodel Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
11 Kriging has been used to build metamodels, but it assumes normality Frequency Fair Market Values (in thousands) Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
12 Use of GB2 distribution GB2 provides a flexible family of distributions to model skewed data: f(z) = Z = Y + c (1) a ( z ) ap 1 [ ( z ) a ] p q 1 +, bb(p, q) b b z > 0, (2) ) E[Z] = bb ( p + 1 a, q 1 a B(p, q), p < 1 < q. (3) a We chose to incorporate covariates through the scale parameter b(z i ) = exp(z i β). MLE is used to estimate parameters and multi-stage optimization approach is used to find optimum parameters. Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
13 Accuracy of the GB2 model and the kriging model with different number of representative VA contracts s = 220 s = 440 s = 880 GB2 Kriging GB2 Kriging GB2 Kriging P E (0.0018) (0.0120) (0.0123) (0.0258) R AAP E Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
14 FMV(Kriging) FMV(GB2) Scatter plots of the given fair market values and predicted fair market values when s = FMV(MC) FMV(MC) (a) (b) Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
15 Kriging GB QQ plots of the given fair market values and predicted fair market values when s = Empirical Empirical (a) Gan/Valdez (U. of Connecticut) 50 (b) Dependence Modeling Workshop May / 32
16 Choosing for the optimal experimental design method An important step in the metamodeling process is the selection of representative policies. We compared five different approaches to experimental designs: The random sampling method (RS) The low-discrepancy sequence method (LDS) The data clustering method (DC) The Latin hypercube sampling method (LHS) The conditional Latin hypercube sampling method (clhs) Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
17 Comparing the accuracy and speed RS LDS DC LHS clhs P E 0.16 (0.34) 0.39 (0.49) 0.02 (0.05) 0.14 (0.4) (0.03) R (0.25) (1.06) 0.63 (0.02) 0.26 (0.58) 0.61 (0.03) AAP E 7.58 (3.23) 8.95 (5.73) 3 (0.54) 7.56 (4.44) 2.6 (0.18) Runtime (0.66) (1.28) (59.28) (0.34) (1.73) Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
18 RS LDS DC LHS clhs (a) P E RS LDS DC LHS clhs (b) R RS LDS DC LHS clhs RS LDS DC LHS clhs (c) AAP E (d) Runtime Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
19 Examining the effect of dependence on partial greeks We refer to Greeks as the sensitivities of the VA guaranteed values on major market indices. For h = 1, 2,..., 5, the partial dollar delta of a VA contract on the hth market index is calculated as Delta(h) = F MV (AV 1,, AV h 1, 1.01AV h, AV h+1,, AV 5 ) 0.02 F MV (AV 1,, AV h 1, 0.99AV h, AV h+1,, AV 5 ), 0.02 where AV h is the partial account value on the hth index and F MV ( ) denotes the fair market value calculated by Monte Carlo simulation. The shock size we used is 1% of the partial account value. Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
20 Summary statistics on the five indices Account Values of the five indices Variable Description Min Mean Max AV1 Account value of index AV2 Account value of index AV3 Account value of index AV4 Account value of index AV5 Account value of index Partial dollar deltas on market indices Variable Description Min Mean Max Delta1 On large cap (205,141.33) (13,215.66) 0 Delta2 On small cap (193,899.27) (8,670.87) 0 Delta3 On international equity (386,730.84) (9,616.43) 0 Delta4 On government bond (286,365.30) (8,994.71) 0 Delta5 On money market (412,226.54) (7,068.12) 0 Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
21 Description and summary of the predictor variables Categorical variables Variable Description Count by Category gender Gender of the policyholder F:4071, M:5929 producttype Product type of the VA contract DBRP:2028, DBRU:2018, MB:1959, WB:1991, WBSU:2004 Continuous variables with the original funds Variable Description Min Mean Max gmdbamt GMDB amount gmwbamt GMWB amount gmwbbalance GMWB balance gmmbamt GMMB amount FundValue1 Account value of fund FundValue2 Account value of fund FundValue3 Account value of fund FundValue4 Account value of fund FundValue5 Account value of fund FundValue6 Account value of fund FundValue7 Account value of fund FundValue8 Account value of fund FundValue9 Account value of fund FundValue10 Account value of fund age Age of the policyholder ttm Time to maturity in years Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
22 Scatter plots of dollar deltas - in thousands Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
23 Model specification and comparison measures Marginals: Gamma (conditional on non-zero, negative) Copulas: Independent, Gaussian, t copula, Gumbel and Clayton Validation Measures: n i=1 Percentage Error: P E h = (ŷ ih y ih ) n i=1 y ih Model producing a PE closer to zero is better. Mean Squared Error :MSE h = 1 n n i=1 (ŷ ih y ih ) 2 Model that produces a lower MSE is better. Concordance Correlation Coefficient: CCC h = Model that produces a higher CCC is better. 2ρσ 1 σ 2 σ σ2 2 + (µ 1 µ 2 ) 2 Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
24 Dependence parameter estimates Estimated dependence of the fitted copulas when s = 320 Normal t Gumbel Clayton Estimated ρ=0.783 ρ=0.850 α=2.038 α=0.979 Parameters df =3.340 Cramer-von Mises test statistics of copula models when s = 320 Normal t Gumbel Clayton S n Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
25 Numerical results when s = 320 Independence copula Delta1 Delta2 Delta3 Delta4 Delta5 PE MSE CCC t copula Delta1 Delta2 Delta3 Delta4 Delta5 PE MSE CCC Gumbel copula Delta1 Delta2 Delta3 Delta4 Delta5 PE MSE CCC Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
26 QQ plots: Monte Carlo vs independence copula when s = 320 Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
27 QQ plots: Monte Carlo vs t copula when s = 320 Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
28 QQ plots: Monte Carlo vs Gumbel copula when s = 320 Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
29 Impact of changing the portfolio compositions Feature Value Policyholder birth date [1/1/1950, 1/1/1980] Issue date [1/1/2000, 1/1/2014] Valuation date 1/1/2014 Maturity [15, 30] years Account value [50000, ] Female percent 40% Product type 20% DBRP, 10% MB, 20% WB, 50% WBSU Fund fee 30, 50, 60, 80, 10, 38, 45, 55, 57, 46bps for Funds 1 to 10, respectively Base fee Rider fee Number of funds invested [1,10] 200 bps 20, 50, 60, 50, 50bps for DBRP, DBRU, WB, WBSU, MB, respectively Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
30 Numerical results when s = 320 Independence copula Delta1 Delta2 Delta3 Delta4 Delta5 PE MSE CCC t copula Delta1 Delta2 Delta3 Delta4 Delta5 PE MSE CCC Gumbel copula Delta1 Delta2 Delta3 Delta4 Delta5 PE MSE CCC Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
31 QQ plots: Monte Carlo vs t copula when s = 320 Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
32 Acknowledgment Guojun and I want to thank the Society of Actuaries through the CKER Individual Grant for supporting this research. Gan/Valdez (U. of Connecticut) Dependence Modeling Workshop May / 32
Efficient Valuation of Large Variable Annuity Portfolios
Efficient Valuation of Large Variable Annuity Portfolios Emiliano A. Valdez joint work with Guojun Gan University of Connecticut Seminar Talk at Wisconsin School of Business University of Wisconsin Madison,
More informationEfficient Valuation of Large Variable Annuity Portfolios
Efficient Valuation of Large Variable Annuity Portfolios Emiliano A. Valdez joint work with Guojun Gan University of Connecticut Seminar Talk at Hanyang University Seoul, Korea 13 May 2017 Gan/Valdez (U.
More informationValuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Benchmark Datasets
Valuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Benchmark Datasets Guojun Gan and Emiliano Valdez Department of Mathematics University of Connecticut Storrs CT USA ASTIN/AFIR
More informationValuation of Large Variable Annuity Portfolios using Linear Models with Interactions
Article Valuation of Large Variable Annuity Portfolios using Linear Models with Interactions Guojun Gan Department of Mathematics, University of Connecticut. Email: guojun.gan@uconn.edu; Tel.: +1-860-486-3919
More informationNested Stochastic Valuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Synthetic Datasets
Nested Stochastic Valuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Synthetic Datasets Guoun Gan a, Emiliano A. Valdez a a Department of Mathematics, University of Connecticut,
More informationEfficient Greek Calculation of Variable Annuity Portfolios for Dynamic Hedging: A Two-Level Metamodeling Approach
North American Actuarial Journal ISSN: 1092-0277 (Print) 2325-0453 (Online) Journal homepage: http://www.tandfonline.com/loi/uaaj20 Efficient Greek Calculation of Variable Annuity Portfolios for Dynamic
More informationValuation of large variable annuity portfolios: Monte Carlo simulation and synthetic datasets
Depend. Model. 2017; 5:354 374 Research Article Open Access Guoun Gan* and Emiliano A. Valdez Valuation of large variable annuity portfolios: Monte Carlo simulation and synthetic datasets https://doi.org/10.1515/demo-2017-0021
More informationMultivariate longitudinal data analysis for actuarial applications
Multivariate longitudinal data analysis for actuarial applications Priyantha Kumara and Emiliano A. Valdez astin/afir/iaals Mexico Colloquia 2012 Mexico City, Mexico, 1-4 October 2012 P. Kumara and E.A.
More informationEfficient Nested Simulation for CTE of Variable Annuities
Ou (Jessica) Dang jessica.dang@uwaterloo.ca Dept. Statistics and Actuarial Science University of Waterloo Efficient Nested Simulation for CTE of Variable Annuities Joint work with Dr. Mingbin (Ben) Feng
More informationThe Impact of Clustering Method for Pricing a Large Portfolio of VA Policies. Zhenni Tan. A research paper presented to the. University of Waterloo
The Impact of Clustering Method for Pricing a Large Portfolio of VA Policies By Zhenni Tan A research paper presented to the University of Waterloo In partial fulfillment of the requirements for the degree
More informationWHITE PAPER THINKING FORWARD ABOUT PRICING AND HEDGING VARIABLE ANNUITIES
WHITE PAPER THINKING FORWARD ABOUT PRICING AND HEDGING VARIABLE ANNUITIES We can t solve problems by using the same kind of thinking we used when we created them. Albert Einstein As difficult as the recent
More informationMarket Risk Analysis Volume IV. Value-at-Risk Models
Market Risk Analysis Volume IV Value-at-Risk Models Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume IV xiii xvi xxi xxv xxix IV.l Value
More informationStatistical Analysis of Life Insurance Policy Termination and Survivorship
Statistical Analysis of Life Insurance Policy Termination and Survivorship Emiliano A. Valdez, PhD, FSA Michigan State University joint work with J. Vadiveloo and U. Dias Sunway University, Malaysia Kuala
More informationReal-time Valuation of Large Variable Annuity Portfolios: A Green Mesh Approach
Real-time Valuation of Large Variable Annuity Portfolios: A Green Mesh Approach Kai Liu k26liu@uwaterloo.ca Ken Seng Tan kstan@uwaterloo.ca Department of Statistics and Actuarial Science University of
More informationFinancial Risk Management for the Life Insurance / Wealth Management Industry. Wade Matterson
Financial Risk Management for the Life Insurance / Wealth Management Industry Wade Matterson Agenda 1. Introduction 2. Products with Guarantees 3. Understanding & Managing the Risks INTRODUCTION The Argument
More informationInsights. Variable Annuity Hedging Practices in North America Selected Results From the 2011 Towers Watson Variable Annuity Hedging Survey
Insights October 2011 Variable Annuity Hedging Practices in North America Selected Results From the 2011 Towers Watson Variable Annuity Hedging Survey Introduction Hedging programs have risen to prominence
More informationFinancial Modeling of Variable Annuities
0 Financial Modeling of Variable Annuities Robert Chen 18 26 June, 2007 1 Agenda Building blocks of a variable annuity model A Stochastic within Stochastic Model Rational policyholder behaviour Discussion
More informationProceedings of the 2015 Winter Simulation Conference L. Yilmaz, W. K. V. Chan, I. Moon, T. M. K. Roeder, C. Macal, and M. D. Rossetti, eds.
Proceedings of the 2015 Winter Simulation Conference L Yilmaz, W K V Chan, I Moon, T M K Roeder, C Macal, and M D Rossetti, eds APPLICATION OF METAMODELING TO THE VALUATION OF LARGE VARIABLE ANNUITY PORTFOLIOS
More informationVariable Annuities with fees tied to VIX
Variable Annuities with fees tied to VIX Carole Bernard Accounting, Law and Finance Grenoble Ecole de Management Junsen Tang Statistics and Actuarial Science University of Waterloo June 13, 2016, preliminary
More informationLecture 1 of 4-part series. Spring School on Risk Management, Insurance and Finance European University at St. Petersburg, Russia.
Principles and Lecture 1 of 4-part series Spring School on Risk, Insurance and Finance European University at St. Petersburg, Russia 2-4 April 2012 s University of Connecticut, USA page 1 s Outline 1 2
More informationModeling. joint work with Jed Frees, U of Wisconsin - Madison. Travelers PASG (Predictive Analytics Study Group) Seminar Tuesday, 12 April 2016
joint work with Jed Frees, U of Wisconsin - Madison Travelers PASG (Predictive Analytics Study Group) Seminar Tuesday, 12 April 2016 claim Department of Mathematics University of Connecticut Storrs, Connecticut
More informationVALUATION OF VARIABLE ANNUITIES USING GRID COMPUTING AXA LIFE EUROPE HEDGING SERVICES (ALEHS) 05/06/2008
VALUATION OF VARIABLE ANNUITIES USING GRID COMPUTING AXA LIFE EUROPE HEDGING SERVICES (ALEHS) 05/06/2008 Structure Variable annuities ALEHS liability valuation software (MoSes. Tower Perrin) The run time
More informationStochastic Modeling Concerns and RBC C3 Phase 2 Issues
Stochastic Modeling Concerns and RBC C3 Phase 2 Issues ACSW Fall Meeting San Antonio Jason Kehrberg, FSA, MAAA Friday, November 12, 2004 10:00-10:50 AM Outline Stochastic modeling concerns Background,
More informationQuantitative Finance Investment Advanced Exam
Quantitative Finance Investment Advanced Exam Important Exam Information: Exam Registration Order Study Notes Introductory Study Note Case Study Past Exams Updates Formula Package Table Candidates may
More informationBASIS RISK AND SEGREGATED FUNDS
BASIS RISK AND SEGREGATED FUNDS Capital oversight of financial institutions June 2017 June 2017 1 INTRODUCTION The view expressed in this presentation are those of the author. No responsibility for them
More informationMachine Learning for Quantitative Finance
Machine Learning for Quantitative Finance Fast derivative pricing Sofie Reyners Joint work with Jan De Spiegeleer, Dilip Madan and Wim Schoutens Derivative pricing is time-consuming... Vanilla option pricing
More information2016 Variable Annuity Guaranteed Benefits Survey Survey of Assumptions for Policyholder Behavior in the Tail
2016 Variable Annuity Guaranteed Benefits Survey Survey of Assumptions for Policyholder Behavior in the Tail October 2016 2 2016 Variable Annuity Guaranteed Benefits Survey Survey of Assumptions for Policyholder
More informationNatural Balance Sheet Hedge of Equity Indexed Annuities
Natural Balance Sheet Hedge of Equity Indexed Annuities Carole Bernard (University of Waterloo) & Phelim Boyle (Wilfrid Laurier University) WRIEC, Singapore. Carole Bernard Natural Balance Sheet Hedge
More information**BEGINNING OF EXAMINATION** A random sample of five observations from a population is:
**BEGINNING OF EXAMINATION** 1. You are given: (i) A random sample of five observations from a population is: 0.2 0.7 0.9 1.1 1.3 (ii) You use the Kolmogorov-Smirnov test for testing the null hypothesis,
More informationA Data Mining Framework for Valuing Large Portfolios of Variable Annuities
A Data Mining Framework for Valuing Large Portfolios of Variable Annuities ABSTRACT Guojun Gan Department of Mathematics University of Connecticut 34 Manseld Road Storrs, CT 06269-009, USA guojungan@uconnedu
More informationINSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS. 20 th May Subject CT3 Probability & Mathematical Statistics
INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 20 th May 2013 Subject CT3 Probability & Mathematical Statistics Time allowed: Three Hours (10.00 13.00) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1.
More informationTwo hours. To be supplied by the Examinations Office: Mathematical Formula Tables and Statistical Tables THE UNIVERSITY OF MANCHESTER
Two hours MATH20802 To be supplied by the Examinations Office: Mathematical Formula Tables and Statistical Tables THE UNIVERSITY OF MANCHESTER STATISTICAL METHODS Answer any FOUR of the SIX questions.
More informationRisk analysis of annuity conversion options in a stochastic mortality environment
Risk analysis of annuity conversion options in a stochastic mortality environment Joint work with Alexander Kling and Jochen Russ Research Training Group 1100 Katja Schilling August 3, 2012 Page 2 Risk
More informationLoss Simulation Model Testing and Enhancement
Loss Simulation Model Testing and Enhancement Casualty Loss Reserve Seminar By Kailan Shang Sept. 2011 Agenda Research Overview Model Testing Real Data Model Enhancement Further Development Enterprise
More informationA Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities
http://www.aimspress.com/journal/qfe QFE, 1(2): 125 144 DOI:10.3934/QFE.2017.2.125 Received date: 29 April 2017 Accepted date: 13 June 2017 Published date: 14 July 2017 Research article A Spatial Interpolation
More informationThe data-driven COS method
The data-driven COS method Á. Leitao, C. W. Oosterlee, L. Ortiz-Gracia and S. M. Bohte Delft University of Technology - Centrum Wiskunde & Informatica Reading group, March 13, 2017 Reading group, March
More informationDynamic Response of Jackup Units Re-evaluation of SNAME 5-5A Four Methods
ISOPE 2010 Conference Beijing, China 24 June 2010 Dynamic Response of Jackup Units Re-evaluation of SNAME 5-5A Four Methods Xi Ying Zhang, Zhi Ping Cheng, Jer-Fang Wu and Chee Chow Kei ABS 1 Main Contents
More informationSession 76 PD, Modeling Indexed Products. Moderator: Leonid Shteyman, FSA. Presenters: Trevor D. Huseman, FSA, MAAA Leonid Shteyman, FSA
Session 76 PD, Modeling Indexed Products Moderator: Leonid Shteyman, FSA Presenters: Trevor D. Huseman, FSA, MAAA Leonid Shteyman, FSA Modeling Indexed Products Trevor Huseman, FSA, MAAA Managing Director
More informationSession 7 PD Pricing Risk Management
Session 7 PD Pricing Risk Management Society of Actuaries Spring Meeting Washington, DC May 29, 2003 10:30 AM 12 PM Session 7 PD Pricing Risk Management Keith A. Dall Todd Henderson Douglas L. Robbins
More informationINTEREST RATES AND FX MODELS
INTEREST RATES AND FX MODELS 7. Risk Management Andrew Lesniewski Courant Institute of Mathematical Sciences New York University New York March 8, 2012 2 Interest Rates & FX Models Contents 1 Introduction
More informationSOCIETY OF ACTUARIES Exam FETE Financial Economic Theory and Engineering Exam (Finance/ERM/Investment) Exam FETE MORNING SESSION
SOCIETY OF ACTUARIES Exam FETE Financial Economic Theory and Engineering Exam (Finance/ERM/Investment) Exam FETE MORNING SESSION Date: Thursday, April 26, 2012 Time: 8:30 a.m. 11:45 a.m. INSTRUCTIONS TO
More informationMarket Risk: FROM VALUE AT RISK TO STRESS TESTING. Agenda. Agenda (Cont.) Traditional Measures of Market Risk
Market Risk: FROM VALUE AT RISK TO STRESS TESTING Agenda The Notional Amount Approach Price Sensitivity Measure for Derivatives Weakness of the Greek Measure Define Value at Risk 1 Day to VaR to 10 Day
More informationJaime Frade Dr. Niu Interest rate modeling
Interest rate modeling Abstract In this paper, three models were used to forecast short term interest rates for the 3 month LIBOR. Each of the models, regression time series, GARCH, and Cox, Ingersoll,
More informationHedging insurance products combines elements of both actuarial science and quantitative finance.
Guaranteed Benefits Financial Math Seminar January 30th, 2008 Andrea Shaeffer, CQF Sr. Analyst Nationwide Financial Dept. of Quantitative Risk Management shaeffa@nationwide.com (614) 677-4994 Hedging Guarantees
More informationMathematics of Finance Final Preparation December 19. To be thoroughly prepared for the final exam, you should
Mathematics of Finance Final Preparation December 19 To be thoroughly prepared for the final exam, you should 1. know how to do the homework problems. 2. be able to provide (correct and complete!) definitions
More informationarxiv: v1 [q-fin.cp] 6 Oct 2016
Efficient Valuation of SCR via a Neural Network Approach Seyed Amir Hejazi a, Kenneth R. Jackson a arxiv:1610.01946v1 [q-fin.cp] 6 Oct 2016 a Department of Computer Science, University of Toronto, Toronto,
More informationMFE/3F Questions Answer Key
MFE/3F Questions Download free full solutions from www.actuarialbrew.com, or purchase a hard copy from www.actexmadriver.com, or www.actuarialbookstore.com. Chapter 1 Put-Call Parity and Replication 1.01
More informationSOCIETY OF ACTUARIES Enterprise Risk Management Investment Extension Exam ERM-INV
SOCIETY OF ACTUARIES Exam ERM-INV Date: Tuesday, October 7, 015 Time: 8:30 a.m. 1:45 p.m. INSTRUCTIONS TO CANDIDATES General Instructions 1. This examination has a total of 80 points. This exam consists
More information2. Copula Methods Background
1. Introduction Stock futures markets provide a channel for stock holders potentially transfer risks. Effectiveness of such a hedging strategy relies heavily on the accuracy of hedge ratio estimation.
More informationMarket risk measurement in practice
Lecture notes on risk management, public policy, and the financial system Allan M. Malz Columbia University 2018 Allan M. Malz Last updated: October 23, 2018 2/32 Outline Nonlinearity in market risk Market
More informationIn physics and engineering education, Fermi problems
A THOUGHT ON FERMI PROBLEMS FOR ACTUARIES By Runhuan Feng In physics and engineering education, Fermi problems are named after the physicist Enrico Fermi who was known for his ability to make good approximate
More informationAsymmetric Price Transmission: A Copula Approach
Asymmetric Price Transmission: A Copula Approach Feng Qiu University of Alberta Barry Goodwin North Carolina State University August, 212 Prepared for the AAEA meeting in Seattle Outline Asymmetric price
More informationKing s College London
King s College London University Of London This paper is part of an examination of the College counting towards the award of a degree. Examinations are governed by the College Regulations under the authority
More informationThe data-driven COS method
The data-driven COS method Á. Leitao, C. W. Oosterlee, L. Ortiz-Gracia and S. M. Bohte Delft University of Technology - Centrum Wiskunde & Informatica CMMSE 2017, July 6, 2017 Álvaro Leitao (CWI & TUDelft)
More informationAsset Allocation Model with Tail Risk Parity
Proceedings of the Asia Pacific Industrial Engineering & Management Systems Conference 2017 Asset Allocation Model with Tail Risk Parity Hirotaka Kato Graduate School of Science and Technology Keio University,
More informationImplementing Risk Appetite for Variable Annuities
Implementing Risk Appetite for Variable Annuities Nick Jacobi, FSA, CERA Presented at the: 2011 Enterprise Risk Management Symposium Society of Actuaries March 14-16, 2011 Copyright 2011 by the Society
More informationMarket Risk Analysis Volume II. Practical Financial Econometrics
Market Risk Analysis Volume II Practical Financial Econometrics Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume II xiii xvii xx xxii xxvi
More information2.1 Mathematical Basis: Risk-Neutral Pricing
Chapter Monte-Carlo Simulation.1 Mathematical Basis: Risk-Neutral Pricing Suppose that F T is the payoff at T for a European-type derivative f. Then the price at times t before T is given by f t = e r(t
More informationAccelerated Option Pricing Multiple Scenarios
Accelerated Option Pricing in Multiple Scenarios 04.07.2008 Stefan Dirnstorfer (stefan@thetaris.com) Andreas J. Grau (grau@thetaris.com) 1 Abstract This paper covers a massive acceleration of Monte-Carlo
More informationEuropean option pricing under parameter uncertainty
European option pricing under parameter uncertainty Martin Jönsson (joint work with Samuel Cohen) University of Oxford Workshop on BSDEs, SPDEs and their Applications July 4, 2017 Introduction 2/29 Introduction
More informationGamma. The finite-difference formula for gamma is
Gamma The finite-difference formula for gamma is [ P (S + ɛ) 2 P (S) + P (S ɛ) e rτ E ɛ 2 ]. For a correlation option with multiple underlying assets, the finite-difference formula for the cross gammas
More informationPractical example of an Economic Scenario Generator
Practical example of an Economic Scenario Generator Martin Schenk Actuarial & Insurance Solutions SAV 7 March 2014 Agenda Introduction Deterministic vs. stochastic approach Mathematical model Application
More informationBloomberg. Portfolio Value-at-Risk. Sridhar Gollamudi & Bryan Weber. September 22, Version 1.0
Portfolio Value-at-Risk Sridhar Gollamudi & Bryan Weber September 22, 2011 Version 1.0 Table of Contents 1 Portfolio Value-at-Risk 2 2 Fundamental Factor Models 3 3 Valuation methodology 5 3.1 Linear factor
More informationMarket Risk Life Insurers Compared to Banks Rob Daly & Anton Kapel
Market Risk Life Insurers Compared to Banks Rob Daly & Anton Kapel Copyright 2006, the Tillinghast business of Towers Perrin. All rights reserved. A licence to publish is granted to the Institute of Actuaries
More informationifa Institut für Finanz- und Aktuarwissenschaften
The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Variable Annuity Guarantees Alexander Kling, Frederik Ruez, and Jochen Ruß Helmholtzstraße 22 D-89081 Ulm phone +49 (731)
More informationCredit Risk Summit Europe
Fast Analytic Techniques for Pricing Synthetic CDOs Credit Risk Summit Europe 3 October 2004 Jean-Paul Laurent Professor, ISFA Actuarial School, University of Lyon & Scientific Consultant, BNP-Paribas
More informationDynamic Replication of Non-Maturing Assets and Liabilities
Dynamic Replication of Non-Maturing Assets and Liabilities Michael Schürle Institute for Operations Research and Computational Finance, University of St. Gallen, Bodanstr. 6, CH-9000 St. Gallen, Switzerland
More informationTests for Intraclass Correlation
Chapter 810 Tests for Intraclass Correlation Introduction The intraclass correlation coefficient is often used as an index of reliability in a measurement study. In these studies, there are K observations
More informationarxiv: v2 [q-fin.pr] 11 May 2017
A note on the impact of management fees on the pricing of variable annuity guarantees Jin Sun a,b,, Pavel V. Shevchenko c, Man Chung Fung b a Faculty of Sciences, University of Technology Sydney, Australia
More informationPricing Dynamic Guaranteed Funds Under a Double Exponential. Jump Diffusion Process. Chuang-Chang Chang, Ya-Hui Lien and Min-Hung Tsay
Pricing Dynamic Guaranteed Funds Under a Double Exponential Jump Diffusion Process Chuang-Chang Chang, Ya-Hui Lien and Min-Hung Tsay ABSTRACT This paper complements the extant literature to evaluate the
More informationProxy Function Fitting: Some Implementation Topics
OCTOBER 2013 ENTERPRISE RISK SOLUTIONS RESEARCH OCTOBER 2013 Proxy Function Fitting: Some Implementation Topics Gavin Conn FFA Moody's Analytics Research Contact Us Americas +1.212.553.1658 clientservices@moodys.com
More informationBusiness Statistics: A First Course
Business Statistics: A First Course Fifth Edition Chapter 12 Correlation and Simple Linear Regression Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc. Chap 12-1 Learning Objectives In this
More informationA Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities
A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities Seyed Amir Hejazi a, Kenneth R. Jackson a, Guojun Gan b a Department of Computer Science, University
More informationVariable Annuity Market Trends. Presented by : Ken Mungan, FSA, MAAA Financial Risk Management, Practice Leader
Variable Annuity Market Trends Presented by : Ken Mungan, FSA, MAAA Financial Risk Management, Practice Leader Agenda Current Market Update Industry issues Product trends Risk management trends Low interest
More informationMaster Thesis. Variable Annuities. by Tatevik Hakobyan. Supervisor: Prof. Dr. Michael Koller
Master Thesis Variable Annuities by Tatevik Hakobyan Supervisor: Prof. Dr. Michael Koller Department of Mathematics Swiss Federal Institute of Technology (ETH) Zurich August 01, 2013 Acknowledgments I
More informationInternet Appendix for Asymmetry in Stock Comovements: An Entropy Approach
Internet Appendix for Asymmetry in Stock Comovements: An Entropy Approach Lei Jiang Tsinghua University Ke Wu Renmin University of China Guofu Zhou Washington University in St. Louis August 2017 Jiang,
More informationMultilevel Monte Carlo for Basket Options
MLMC for basket options p. 1/26 Multilevel Monte Carlo for Basket Options Mike Giles mike.giles@maths.ox.ac.uk Oxford University Mathematical Institute Oxford-Man Institute of Quantitative Finance WSC09,
More informationERM. Variable Annuities. Aymeric KALIFE, Head of Savings & Variable Annuities Group Risk Management, AXA GIE
ERM Variable Annuities 2017 1 Aymeric KALIFE, Head of Savings & Variable Annuities Group Risk Management, AXA GIE Recent VA market trends In the U.S. insurance issued annuity products are the main vehicle
More informationMonte Carlo Methods in Financial Engineering
Paul Glassennan Monte Carlo Methods in Financial Engineering With 99 Figures
More informationOptimal Search for Parameters in Monte Carlo Simulation for Derivative Pricing
Optimal Search for Parameters in Monte Carlo Simulation for Derivative Pricing Prof. Chuan-Ju Wang Department of Computer Science University of Taipei Joint work with Prof. Ming-Yang Kao March 28, 2014
More informationSOLUTIONS 913,
Illinois State University, Mathematics 483, Fall 2014 Test No. 3, Tuesday, December 2, 2014 SOLUTIONS 1. Spring 2013 Casualty Actuarial Society Course 9 Examination, Problem No. 7 Given the following information
More informationσ e, which will be large when prediction errors are Linear regression model
Linear regression model we assume that two quantitative variables, x and y, are linearly related; that is, the population of (x, y) pairs are related by an ideal population regression line y = α + βx +
More informationDiploma in Financial Management with Public Finance
Diploma in Financial Management with Public Finance Cohort: DFM/09/FT Jan Intake Examinations for 2009 Semester II MODULE: STATISTICS FOR FINANCE MODULE CODE: QUAN 1103 Duration: 2 Hours Reading time:
More informationINSTITUTE AND FACULTY OF ACTUARIES. Curriculum 2019 SPECIMEN EXAMINATION
INSTITUTE AND FACULTY OF ACTUARIES Curriculum 2019 SPECIMEN EXAMINATION Subject CS1A Actuarial Statistics Time allowed: Three hours and fifteen minutes INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate
More informationSOCIETY OF ACTUARIES Quantitative Finance and Investment Advanced Exam Exam QFIADV AFTERNOON SESSION
SOCIETY OF ACTUARIES Exam Exam QFIADV AFTERNOON SESSION Date: Thursday, April 27, 2017 Time: 1:30 p.m. 3:45 p.m. INSTRUCTIONS TO CANDIDATES General Instructions 1. This afternoon session consists of 6
More informationMFE/3F Questions Answer Key
MFE/3F Questions Download free full solutions from www.actuarialbrew.com, or purchase a hard copy from www.actexmadriver.com, or www.actuarialbookstore.com. Chapter 1 Put-Call Parity and Replication 1.01
More informationProxy Techniques for Estimating Variable Annuity Greeks. Presenter(s): Aubrey Clayton, Aaron Guimaraes
Sponsored by and Proxy Techniques for Estimating Variable Annuity Greeks Presenter(s): Aubrey Clayton, Aaron Guimaraes Proxy Techniques for Estimating Variable Annuity Greeks Aubrey Clayton, Moody s Analytics
More informationLecture 6: Non Normal Distributions
Lecture 6: Non Normal Distributions and their Uses in GARCH Modelling Prof. Massimo Guidolin 20192 Financial Econometrics Spring 2015 Overview Non-normalities in (standardized) residuals from asset return
More informationMulti-Curve Pricing of Non-Standard Tenor Vanilla Options in QuantLib. Sebastian Schlenkrich QuantLib User Meeting, Düsseldorf, December 1, 2015
Multi-Curve Pricing of Non-Standard Tenor Vanilla Options in QuantLib Sebastian Schlenkrich QuantLib User Meeting, Düsseldorf, December 1, 2015 d-fine d-fine All rights All rights reserved reserved 0 Swaption
More informationAsymptotic methods in risk management. Advances in Financial Mathematics
Asymptotic methods in risk management Peter Tankov Based on joint work with A. Gulisashvili Advances in Financial Mathematics Paris, January 7 10, 2014 Peter Tankov (Université Paris Diderot) Asymptotic
More informationPortfolio Risk Management and Linear Factor Models
Chapter 9 Portfolio Risk Management and Linear Factor Models 9.1 Portfolio Risk Measures There are many quantities introduced over the years to measure the level of risk that a portfolio carries, and each
More informationSOCIETY OF ACTUARIES Enterprise Risk Management Individual Life & Annuities Extension Exam ERM-ILA
SOCIETY OF ACTUARIES Exam ERM-ILA Date: Tuesday, October 31, 2017 Time: 8:30 a.m. 12:45 p.m. INSTRUCTIONS TO CANDIDATES General Instructions 1. This examination has a total of 80 points. This exam consists
More informationMeasurement of Market Risk
Measurement of Market Risk Market Risk Directional risk Relative value risk Price risk Liquidity risk Type of measurements scenario analysis statistical analysis Scenario Analysis A scenario analysis measures
More informationDATA SUMMARIZATION AND VISUALIZATION
APPENDIX DATA SUMMARIZATION AND VISUALIZATION PART 1 SUMMARIZATION 1: BUILDING BLOCKS OF DATA ANALYSIS 294 PART 2 PART 3 PART 4 VISUALIZATION: GRAPHS AND TABLES FOR SUMMARIZING AND ORGANIZING DATA 296
More informationก ก ก ก ก ก ก. ก (Food Safety Risk Assessment Workshop) 1 : Fundamental ( ก ( NAC 2010)) 2 3 : Excel and Statistics Simulation Software\
ก ก ก ก (Food Safety Risk Assessment Workshop) ก ก ก ก ก ก ก ก 5 1 : Fundamental ( ก 29-30.. 53 ( NAC 2010)) 2 3 : Excel and Statistics Simulation Software\ 1 4 2553 4 5 : Quantitative Risk Modeling Microbial
More informationCombined Accumulation- and Decumulation-Plans with Risk-Controlled Capital Protection
Combined Accumulation- and Decumulation-Plans with Risk-Controlled Capital Protection Peter Albrecht and Carsten Weber University of Mannheim, Chair for Risk Theory, Portfolio Management and Insurance
More informationJUNE 2017 ANNUAL MEETING QUÉBEC CITY (SESSION 42) 1
JUNE 2017 ANNUAL MEETING QUÉBEC CITY (SESSION 42) 1 Session 42: Séance 42 : BASIS RISK EFFECT ON SEGREGATED FUNDS HEDGING IMPACT DU RISQUE DE BASE AU SEIN DE LA COUVERTURE DES FONDS DISTINCTS INTERMÉDIAIRE
More informationApplication of statistical methods in the determination of health loss distribution and health claims behaviour
Mathematical Statistics Stockholm University Application of statistical methods in the determination of health loss distribution and health claims behaviour Vasileios Keisoglou Examensarbete 2005:8 Postal
More informationLecture 3: Probability Distributions (cont d)
EAS31116/B9036: Statistics in Earth & Atmospheric Sciences Lecture 3: Probability Distributions (cont d) Instructor: Prof. Johnny Luo www.sci.ccny.cuny.edu/~luo Dates Topic Reading (Based on the 2 nd Edition
More informationDependent Loss Reserving Using Copulas
Dependent Loss Reserving Using Copulas Peng Shi Northern Illinois University Edward W. Frees University of Wisconsin - Madison July 29, 2010 Abstract Modeling the dependence among multiple loss triangles
More information