EquityBased Insurance Guarantees Conference November 12, New York, NY. Operational Risks


 Tamsin Williams
 1 years ago
 Views:
Transcription
1 EquityBased Insurance Guarantees Conference November , 00 New York, NY Operational Risks Peter Phillips
2 Operational Risk Associated with Running a VA Hedging Program Annuity Solutions Group Aon Benfield Securities, Inc hours November, 00 EBIG Conference November, 00
3 Legal Disclaimer This was prepared for informational purposes only and is intended only for the designated recipient. It is neither intended, nor should be considered, as () an offer to sell, () a solicitation or basis for any contract for purchase of any security, loan or other financial product, (3) an official confirmation, or (4) a statement of Aon Benfield Securities, Inc. or any of their affiliates. With respect to indicative values, no representation is made that any transaction can be effected at the values provided and the values provided are not necessarily the value carried on Aon Benfield Securities, Inc. books and records. The recipient of this document is advised to undertake an independent review of the legal, tax, regulatory, actuarial and accounting implications of any transaction described herein Aon Benfield Securities, Inc. does not provide legal, tax, regulatory, actuarial or accounting opinions. Any offer will be made only through definitive agreements and such other offering materials as provided by Aon Benfield Securities, Inc. or their appropriately licensed affiliate(s) prior to closing which contain important information regarding, among other things, certain risks associated with any transaction described in this document and should be read carefully before determining to enter into such a transaction. November, 00
4 Agenda Section Introduction Section Model Implementation Risks Section 3 Quantifying Greeks Estimation Error Section 4 Intraday Greeks Approximation Risks Section 5 Summary November, 00 3
5 Section : Introduction 4
6 Introduction Running a Variable Annuities hedging program is extremely challenging and prone to serious risks, such as: market risk, strategy risk and operational risk The performance of a hedging program, capital requirements and reserves are highly dependent on the choice of stochastic models that are used to model the Liability We believe that Rho is the largest risk factor by far many VA products, however, some direct writers that hedge their Rho risk are not using a stochastic interest rate model (such as HullWhite F/F model) due to runtime constraints, and as more direct writers use stochastic interest rate models, care must taken to ensure they are properly implemented There are multiple approaches to calculate a pointintime Greeks on a book of business Some companies are not aware of the estimation risk associated with different approaches which in turn can have a potentially important impact on hedge program performance Most companies are not able to calculate book level seriatim Greeks on an intraday basis, and therefore use approximation techniques, such as grid interpolation or Taylor Series expansion ( by using st, nd and some 3 rd order Greeks) These techniques work great when the market goes sideways What happens when the market moves sharply? This presentation will concentrate on some of the operational risks associated with: Implementation risk associated with stochastic interest rate scenario generators Pointintime Greeks estimation risk Intraday Greeks estimation risk for trade decision support November,
7 Section : Model Implementation Risks 6
8 Model Implementation Risks Design Inventory Design choices to make when implementing a Liability model Economic Scenario Generator How do you model bond fund risk? How do you model interest rate risk? How do you model volatility risk? Which calibration technique should you use? Liability Cash Flow Model Time step discretization logic Daily, Monthly or Yearly? How to properly implement stub logic? Mortality model selection Lapse model selection Survivorship model selection Joint Life modeling Cohorting logic and rationale Mixed, single or double precision Stand alone implementation testing of Models Integration testing of the Liability Cash Flow Models and Scenario Generation Models November,
9 Model Implementation Risks Model Description HullWhite TwoFactor Model Description The short interest rate is defined as: r( t) ( t) X ( t) Y ( t) With the two factors X and Y defined by the linear SDE s dx axdt dw ( t) dy bydt dw ( t) W and W define a twodimensional wiener process with correlation: The deterministic function φ is given by: ( T ) dw dw dt at bt at bt e e e e aa bb M f (0, T ) Where f(0,t) is the initial instantaneous forward rate term structure ab November,
10 9 Model Implementation Risks Scenario Generator The scenario generator is constructed by discretizing the solution to the linear SDE s that define X and Y HullWhite TwoFactor Scenario Generation The scenario generator is constructed by discretizing the solution to the linear SDE s that define X and Y Where Δt is the time step and Z and Z are independent standard normal random variables (0,) (0,) ) ( ) ( (0,) ) ( ) ( i i t b i t b i i t a i t a i Z Z e b t Y e t Y Z e a t X e t X Due to runtime constraints an Euler scheme ( st order approximation) is often used. This leads to the simplification: (0,) (0,) ) ( ) ( ) ( (0,) ) ( ) ( ) ( i i i i i i i Z Z t t Y t b t Y Z t t X t a t X November, 00 8
11 Model Implementation Risks Testing of Proper Implementation Probability of Negative Rates The short rate has a normal distribution with mean and variance given by: r ( t) ( t) r ( t) a at bt ( ab) t e e e b This allows for the possibility of negative rates and also serves as a test of the implementation. The probability of negative rates is given by: a b ( t) r r ( t) 0 r ( t) where Φ denotes the standard normal cumulative distribution function. P Aside from the theory one needs to consider in practice what do with negative short rates Use them Set them to a very small number November,
12 Model Implementation Risks Testing of Proper Implementation Plot of Probability of Negative Rates Using the Euler approximation to the SDE s results in a higher probability of negative rates November, 00 0
13 Model Implementation Risks Testing of Proper Implementation Probability Distribution Check The short rate in the HWF model is normally distributed The mean and variance of the short rate can be checked against the theoretical results of the model Discretization errors introduced in simulating the short rate can lead to an incorrect distribution November, 00
14 Model Implementation Risks Discount Factors Discretization Error And The Affect on Discount Factors Often times one is interested in calculating discount factors from the short rate. This involves computing: DF exp t r( u) du 0 The discretization errors introduced by the scenario generator for the short rate are propagated through to the discount factors. Furthermore, additional errors can be introduced by numerically approximating the integral in the expression above. A common approach is to use: Y ( t ) t 0 r ( u ) du i j r ( t ) j t j t j But this can be avoided by simulating paths of the pair {r(t),y(t)} ( )} without discretization error given that, under the HullWhite model, the pair is jointly Gaussian November, 00 3
15 Model Implementation Risks Testing of Proper Implementation Interest Rate Option Monte Carlo Valuation versus HullWhite Closed Form Use Interest Rate Scenario Generator to price European Interest Rate options with known closedform solution HWF parameters Riskfree rate: 5% Volatility: % MeanReversion Strength:.0 European Bond call option Bond notional: $00 Bond maturity: 0 years Strike price: $77 Option Expiry: 5 years Monte Carlo runs 00 paths each November,
16 Model Implementation Risks Conclusion It is not simple as it looks to implement and thoroughly test a stochastic interest rate model Testing for proper model implementation is not the same thing as running model calibration tests When implementing a stochastic interest rate model it is important to validate that the scenario generator leads to results that are consistent with the model, otherwise the pricing of instruments that rely on the output of such scenario engines may be grossly inaccurate The HullWhite model is a simple and well understood model, but there are several ways to implement the model. For example, one can use bond prices, short rates or forward rates in the simulation process There are many parts to a term structure model (interpolation, discretization) and each in turn can have an impact on the validity of the outputs of the model so implementation testing is a must If you are going to use a third party model or use an internal IRSG you should exhaustively check to make sure it has been implemented properly November,
17 Section 3: Quantifying Greeks Estimation Error 6
18 Quantifying Greeks Estimation Error Overview Monte Carlo Simulation Error Greeks drive the trading activity and the risk management strategy of a dynamic hedging program There are no simple closedform solutions for VA Greeks and hence the reliance on Monte Carlo simulation How accurate are these important numbers? What are the different methods to calculate the Greeks for a portfolio of policy holders? How many stochastic paths are required to get acceptable level of convergence? What is the error associated with the estimation for first, second and even third order and cross Greeks? Confidence intervals for Liability models are easy to calculate if you are using the same paths for every policyholder, like where companies load a flat file to feed the scenario generation process in a projection system that is use to calculate the Greeks for a hedge program However many companies use a different seed for each policyholder, because they have stub logic or because they seek rapid convergence for expected values, and finding a confidence interval here becomes a more difficult and complicated process We believe a hedge program manager should know the sampling error for any important Greek in the hedge program The experiments on the following slides are based on: $30Bn of Guaranteed Withdrawal For Life product with million policy holders November,
19 Quantifying Greeks Estimation Error Standard Confidence Interval Book Level Standard Confidence Interval When every policyholder is valued using a common set of scenarios the 95% confidence interval for the FMV is simple to calculate The formula for a confidence interval for a mean is Where Z = Z a/. For example, the value of Z in a 95% confidence interval is.96 because P(Z >.96) = For a 90% confidence interval, Z =.645. Co ount $ Delta in millons for the book using 00 scenarios and same seed Mean 5.39 Std Total $ Delta in Millons November,
20 Quantifying Greeks Estimation Error Using Different Seed for Every Policy Confidence Interval When Using Different Seed for Every Policy If a different seed is used for each policyholder how do you calculate a CI? There are several techniques but we will talk about two techniques today Resampling Well suited technique when the theoretical distribution of a statistic is complicated or unknown It is distributionindependent and is indirect way to asses the properties of the distribution underlying the sample and the statistics of interest Provides us with a way of understanding the consequences of sampling variability for drawing inferences about the population based on our data Care must be taken to do this properly Rerun the valuation process again and again but with different starting seeds for each policyholder A brute force way to understand the variability of your statistics of interest Requires very fast and flexible simulation environment November,
21 Quantifying Greeks Estimation Error Resampled Confidence Interval The Bootstrapping Method Here we resample with replacement from each drawing Now we can obtain fast convergence for an expected result Resampled $ Delta in millons for the book using diffrent seeds Mean 4.94 Std.005 Count $ Delta in Millions November,
22 Quantifying Greeks Estimation Error Brute Force Confidence Interval Resimulating the Greeks 00 times In this case we calculate the expected value of over MM individual policyholders Here we rerun the valuation process 00 times, calculating base, up and down values, or calculating 300 MM expected policyholder values in the process Next we approximate where 95 of the observations are found to estimate the confidence interval Resampled $ Delta in millons for the book using 00 scenarios with diffrent se 300 Count Mean 4.94 Std $ Delta in Millions November, 00 0
23 Quantifying Greeks Estimation Error Summary of Results This table compares the 95% confidence interval for $ Delta Method Mean 95% Confidence Interval Same Seed 00 paths 5,387,378,88,404 Different Seed 00 path Resample 4,943,870 0,64 Different Seed Brute Force 00 samples 4,94,68,36 Deltathe amount the FMV will change for a % move in the market However you are generating your scenarios, and whatever Greeks you are calculating, make sure you think about sampling error If a number is used in a hedging operation chances are it is important, and if it is important, then a confidence interval should be provided with the number It is important to remember that some Greeks have huge sampling errors but are still very important, such as Gamma and other second order Greeks You should measure the accuracy of each one of your Greeks on a regular basis because ) the higher order Greeks are difficult to estimate in practice, ) they can have a large impact intra day trading decisions, and 3) they can change rapidly as markets move November, 00
24 Section 4: Intraday Greeks Approximation Risks 3
25 Intraday Greeks Approximation Risks Overview Most Direct Writers make today s trading decisions using information on the Liability from last night Trading grids are generated via overnight runs using closing values from the day before Hedge Portfolio asset positions and Greeks are updated as the markets change throughout the day, but the Liability value and Greeks, are estimated on a heuristically basis and hence so are net exposures for the hedge program Overnight runs create trading grids, and once combined with some type of interpolation or extrapolation process, are used to reestimate the Liability Greeks during normal market hours The curse of dimensionality and of runtimes limit the number of book level valuations that can be completed in the overnight runs to derive this information or grid The curse of Liability dimensionality is caused by following: Equity sub accounts ( 58 ) + volatility (35) + term structure buckets ( 58) >> 0 dimensions If you pick points for each dimension, the meshgrid would have over million points Chances are you want to calculate Greeks too, so there would many calculation to perform at each one of these million points What is done in practice? Some companies rely on FMV surface and use multidimensional interpolation processes Other companies rely on Taylor Series Expansion A few calculate realtime Greeks November,
26 Intraday Greeks Approximation Risks Test Design for Taylor Series Expansion (TSE) Here we take a book of about million policyholders and evaluated the book across a mesh grid, with 5 different account value levels and 3 different interest rate levels This creates 5*3 or 345 different points (shocks) where the book value and the Greeks are calculated We calculate Delta and Rho using 00 paths with different seeds at each of these points and then compare the results to a second order estimate for Delta and Rho using TSE with cross Greeks In the naïve approach the calculated base case and Greeks results will feed the intraday estimate of Delta and Rho using a TSE We have simplified the Liability estimation problem because we have boiled it down to only two state variables, changes in total account value and parallel changes in the yield curve, versus the real problem direct writers face in practice November,
27 Intraday Greeks Approximation Risks Result Summary The % errors are large considering a starting dollar Delta of 5 MM and can easily exceed MM. Note the critical role second order Greeks play in TSE for large market movements November,
28 Intraday Greeks Approximation Risks Test Design for Fair Market Value (FMV) surface Here we take a book of about M policyholders and calculate the FMV and the Greeks for the book across a mesh grid, with 5 different account value levels and 3 different interest rate levels However we select only a portion of the FMV points to feed a two dimensional spline We then calculate Delta and Rho using the spline and compare to actual results This test will allow us to get a better sense of how well a FMV surface created from yesterday s close will help us estimate the intraday Liability Greeks in practice Remember we have boiled it down to only two state variables, changes in total account value and parallel changes in the yield curve, versus most direct writers who face the curse of dimensionality and are basically limited to under 00 runs to create the trading grid November,
29 Intraday Greeks Approximation Risks Interpolated FMV overnight run spline training set Multidimensional splines need to be provided appropriate training set and even then can fail to provide reasonable outputs, and here we use the yellow FMV points in our two dimensional spline November,
30 Intraday Greeks Approximation Risks Interpolated FMV Delta spline error Here we can see that using a FMV surface from the day before is subject to spline issues. It is almost like you are not sure what size of error you will get and often it can be very large November,
31 Intraday Greeks Approximation Risks Interpolated FMV DVO spline error Here we can see using a FMV surface from the day before is subject to spline issues for interest rate sensitivities too November,
32 Intraday Greeks Approximation Risks Delta error expressed in S&P500 emini contracts to reblance Trading extra contracts means adding noise to your hedge program, day after day, and when there is a large market movement the noise problem can increase exponentially November,
33 Intraday Greeks Approximation Risks Conclusion Making trading decisions today based on information from yesterday may result in adding a lot of noise to your hedge program results Taylor Series Expansion interpolation results The size of the noise or error grows with the size and nature of the market change using a TSE as intraday interpolator Second order and cross Greeks drive the performance of intraday Greeks estimation when markets move a lot but the problem is these Greeks are notoriously unstable On the plus side a TSE interpolator is simple to set up and use FMV surface interpolation results Even in two dimensions a FMV interpolation process to estimate the Liability Greeks and value is subject to large errors at times, and the pattern of the errors is hard to understand Overall Summary Trading today is based on grids from yesterday using FMV spline is far from a perfect approach The best alternative is to trade with timely and accurate information VA hedge program managers should monitor this risk in their hedge program and try to measure and assess the impact of trading with stale information on their hedge breakage numbers November,
Using least squares Monte Carlo for capital calculation 21 November 2011
Life Conference and Exhibition 2011 Adam Koursaris, Peter Murphy Using least squares Monte Carlo for capital calculation 21 November 2011 Agenda SCR calculation Nested stochastic problem Limitations of
More informationFinancial Engineering g and Actuarial Science In the Life Insurance Industry
Financial Engineering g and Actuarial Science In the Life Insurance Industry Presentation at USC October 31, 2013 Frank Zhang, CFA, FRM, FSA, MSCF, PRM Vice President, Risk Management Pacific Life Insurance
More informationHedging Variable Annuity Guarantees
p. 1/4 Hedging Variable Annuity Guarantees Actuarial Society of Hong Kong Hong Kong, July 30 Phelim P Boyle Wilfrid Laurier University Thanks to Yan Liu and Adam Kolkiewicz for useful discussions. p. 2/4
More informationPractical Applications of Stochastic Modeling for Disability Insurance
Practical Applications of Stochastic Modeling for Disability Insurance Society of Actuaries Session 8, Spring Health Meeting Seattle, WA, June 007 Practical Applications of Stochastic Modeling for Disability
More informationTHE INSURANCE BUSINESS (SOLVENCY) RULES 2015
THE INSURANCE BUSINESS (SOLVENCY) RULES 2015 Table of Contents Part 1 Introduction... 2 Part 2 Capital Adequacy... 4 Part 3 MCR... 7 Part 4 PCR... 10 Part 5  Internal Model... 23 Part 6 Valuation... 34
More informationTraditional, investment, and risk management actuaries in the life insurance industry
Traditional, investment, and risk management actuaries in the life insurance industry Presentation at California Actuarial Student Conference University of California, Santa Barbara April 4, 2015 Frank
More informationFacilitating OnDemand Risk and Actuarial Analysis in MATLAB. Timo Salminen, CFA, FRM Model IT
Facilitating OnDemand Risk and Actuarial Analysis in MATLAB Timo Salminen, CFA, FRM Model IT Introduction It is common that insurance companies can valuate their liabilities only quarterly Sufficient
More informationStochastic Analysis of LongTerm MultipleDecrement Contracts
Stochastic Analysis of LongTerm MultipleDecrement Contracts Matthew Clark, FSA, MAAA, and Chad Runchey, FSA, MAAA Ernst & Young LLP Published in the July 2008 issue of the Actuarial Practice Forum Copyright
More informationGENERALI PANEUROPE LIMITED
GENERALI PANEUROPE LIMITED Considerations for Variable Annuity Writers when internalising their hedging activities Michael Sharpe 27th November 2014 1 Contents 1. About Generali PanEurope 2. Variable Annuities
More informationUsage of Modeling Efficiency Techniques in the US Life Insurance Industry
Usage of Modeling Efficiency Techniques in the US Life Insurance Industry April 2013 Results of a survey analyzed by the American Academy of Actuaries Modeling Efficiency Work Group The American Academy
More informationHedging at Your Insurance Company
Hedging at Your Insurance Company SEAC Spring 2007 Meeting Winter Liu, FSA, MAAA, CFA June 2007 2006 Towers Perrin Primary Benefits and Motives of Establishing Hedging Programs Hedging can mitigate some
More informationGuaranteed Annuity Options
Guaranteed Annuity Options Hansjörg Furrer Marketconsistent Actuarial Valuation ETH Zürich, Frühjahrssemester 2008 Guaranteed Annuity Options Contents A. Guaranteed Annuity Options B. Valuation and Risk
More informationEuropean Options Pricing Using Monte Carlo Simulation
European Options Pricing Using Monte Carlo Simulation Alexandros Kyrtsos Division of Materials Science and Engineering, Boston University akyrtsos@bu.edu European options can be priced using the analytical
More informationHedging Illiquid FX Options: An Empirical Analysis of Alternative Hedging Strategies
Hedging Illiquid FX Options: An Empirical Analysis of Alternative Hedging Strategies Drazen Pesjak Supervised by A.A. Tsvetkov 1, D. Posthuma 2 and S.A. Borovkova 3 MSc. Thesis Finance HONOURS TRACK Quantitative
More informationMarket Value of Insurance Contracts with Profit Sharing 1
Market Value of Insurance Contracts with Profit Sharing 1 Pieter Bouwknegt NationaleNederlanden Actuarial Dept PO Box 796 3000 AT Rotterdam The Netherlands Tel: (31)10513 1326 Fax: (31)10513 0120 Email:
More informationVariable Annuities and Policyholder Behaviour
Variable Annuities and Policyholder Behaviour Prof Dr Michael Koller, ETH Zürich Risk Day, 1192015 Aim To understand what a Variable Annuity is, To understand the different product features and how they
More informationFX OPTIONS MARGIN MODEL SEPTEMBER 2015, SAXO BANK
F PTINS MRGIN MDEL SEPTEMER 2015, S NK F Expiry Margin Description (1/2) Calculation For a given currency pair the F Expiry Margin model calculates a potential maximum future loss in a given F option strategy
More informationHPCFinance: New Thinking in Finance. Calculating Variable Annuity Liability Greeks Using Monte Carlo Simulation
HPCFinance: New Thinking in Finance Calculating Variable Annuity Liability Greeks Using Monte Carlo Simulation Dr. Mark Cathcart, Standard Life February 14, 2014 0 / 58 Outline Outline of Presentation
More informationFeatured article: Evaluating the Cost of Longevity in Variable Annuity Living Benefits
Featured article: Evaluating the Cost of Longevity in Variable Annuity Living Benefits By Stuart Silverman and Dan Theodore This is a followup to a previous article Considering the Cost of Longevity Volatility
More informationEEV, MCEV, Solvency, IFRS a chance for actuarial mathematics to get to mainstream of insurance value chain
EEV, MCEV, Solvency, IFRS a chance for actuarial mathematics to get to mainstream of insurance value chain dr Krzysztof Stroiński, dr Renata Onisk, dr Konrad Szuster, mgr Marcin Szczuka 9 June 2008 Presentation
More informationUsing the SABR Model
Definitions Ameriprise Workshop 2012 Overview Definitions The Black76 model has been the standard model for European options on currency, interest rates, and stock indices with it s main drawback being
More informationAutumn Investor Seminar. Workshops. Managing Variable Annuity Risk
Autumn Investor Seminar Workshops Managing Variable Annuity Risk JeanChristophe Menioux Kevin Byrne Denis Duverne Group CRO CIO AXA Equitable Chief Financial Officer Paris November 25, 2008 Cautionary
More informationYou can find the Report on the SaxoTrader under the Account tab. On the SaxoWebTrader, it is located under the Account tab, on the Reports menu.
The FX Options Report What is the FX Options Report? The FX Options Report gives you a detailed analysis of your FX and FX Options positions across multiple currency pairs, enabling you to manage your
More informationPricing Variable Annuity With Embedded Guarantees.  a case study. David Wang, FSA, MAAA May 21, 2008 at ASHK
Pricing Variable Annuity With Embedded Guarantees  a case study David Wang, FSA, MAAA May 21, 2008 at ASHK Set The Stage Peter is the pricing actuary of company LifeGoesOn and LifeGoesOn wishes to launch
More informationImportant Exam Information:
Important Exam Information: Exam Registration Candidates may register online or with an application. Order Study Notes Study notes are part of the required syllabus and are not available electronically
More informationτ θ What is the proper price at time t =0of this option?
Now by Itô s formula But Mu f and u g in Ū. Hence τ θ u(x) =E( Mu(X) ds + u(x(τ θ))) 0 τ θ u(x) E( f(x) ds + g(x(τ θ))) = J x (θ). 0 But since u(x) =J x (θ ), we consequently have u(x) =J x (θ ) = min
More informationVilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis
Vilnius University Faculty of Mathematics and Informatics Gintautas Bareikis CONTENT Chapter 1. SIMPLE AND COMPOUND INTEREST 1.1 Simple interest......................................................................
More informationMaster of Mathematical Finance: Course Descriptions
Master of Mathematical Finance: Course Descriptions CS 522 Data Mining Computer Science This course provides continued exploration of data mining algorithms. More sophisticated algorithms such as support
More informationQuantitative Impact Study 1 (QIS1) Summary Report for Belgium. 21 March 2006
Quantitative Impact Study 1 (QIS1) Summary Report for Belgium 21 March 2006 1 Quantitative Impact Study 1 (QIS1) Summary Report for Belgium INTRODUCTORY REMARKS...4 1. GENERAL OBSERVATIONS...4 1.1. Market
More informationHedging Barriers. Liuren Wu. Zicklin School of Business, Baruch College (http://faculty.baruch.cuny.edu/lwu/)
Hedging Barriers Liuren Wu Zicklin School of Business, Baruch College (http://faculty.baruch.cuny.edu/lwu/) Based on joint work with Peter Carr (Bloomberg) Modeling and Hedging Using FX Options, March
More informationAn introduction to ValueatRisk Learning Curve September 2003
An introduction to ValueatRisk Learning Curve September 2003 ValueatRisk The introduction of ValueatRisk (VaR) as an accepted methodology for quantifying market risk is part of the evolution of risk
More informationVariable Annuities. Society of Actuaries in Ireland Evening Meeting September 17, 2008
Variable Annuities Society of Actuaries in Ireland Evening Meeting September 17, 2008 Variable Annuities Working Party Presented paper to Faculty and Institute in March 2008 Working Party members Colin
More information14 Greeks Letters and Hedging
ECG590I Asset Pricing. Lecture 14: Greeks Letters and Hedging 1 14 Greeks Letters and Hedging 14.1 Illustration We consider the following example through out this section. A financial institution sold
More informationConstructing Portfolios of ConstantMaturity Fixed Income ETFs
Constructing Portfolios of ConstantMaturity Fixed Income ETFs Newfound Research LLC December 2013 For more information about Newfound Research call us at +16175319773, visit us at www.thinknewfound.com
More informationGuarantees and Target Volatility Funds
SEPTEMBER 0 ENTERPRISE RISK SOLUTIONS B&H RESEARCH E SEPTEMBER 0 DOCUMENTATION PACK Steven Morrison PhD Laura Tadrowski PhD Moody's Analytics Research Contact Us Americas +..55.658 clientservices@moodys.com
More informationDon t be Intimidated by the Greeks, Part 2 August 29, 2013 Joe Burgoyne, OIC
Don t be Intimidated by the Greeks, Part 2 August 29, 2013 Joe Burgoyne, OIC www.optionseducation.org 2 The Options Industry Council Options involve risks and are not suitable for everyone. Prior to buying
More informationMatching Investment Strategies in General Insurance Is it Worth It? Aim of Presentation. Background 34TH ANNUAL GIRO CONVENTION
Matching Investment Strategies in General Insurance Is it Worth It? 34TH ANNUAL GIRO CONVENTION CELTIC MANOR RESORT, NEWPORT, WALES Aim of Presentation To answer a key question: What are the benefit of
More informationFinancial Options: Pricing and Hedging
Financial Options: Pricing and Hedging Diagrams Debt Equity Value of Firm s Assets T Value of Firm s Assets T Valuation of distressed debt and equitylinked securities requires an understanding of financial
More informationCITIGROUP INC. BASEL II.5 MARKET RISK DISCLOSURES AS OF AND FOR THE PERIOD ENDED MARCH 31, 2013
CITIGROUP INC. BASEL II.5 MARKET RISK DISCLOSURES AS OF AND FOR THE PERIOD ENDED MARCH 31, 2013 DATED AS OF MAY 15, 2013 Table of Contents Qualitative Disclosures Basis of Preparation and Review... 3 Risk
More informationINTEREST RATES AND FX MODELS
INTEREST RATES AND FX MODELS 8. Portfolio greeks Andrew Lesniewski Courant Institute of Mathematical Sciences New York University New York March 27, 2013 2 Interest Rates & FX Models Contents 1 Introduction
More informationEconomic Scenario Generator Version 7 Release Notes
Economic Scenario Generator Version 7 Release Notes These release notes describe the changes to the Academy s Economic Scenario Generator that are included in version 7. This release includes updated versions
More informationAXA EQUITABLE VARIABLE ANNUITY GUARANTEED BENEFITS DYNAMIC HEDGING CONSIDERATIONS
AXA EQUITABLE VARIABLE ANNUITY GUARANTEED BENEFITS DYNAMIC HEDGING CONSIDERATIONS STAN TULIN VICE CHAIRMAN AND CHIEF FINANCIAL OFFICER AXA FINANCIAL MARCH 21, 2005 Cautionary Statements Concerning Forwardlooking
More informationComparing Life Insurer Longevity Risk Transfer Strategies in a MultiPeriod Valuation Framework
1 / 28 Comparing Life Insurer Longevity Risk Transfer Strategies in a MultiPeriod Valuation Framework Craig Blackburn, Katja Hanewald, Annamaria Olivieri and Michael Sherris Australian School of Business
More informationVariable Annuities in Australia: Managing the Risks. Jeff Gebler & Warren Manners
Variable Annuities in Australia: Managing the Risks Jeff Gebler & Warren Manners Agenda VA Risks: Lessons learned from the past Dynamic Hedging: Ingredients for an optimal hedging strategy VA Risks: Lessons
More informationDiscount Rates in General Insurance Pricing
Discount Rates in General Insurance Pricing Peter Mulquiney, Brett Riley, Hugh Miller and Tim Jeffrey Peter Mulquiney, Brett Riley, Hugh Miller and Tim Jeffrey This presentation has been prepared for the
More informationDIGITAL FOREX OPTIONS
DIGITAL FOREX OPTIONS OPENGAMMA QUANTITATIVE RESEARCH Abstract. Some pricing methods for forex digital options are described. The price in the GarhmanKohlhagen model is first described, more for completeness
More informationSociety of Actuaries in Ireland
Society of Actuaries in Ireland Information and Assistance Note LA1: Actuaries involved in the Own Risk & Solvency Assessment (ORSA) under Solvency II Life Assurance and Life Reinsurance Business Issued
More informationEquitybased Insurance Guarantees Conference October 2728, 2008. Pricing EAI Guarantees. Moderator Dr. K. (Ravi) Ravindran
Equitybased Insurance Guarantees Conference October 2728, 2008 Pricing EAI Guarantees Noel Abkemeier, Eric Petersen Moderator Dr. K. (Ravi) Ravindran Equity Indexed Annuity Pricing Eric Petersen, F.S.A.
More informationThe Effective Dimension of AssetLiability Management Problems in Life Insurance
The Effective Dimension of AssetLiability Management Problems in Life Insurance Thomas Gerstner, Michael Griebel, Markus Holtz Institute for Numerical Simulation, University of Bonn holtz@ins.unibonn.de
More informationMeasurement of Banks Exposure to Interest Rate Risk and Principles for the Management of Interest Rate Risk respectively.
INTEREST RATE RISK IN THE BANKING BOOK Over the past decade the Basel Committee on Banking Supervision (the Basel Committee) has released a number of consultative documents discussing the management and
More informationPricing and Risk Management of Variable Annuity Guaranteed Benefits by Analytical Methods Longevity 10, September 3, 2014
Pricing and Risk Management of Variable Annuity Guaranteed Benefits by Analytical Methods Longevity 1, September 3, 214 Runhuan Feng, University of Illinois at UrbanaChampaign Joint work with Hans W.
More informationBootstrapping the interestrate term structure
Bootstrapping the interestrate term structure Marco Marchioro www.marchioro.org October 20 th, 2012 Bootstrapping the interestrate term structure 1 Summary (1/2) Market quotes of deposit rates, IR futures,
More informationModels Used in Variance Swap Pricing
Models Used in Variance Swap Pricing Final Analysis Report Jason Vinar, Xu Li, Bowen Sun, Jingnan Zhang Qi Zhang, Tianyi Luo, Wensheng Sun, Yiming Wang Financial Modelling Workshop 2011 Presentation Jan
More informationLiquidity premiums and contingent liabilities
Insights Liquidity premiums and contingent liabilities Craig Turnbull Craig.Turbull@barrhibb.com The liquidity premium the concept that illiquid assets have lower prices than equivalent liquid ones has
More informationPricing Barrier Options under Local Volatility
Abstract Pricing Barrier Options under Local Volatility Artur Sepp Mail: artursepp@hotmail.com, Web: www.hot.ee/seppar 16 November 2002 We study pricing under the local volatility. Our research is mainly
More informationOptions/1. Prof. Ian Giddy
Options/1 New York University Stern School of Business Options Prof. Ian Giddy New York University Options Puts and Calls PutCall Parity Combinations and Trading Strategies Valuation Hedging Options2
More informationZeroCoupon Bonds (Pure Discount Bonds)
ZeroCoupon Bonds (Pure Discount Bonds) The price of a zerocoupon bond that pays F dollars in n periods is F/(1 + r) n, where r is the interest rate per period. Can meet future obligations without reinvestment
More informationIL GOES OCAL A TWOFACTOR LOCAL VOLATILITY MODEL FOR OIL AND OTHER COMMODITIES 15 // MAY // 2014
IL GOES OCAL A TWOFACTOR LOCAL VOLATILITY MODEL FOR OIL AND OTHER COMMODITIES 15 MAY 2014 2 MarieLan Nguyen / Wikimedia Commons Introduction 3 Most commodities trade as futures/forwards Cash+carry arbitrage
More informationOpenGamma Quantitative Research Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem
OpenGamma Quantitative Research Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem Marc Henrard marc@opengamma.com OpenGamma Quantitative Research n. 1 November 2011 Abstract
More informationFINANCIAL ECONOMICS OPTION PRICING
OPTION PRICING Options are contingency contracts that specify payoffs if stock prices reach specified levels. A call option is the right to buy a stock at a specified price, X, called the strike price.
More informationLecture 11: The Greeks and Risk Management
Lecture 11: The Greeks and Risk Management This lecture studies market risk management from the perspective of an options trader. First, we show how to describe the risk characteristics of derivatives.
More informationGN47: Stochastic Modelling of Economic Risks in Life Insurance
GN47: Stochastic Modelling of Economic Risks in Life Insurance Classification Recommended Practice MEMBERS ARE REMINDED THAT THEY MUST ALWAYS COMPLY WITH THE PROFESSIONAL CONDUCT STANDARDS (PCS) AND THAT
More informationMarket Consistent Valuation and Funding of Cash Balance Pensions
Market Consistent Valuation and Funding of Cash Balance Pensions Mary R Hardy, David Saunders & Xiaobai Mike Zhu Statistics and Actuarial Science, University of Waterloo. July 31, 213 1 Executive Summary
More informationOption Values. Determinants of Call Option Values. CHAPTER 16 Option Valuation. Figure 16.1 Call Option Value Before Expiration
CHAPTER 16 Option Valuation 16.1 OPTION VALUATION: INTRODUCTION Option Values Intrinsic value  profit that could be made if the option was immediately exercised Call: stock price  exercise price Put:
More informationPortfolio Replication Variable Annuity Case Study. Curt Burmeister Senior Director Algorithmics
Portfolio Replication Variable Annuity Case Study Curt Burmeister Senior Director Algorithmics What is Portfolio Replication? To find a portfolio of assets whose value is equal to the value of a liability
More informationDisclosure of European Embedded Value (summary) as of March 31, 2015
May 28, 2015 SUMITOMO LIFE INSURANCE COMPANY Disclosure of European Embedded Value (summary) as of March 31, 2015 This is the summarized translation of the European Embedded Value ( EEV ) of Sumitomo Life
More informationReplicating Portfolios Complex modelling made simple
Replicating Portfolios Complex modelling made simple SAV Versammlung by Jolanta Tubis 10 September 2010 2010 Towers Watson. All rights reserved. Agenda Smart modelling The replicating portfolio Approach
More informationReturn to Risk Limited website: www.risklimited.com. Overview of Options An Introduction
Return to Risk Limited website: www.risklimited.com Overview of Options An Introduction Options Definition The right, but not the obligation, to enter into a transaction [buy or sell] at a preagreed price,
More informationYour model to successful individual retirement investment plans
Your model to successful individual retirement investment plans Tim Noonan Managing Director, Capital Markets Insights Russell Investments WWW.RISYMPOSIUM.COM Presented by: Important Information Please
More informationCalculating VaR. Capital Market Risk Advisors CMRA
Calculating VaR Capital Market Risk Advisors How is VAR Calculated? Sensitivity Estimate Models  use sensitivity factors such as duration to estimate the change in value of the portfolio to changes in
More informationVariable Annuities Risk Management
Variable Annuities Risk Management Michele Bergantino Risk and Investment Conference Leeds  June 28, 2012 1 Contents VA Key Features VA Risk Management Conclusions Appendix A  VA Option Valuation, an
More informationGenerating Random Numbers Variance Reduction QuasiMonte Carlo. Simulation Methods. Leonid Kogan. MIT, Sloan. 15.450, Fall 2010
Simulation Methods Leonid Kogan MIT, Sloan 15.450, Fall 2010 c Leonid Kogan ( MIT, Sloan ) Simulation Methods 15.450, Fall 2010 1 / 35 Outline 1 Generating Random Numbers 2 Variance Reduction 3 QuasiMonte
More informationNumerical Methods for Option Pricing
Chapter 9 Numerical Methods for Option Pricing Equation (8.26) provides a way to evaluate option prices. For some simple options, such as the European call and put options, one can integrate (8.26) directly
More informationPension Risk Management with Funding and Buyout Options
Pension Risk Management with Funding and Buyout Options Samuel H. Cox, Yijia Lin, Tianxiang Shi Department of Finance College of Business Administration University of NebraskaLincoln FIRM 2015, Beijing
More informationPricing and calibration in local volatility models via fast quantization
Pricing and calibration in local volatility models via fast quantization Parma, 29 th January 2015. Joint work with Giorgia Callegaro and Martino Grasselli Quantization: a brief history Birth: back to
More informationTABLE OF CONTENTS. Executive Summary 3. Introduction 5. Purposes of the Joint Research Project 6
TABLE OF CONTENTS Executive Summary 3 Introduction 5 Purposes of the Joint Research Project 6 Background 7 1. Contract and timeframe illustrated 7 2. Liability measurement bases 9 3. Earnings 10 Consideration
More informationActuarial Guidance Note 9: Best Estimate Assumptions
ACTUARIAL SOCIETY OF HONG KONG Actuarial Guidance Note 9: Best Estimate Assumptions 1. BACKGROUND AND PURPOSE 1.1 Best estimate assumptions are an essential and important component of actuarial work. The
More informationCHAPTER 22 Options and Corporate Finance
CHAPTER 22 Options and Corporate Finance Multiple Choice Questions: I. DEFINITIONS OPTIONS a 1. A financial contract that gives its owner the right, but not the obligation, to buy or sell a specified asset
More informationVIX for Variable Annuities
White Paper VIX for Variable Annuities A study considering the advantages of tying a Variable Annuity fee to VIX March 2013 VIX for Variable Annuities A study considering the advantages of tying a Variable
More informationInsights. Investment strategy design for defined contribution pension plans. An AssetLiability Risk Management Challenge
Insights Investment strategy design for defined contribution pension plans Philip Mowbray Philip.Mowbray@barrhibb.com The widespread growth of Defined Contribution (DC) plans as the core retirement savings
More informationPerspectives September
Perspectives September 2013 Quantitative Research Option Modeling for Leveraged Finance Part I Bjorn Flesaker Managing Director and Head of Quantitative Research Prudential Fixed Income Juan Suris Vice
More informationFixed Income Performance Attribution
Fixed Income Performance Attribution Mary Cait McCarthy August 2014 Content 1 2 3 4 5 6 What is Performance Attribution? Uses of Performance Attribution Drivers of Return in Fixed Income Returns Based
More informationDisclosure of European Embedded Value (summary) as of March 31, 2012
May 25, 2012 SUMITOMO LIFE INSURANCE COMPANY Disclosure of European Embedded Value (summary) as of 2012 This is the summarized translation of the European Embedded Value ( EEV ) of Sumitomo Life Insurance
More informationGN47: Stochastic Modelling for Life Insurance Reserving and Capital Assessment
GN47: Stochastic Modelling for Life Insurance Reserving and Capital Assessment Classification Recommended Practice MEMBERS ARE REMINDED THAT THEY MUST ALWAYS COMPLY WITH THE PROFESSIONAL CONDUCT STANDARDS
More informationLecture Note of Bus 41202, Spring 2012: Stochastic Diffusion & Option Pricing
Lecture Note of Bus 41202, Spring 2012: Stochastic Diffusion & Option Pricing Key concept: Ito s lemma Stock Options: A contract giving its holder the right, but not obligation, to trade shares of a common
More informationFinancial Modeling. An introduction to financial modelling and financial options. Conall O Sullivan
Financial Modeling An introduction to financial modelling and financial options Conall O Sullivan Banking and Finance UCD Smurfit School of Business 31 May / UCD Maths Summer School Outline Introduction
More informationAffinestructure models and the pricing of energy commodity derivatives
Affinestructure models and the pricing of energy commodity derivatives Nikos K Nomikos n.nomikos@city.ac.uk Cass Business School, City University London Joint work with: Ioannis Kyriakou, Panos Pouliasis
More informationAsset Liability Management for Australian Life Insurers Anton Kapel Zac Roberts
Asset Liability Management for Australian Life Insurers Anton Kapel Zac Roberts Copyright 2006, the Tillinghast Business of Towers Perrin. All rights reserved. A licence to publish is granted to the Institute
More informationWebinar #2. Introduction to IAS39 hedge accounting with Fairmat. Fairmat Srl 18/07/2013
Webinar #2 Introduction to IAS39 hedge accounting with Fairmat Fairmat Srl 18/07/2013 Agenda Brief notes on IAS39 hedge accounting 1 Brief notes on IAS39 hedge accounting 2 3 Introduction Prospective
More informationFinancial Modeling. Class #06B. Financial Modeling MSS 2012 1
Financial Modeling Class #06B Financial Modeling MSS 2012 1 Class Overview Equity options We will cover three methods of determining an option s price 1. BlackScholesMerton formula 2. Binomial trees
More informationPricing Variable Annuity Guarantees in a Local Volatility framework
Pricing Variable Annuity Guarantees in a Local Volatility framework Griselda Deelstra and Grégory Rayée Department of Mathematics, Université Libre de Bruxelles, Boulevard du Triomphe, CP 210, Brussels
More informationPricing complex options using a simple Monte Carlo Simulation
A subsidiary of Sumitomo Mitsui Banking Corporation Pricing complex options using a simple Monte Carlo Simulation Peter Fink Among the different numerical procedures for valuing options, the Monte Carlo
More informationMonte Carlo Methods in Finance
Author: Yiyang Yang Advisor: Pr. Xiaolin Li, Pr. Zari Rachev Department of Applied Mathematics and Statistics State University of New York at Stony Brook October 2, 2012 Outline Introduction 1 Introduction
More informationOption pricing in detail
Course #: Title Module 2 Option pricing in detail Topic 1: Influences on option prices  recap... 3 Which stock to buy?... 3 Intrinsic value and time value... 3 Influences on option premiums... 4 Option
More informationValuation of the Surrender Option in Life Insurance Policies
Valuation of the Surrender Option in Life Insurance Policies Hansjörg Furrer Marketconsistent Actuarial Valuation ETH Zürich, Frühjahrssemester 2010 Valuing Surrender Options Contents A. Motivation and
More informationDelta risk on interest rate derivatives
Delta risk on interest rate derivatives The concept of delta risk on interest rate derivatives is a generalization of the traditional one of a single asset option. However, contrary to single asset derivatives,
More informationMargin Calculation Methodology and Derivatives and Repo Valuation Methodology
Margin Calculation Methodology and Derivatives and Repo Valuation Methodology 1 Overview This document presents the valuation formulas for interest rate derivatives and repo transactions implemented in
More informationChapter 3.4. Forex Options
Chapter 3.4 Forex Options 0 Contents FOREX OPTIONS Forex options are the next frontier in forex trading. Forex options give you just what their name suggests: options in your forex trading. If you have
More informationHedging Pension Liabilities
Hedging Pension Liabilities when there are incomplete markets and regulatory uncertainty Sampension, 2012 Outline Introduction 1 Introduction 2 3 4 Outline Introduction 1 Introduction 2 3 4 Sampension
More informationCEIOPS Preparatory Field Study for Life Insurance Firms. Summary Report
CEIOPSFS08/05 S CEIOPS Preparatory Field Study for Life Insurance Firms Summary Report 1 GENERAL OBSERVATIONS AND CONCLUSIONS 1.1 Introduction CEIOPS has been asked to prepare advice for the European
More information