QFI – Quantitative Finance Exam

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QFI – Quantitative Finance ExamSpring 2022/Fall 2022Important Exam Information:Exam RegistrationCandidates may register online or with an application.Order Study NotesStudy notes are part of the required syllabus and are not availableelectronically but may be purchased through the online store.Syllabus ReadingsReadings listed in this syllabus may include study notes, onlinereadings and textbooks. Candidates are responsible for all readingsin their entirety, including sections such as Appendices, unless it isstated otherwise in the syllabus.Introductory Study NoteThe Introductory Study Note has a complete listing of all study notesas well as errata and other important information.Case StudyA case study will not be used for this examination.Past ExamsPast Exams from 2000-present are available on SOA website.UpdatesCandidates should be sure to check the Updates page on the examhome page periodically for additional corrections or notices.Formula PackageA Formula Package will be provided with the exam. Please see theIntroductory Study Note for more information.TableA Cumulative normal distribution table will be provided with the exam.Copyright Society of Actuaries

Quantitative Finance and Investment – Quantitative Finance ExamSpring 2022/Fall 20221. Topic: Stochastic CalculusLearning ObjectivesThe candidate will understand the foundations of quantitative finance.Learning OutcomesThe Candidate will be able to:a)Understand and apply concepts of probability and statistics important in mathematical financeb) Understand the importance of the no-arbitrage condition in asset pricingc)Understand the Ito integral and stochastic differential equationsd) Understand and apply Ito's Lemmae) Understand the Black-Scholes-Merton PDE (partial differential equation)f)Understand and apply Jensen’s Inequalityg)Understand the distinction between complete and incomplete marketsh) Define and apply the concepts of martingale, market price of risk, and measures in single and multiple statevariable contextsi)Demonstrate understanding of the differences and implications of real-world versus risk-neutral probabilitymeasures, and when the use of each is appropriatej)Understand and apply Girsanov’s theorem in changing measuresk)Understand the importance of the Feynman-Kac TheoremResources An Introduction to the Mathematics of Financial Derivatives, Hirsa, Ali and Neftci, Salih N., 3rd Edition 2ndPrinting, 2014oCh. 1-15 (excluding section 8.2.4)Note: Candidates should verify that their copy of the Hirsa & Neftci textbook is the 3rd edition, secondprinting by checking that page iv, Notices section, begins with “Knowledge and best practice in this field ”.If the Notices section begins “No responsibility is assumed ” it is the first printing and should be replaced. QFIQ-113-17 Frequently Asked Questions in Quantitative Finance, Wilmott, Paul, 2nd Edition, 2009, Ch. 2, pp.103-105, 109-115, 155-161 & 248-249 Problems and Solutions in Mathematical Finance: Stochastic Calculus, Chin, Eric, Nel, Dian and Olafsson,Sverrir, 2014Note: Candidates should study the following problems in Chin, Nel, and Ólafsson alongside the matchingchapters of An Introduction to the Mathematics of Financial Derivatives, Hirsa and Neftci to reinforce thestandard techniques used in stochastic calculus. Please note that formulas from Chin, Nel, and Ólafsson arenot included in the formula package.1

Quantitative Finance and Investment – Quantitative Finance ExamSpring 2022/Fall 2022Chin etal.ChapterPages14 to 518 to 1943 to 44Definitions 1.1 to 1.7(Note that statement (b) of Definition 1.7involves integration using a measure-theoreticapproach. An equally valid statement can bemade using a Riemann-Stieltjes integral forcontinuous distributions or a sum for discretedistributions.)Q3 to Q7Q7Q443 to 44Q552525255 to 5757 to 6868 to 71717272 to 7496 to 9797 to 9899 to 100Definitions 2.1, 2.2Theorems 2.3 and 2.4Definitions 2.5 and 2.6Q1 to Q3Q4 to Q13, except Q11Q1, Q2, Q3Q1Q2Q2-Q5Theorem 3.2Theorem 3.3Definition 3.61 to 323Item115Q13Corresponding Hirsa & NeftciChapter sections5.25.215.4.114.2.2Pg. 245 paragraph containingequations from (14.91) - (14.93)8.2.15.82.2.9, 6.26.4.18.2.1***6.6.16.6.26.6.310.421.410.4First part is different approach topart of question #12 in pg. 64123 to 149Q1 to Q2010.5155 to 158175 to 178Q1 to Q3Q104186 to 187Definitions 4.1(a) - (f)10.710.7H&N Introduces self-financingportfolios in 6.11.3 and goes intodetail in 12.35189192 to 194192 to 194194 to 197221 to 242262 to 264Theorem 4.6Q1Q2Q1 to Q3Q1 to Q17Q9 to Q11281 to 285Q1, Q214.36.11 and exercise 1 in pg. 1096.11 and exercise 4 in pg. 11014.3155.5.5, 8.2.2Chapter 11: section on pure jumpframework*** means there is no direct correspondence2

Quantitative Finance and Investment – Quantitative Finance ExamSpring 2022/Fall 20222. Topic: Fixed Income MarketsLearning ObjectivesThe candidate will understand the fundamentals of fixed income markets and traded securities.Learning OutcomesThe Candidate will be able to:a)Understand the characteristics of fixed rate, floating rate, and zero-coupon bondsb) Bootstrap a yield curvec)Understand measures of interest rate risk including duration, convexity, slope, and curvatured) Understand the characteristics and uses of interest rate forwards, swaps, futures, and optionsResources Fixed Income Securities: Valuation, Risk, and Risk Management, Veronesi, Pietro, 2010oCh. 1 (background)oCh. 2 (background)oCh. 3 (excluding Appendix)oCh. 4oCh. 5 (excluding Case Study)oCh. 6QFIQ-121-20: A Guide to Duration, DV01, and Yield Curve Risk Transformations, pp. 1-283

Quantitative Finance and Investment – Quantitative Finance ExamSpring 2022/Fall 20223. Topic: Interest Rate Models and HedgingLearning ObjectivesThe candidate will understand: The quantitative tools and techniques for modeling the term structure of interest rates. The standard yield curve models. The tools and techniques for managing interest rate risk.Learning OutcomesThe Candidate will be able to:a)Understand and apply the concepts of risk-neutral measure, forward measure, normalization, and themarket price of risk, in the pricing of interest rate derivativesb) Understand and apply various one-factor interest rate modelsc)Calibrate a model to observed prices of traded securitiesd) Describe the practical issues related to calibration, including yield curve fittinge) Demonstrate understanding of option pricing theory and techniques for interest rate derivativesf)Apply the models to price common interest sensitive instruments including: callable bonds, bondoptions, caps, floors and swaptionsg)Understand and apply the techniques of interest rate risk hedgingh) Understand the application of Monte Carlo simulation to risk neutral pricing of interest rate securitiesi)Understand the implications of replacing LIBOR with alternative reference ratesj)Understand and apply the Heath-Jarrow-Morton approach including the LIBOR Market modelk)Understand and apply multifactor interest rate modelsl)Demonstrate an understanding of the issues and approaches to building models that admit negativeinterest ratesResources An Introduction to the Mathematics of Financial Derivatives, Hirsa, Ali and Neftci, Salih N., 3rd Edition2nd Printing, 2014o Ch. 16-21Fixed Income Securities: Valuation, Risk, and Risk Management, Veronesi, Pietro, 2010oCh. 14oCh. 15 (excluding Appendix)oCh. 16 (including Case Study, excluding Appendix)oCh. 17oCh. 18 (excluding Appendix)oCh. 19 (excluding Appendix)4

Quantitative Finance and Investment – Quantitative Finance ExamSpring 2022/Fall 2022oCh. 20oCh. 21 (excluding Appendix)oCh. 22.1-22.4 QFIQ-116-17: Low Yield Curves and Absolute/Normal Volatilities QFIQ-129-21: Negative Interest Rates and Their Technical Consequences, AAE, 12/2016 QFIQ-130-21: Interest Rate Models – Theory and Practice, Second Edition, Brigo, Damiano andMercurio, Fabio, 2006, sections 4.2.1, 4.2.2, and 4.2.5 only QFIQ-131-21: Beyond LIBOR: A Primer on the New Reference Rates, BIS, March 20195

Quantitative Finance and Investment – Quantitative Finance ExamSpring 2022/Fall 20224. Topic: Equity Option Pricing and HedgingLearning ObjectivesThe candidate will understand: How to apply the standard models for pricing financial derivatives. The implications for option pricing when markets do not satisfy the common assumptions used inoption pricing theory. How to evaluate risk exposures and the issues in hedging them.Learning OutcomesThe Candidate will be able to:a)Demonstrate an understanding of option pricing techniques and theory for equity derivativesb) Identify limitations of the Black-Scholes-Merton pricing formulac)Demonstrate an understanding of the different approaches to hedging – static and dynamicd) Demonstrate an understanding of how to delta hedge, and the interplay between hedging assumptionsand hedging outcomese) Analyze the Greeks of common option strategiesf)Appreciate how hedge strategies may go awryg)Describe and explain some approaches for relaxing the assumptions used in the Black-Scholes-Mertonformulah) Compare and contrast the various kinds of volatility, e.g., actual, realized, implied and forward, etc.i)Define and explain the concept of volatility smile and some arguments for its existencej)Compare and contrast “floating” and “sticky” smilesk)Describe and contrast several approaches for modeling smiles, including stochastic volatility, localvolatility, jump-diffusions, variance-gamma, and mixture modelsl)Explain various issues and approaches for fitting a volatility surfaceResources The Volatility Smile, Derman, Emanuel and Miller, Michael B., 2016oCh. 1 (background)oCh. 2-11oCh. 14oCh. 17-19 QFIQ-114-17: Chapter 2, pp. 162-173 and 223-225, of Frequently Asked Questions in QuantitativeFinance, Wilmott, Paul, 2nd Edition, 2009 QFIQ-115-17: Which Free Lunch Would You Like Today, Sir?: Delta Hedging, Volatility Arbitrage andOptimal Portfolios6

Quantitative Finance and Investment – Quantitative Finance ExamSpring 2022/Fall 2022 QFIQ-120-19: Chapters 6 and 7 of Pricing and Hedging Financial Derivatives, Marroni, Leonardo andPerdomo, Irene, 20147

Quantitative Finance and Investment – Quantitative Finance ExamSpring 2022/Fall 20225. Topic: ApplicationsLearning ObjectivesThe candidate will learn how to apply the techniques of quantitative finance to applied business contexts.Learning OutcomesThe Candidate will be able to:a)Identify and evaluate embedded options in liabilities, e.g., indexed annuity, structured product basedvariable annuity, and variable annuity guarantee riders including GMxB, etc.b) Demonstrate an understanding of embedded guarantee risk including market, insurance, policyholderbehavior, and basis riskc)Demonstrate an understanding of dynamic and static hedging for embedded guarantees, including:i.Risks that can be hedged, including equity, interest rate, volatility, and cross Greeksii.Risks that can only be partially hedged or cannot be hedged including policyholder behavior,mortality and lapse, basis risk, counterparty exposure, foreign bonds and equities, correlation,and operational failuresd) Demonstrate an understanding of target volatility funds and their effect on guarantee cost and riskcontrole) Demonstrate an understanding of how differences between modeled and actual outcomes forguarantees affect financial results over timeResources QFIQ-124-20: Variable Annuity Volatility Management: An Era of Risk-Control QFIQ-128-20: Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectivenessunder Model Risk QFIQ-132-21: Investment Instruments with Volatility Target Mechanism, Albeverio, Steblovskaya, andWallbaum, 2013 QFIQ-134-22: An Introduction to Computational Risk Management of Equity-Linked Insurance, Feng,2018 (Ch 1.2-1.3, 4.7-4.8, 6.2-6.3) QFIQ-135-22: Structured Product Based Variable Annuities, Deng, Dulaney, Husson, McCann (sections 2& 3)8

Quantitative Finance and Investment – Quantitative Finance Exam Spring 2022/Fall

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