Actuarial Notes

Exam INV-201

INV 201 – Quantitative Finance is an exam of the Society of Actuaries' Fellowship (FSA) pathway. Its syllabus covers the Nov 2026/Mar 2027/Jul 2027 sittings.

Learning Objectives

Key Types of Derivatives (5–15%) The candidate will understand key types of derivatives.

  1. Understand the payoffs of basic derivative instruments including:
  2. Be able to identify the key differences between forwards and futures
  3. Be able to compare European, American, Bermudan, Asian options, and various exotic options
  4. Understand the mechanics of derivatives trading including:
  5. Understand basic derivatives strategies including:

Readings:

  • Options, Futures, and Other Derivatives, Hull, John C., Pearson, 11th Edition, 2021
    • Ch. 1: Introduction (Sections 1.1-1.5) (1a, 1c, 1d)
    • Ch. 2: Futures Markets and Central Counterparties (Sections 2.1-2.8 & 2.11) (1b, 1d)
    • Ch. 7: Swaps (Sections 7.1-7.5 & 7.8-7.13) (1a, 1d)
    • Ch. 12: Trading Strategies Involving Options (Sections 12.1-12.5) (1e)
    • Ch. 17: Options on Stock Indices and Currencies (Sections 17.2) (1a, 1b, 1c)
    • Ch. 26: Exotic Options (Sections 26.3, 26.8-26.11, 26.13 & 26.16) (1c)
    • Ch. 29: Interest Rate Derivatives: The Standard Market Models (Sections 29.2-29.3) (1a)

Valuation of Derivatives (40–60%) The candidate will understand the principles and techniques for the valuation of derivatives.

  1. Understand the principles of no-arbitrage and replication in asset pricing.
  2. Understand Arrow-Debreau security and the distinction between complete and incomplete markets
  3. Understand put-call parity and price bounds
  4. Understand Stochastic Calculus theory and technique used in pricing derivatives including:
  5. Understand and apply the concepts of risk-neutral measure, forward measure, normalization, and the market price of risk
  6. Understand option pricing techniques including:
    • Calculating an expectation
    • By solving an PDE
  7. Understand the limitations of the Black-Scholes-Merton model
  8. Understand and apply numerical discretization methods to price options including Euler-Maruyama discretization and transition density methods
  9. Calibrate a model to observed prices of traded securities including fitting to a given yield curve
  10. Define and explain the concept of volatility smiles and describe several approaches for modeling smiles, including stochastic volatility, local- volatility, jump-diffusions.

Readings:

  • Options, Futures, and Other Derivatives, Hull, John C., Pearson, 11th Edition, 2021 (2a, 2b)
    • Ch. 5: Determination of Forward and Futures Prices (Sections 5.1-5.14)
    • Ch. 7: Swaps (Sections 7.6-7.7)
    • Ch. 13: Binomial Trees (Sections 13.1-13.3)
  • INV201-100-25: Chapter 5 of Financial Mathematics – A Comprehensive Treatment, Campolieti (2a, 2b)
  • Options, Futures, and Other Derivatives, Hull, John C., Pearson, 11th Edition, 2021
    • Ch. 11: Properties of Stock Options (Sections 11.1-11.7) (2c)
    • Ch. 14: Wiener Processes and Ito’s Lemma (Sections 14.1-14.8) (2d, 2e)
    • Ch. 28: Martingales and Measures (Sections 28.1-28.4 & 28.7-28.8) (2d, 2e)
    • Ch. 31: Equilibrium Models of the Short Rate (Section 31.3) (2d, 2e)
  • Understanding the Connection Between Real-World and Risk-Neutral Generators, SOA Research, Aug 2022, Sections 1-5, and Appendices A & D (2d, 2e)
    • Companion Excel Tool
  • Options, Futures, and Other Derivatives, Hull, John C., Pearson, 11th Edition, 2021 (2e, 2f)
    • Ch. 15: The Black-Scholes-Merton Model (Sections 15.1-15.12)
  • INV201-101-25: Chapter 6 of Introduction to Stochastic Finance with Market Examples by Privault (Sections 6.1-6.4) (2f)
  • INV201-102-25: How to Use the Holes in Black-Scholes (2g)
  • Calibrating Interest Rate Models, SOA Research, Oct 2023, Section 1.1-4.3 (excluding 4.1.2) (2g-2i)
  • The Volatility Smile, Derman, Emanuel and Miller, Michael, 2016 (2j)
    • Ch. 8: The Smile: Stylized Facts and Their Interpretation
    • Ch. 10: A Survey of Smile Models
  • Options, Futures, and Other Derivatives, Hull, John C., Pearson, 11th Edition, 2021 (2j)
    • Ch. 20: Volatility Smiles and Volatility Surfaces (Sections 20.1-20.8)
    • Ch. 27: More on Models and Numerical Procedures (Sections 27.1-27.3)
  • Problems and Solutions in Mathematical Finance: Stochastic Calculus, Chin, Eric, Nel, Dian and Olafsson, Sverrir, 2014 (2a, 2b, 2d, 2f)
    • Pg. 52: Definitions 2.1 & 2.2; Theorems 2.3 & 2.4
    • Pp. 57-58: Question 4
    • Pp. 72-73: Question 3
    • Pp. 97-98: Theorems 3.3
    • Pp. 113-114: Itō Isometry
    • Pp. 128-130: Questions 6 & 7
    • Pp. 132-137: Questions 10-12
    • Pp. 146-147: Question 19
    • Pp. 186-188: Definition 4.1(b), Definition 4.1(f) and Theorem 4.2
    • Pp. 221-227: Questions 1-5
    • Pp. 233-242: Questions 12-17

Applications and Risks of Derivatives (30–50%) The candidate will understand various applications and risks of derivatives.

  1. Understand the Greeks of derivatives
  2. Understand static and dynamic hedging
  3. Understand delta hedging, and the interplay between hedging assumptions and hedging outcomes
  4. Understand the concepts of realized versus implied volatility
  5. Understand how hedge strategies may fail
  6. Identify and evaluate embedded options in liabilities (e.g., indexed annuity, structured product based variable annuity, and variable annuity guarantee riders including GMxB, etc.)
  7. Demonstrate an understanding of hedging for embedded option in liabilities with:
  8. Risks that can be hedged, including those of equity, interest rate, volatility, and cross Greeks,
  9. Risks that can only be partially hedged or cannot be hedged, including those of policyholder behavior, mortality, basis, counterparty, correlation, and operational failures
  10. Demonstrate an understanding of target volatility funds and their effect on fund performance, guarantee cost, and risk control

Readings:

  • Options, Futures, and Other Derivatives, Hull, John C., Pearson, 11th Edition, 2021
    • Ch. 19: The Greek Letters (Sections 19.1-19.9 & 19.13) (3a, 3b)
    • Ch. 26: Exotic Options (Section 26.17) (3b)
  • The Volatility Smile, Derman, Emanuel and Miller, Michael, 2016
    • Ch. 3: Static and Dynamic Replication (3c, 3e)
    • Ch. 5: The P&L of Hedged Option Strategies in a Black-Scholes-Merton World (3c, 3d)
    • Ch. 6: The Effect of Discrete Hedging on P&L (3c, 3e)
    • Ch. 7: The Effect of Transaction Costs on P&L (3c, 3e)
  • INV201-104-25: Which Free Lunch Would You Like Today, Sir? (3e)
  • Options, Futures, and Other Derivatives, Hull, John C., Pearson, 11th Edition, 2021 (3e)
    • Ch. 37: Derivatives Mishaps and What We Can Learn from Them (Sections 37.1-37.3)
  • INV201-105-25: An Introduction to Computational Risk Management of Equity-Linked Insurance, Feng, 2018 (sections 1.2-1.3, 4.7 & 6.2-6.3) (3f, 3g)
  • INV201-106-25: Variable Annuity Volatility Management: An Era of Risk-Control (3f, 3g)
  • INV201-108-25: Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk (3f, 3g)
  • INV201-107-25: It's RILA time: An introduction to registered index-linked annuities (excluding Appendices) (3g)
  • INV201-109-25: Investment Instruments with Volatility Target Mechanism (3h)

Source Material

Source Material

  • Options, Futures, and Other Derivatives, Hull, John C., Pearson, 11th Edition, 2021
    • Ch. 1: Introduction (Sections 1.1-1.5) (1a, 1c, 1d)
    • Ch. 2: Futures Markets and Central Counterparties (Sections 2.1-2.8 & 2.11) (1b, 1d)
    • Ch. 7: Swaps (Sections 7.1-7.5 & 7.8-7.13) (1a, 1d)
    • Ch. 12: Trading Strategies Involving Options (Sections 12.1-12.5) (1e)
    • Ch. 17: Options on Stock Indices and Currencies (Sections 17.2) (1a, 1b, 1c)
    • Ch. 26: Exotic Options (Sections 26.3, 26.8-26.11, 26.13 & 26.16) (1c)
    • Ch. 29: Interest Rate Derivatives: The Standard Market Models (Sections 29.2-29.3) (1a)
    • Ch. 5: Determination of Forward and Futures Prices (Sections 5.1-5.14) (2a, 2b)
    • Ch. 7: Swaps (Sections 7.6-7.7) (2a, 2b)
    • Ch. 13: Binomial Trees (Sections 13.1-13.3) (2a, 2b)
    • Ch. 11: Properties of Stock Options (Sections 11.1-11.7) (2c)
    • Ch. 14: Wiener Processes and Ito’s Lemma (Sections 14.1-14.8) (2d, 2e)
    • Ch. 28: Martingales and Measures (Sections 28.1-28.4 & 28.7-28.8) (2d, 2e)
    • Ch. 31: Equilibrium Models of the Short Rate (Section 31.3) (2d, 2e)
    • Ch. 15: The Black-Scholes-Merton Model (Sections 15.1-15.12) (2e, 2f)
    • Ch. 20: Volatility Smiles and Volatility Surfaces (Sections 20.1-20.8) (2j)
    • Ch. 27: More on Models and Numerical Procedures (Sections 27.1-27.3) (2j)
    • Ch. 19: The Greek Letters (Sections 19.1-19.9 & 19.13) (3a, 3b)
    • Ch. 26: Exotic Options (Section 26.17) (3b)
    • Ch. 37: Derivatives Mishaps and What We Can Learn from Them (Sections 37.1-37.3) (3e)
  • INV201-100-25: Chapter 5 of Financial Mathematics – A Comprehensive Treatment, Campolieti
    • Outcomes 2a, 2b
  • Understanding the Connection Between Real-World and Risk-Neutral Generators, SOA Research, Aug 2022, Sections 1-5, and Appendices A & D
    • Companion Excel Tool (2d, 2e)
  • INV201-101-25: Chapter 6 of Introduction to Stochastic Finance with Market Examples by Privault (Sections 6.1-6.4)
    • Outcomes 2f
  • INV201-102-25: How to Use the Holes in Black-Scholes
    • Outcomes 2g
  • Calibrating Interest Rate Models, SOA Research, Oct 2023, Section 1.1-4.3 (excluding 4.1.2)
    • Outcomes 2g-2i
  • The Volatility Smile, Derman, Emanuel and Miller, Michael, 2016
    • Ch. 8: The Smile: Stylized Facts and Their Interpretation (2j)
    • Ch. 10: A Survey of Smile Models (2j)
    • Ch. 3: Static and Dynamic Replication (3c, 3e)
    • Ch. 5: The P&L of Hedged Option Strategies in a Black-Scholes-Merton World (3c, 3d)
    • Ch. 6: The Effect of Discrete Hedging on P&L (3c, 3e)
    • Ch. 7: The Effect of Transaction Costs on P&L (3c, 3e)
  • Problems and Solutions in Mathematical Finance: Stochastic Calculus, Chin, Eric, Nel, Dian and Olafsson, Sverrir, 2014
    • Pg. 52: Definitions 2.1 & 2.2; Theorems 2.3 & 2.4 (2a, 2b, 2d, 2f)
    • Pp. 57-58: Question 4 (2a, 2b, 2d, 2f)
    • Pp. 72-73: Question 3 (2a, 2b, 2d, 2f)
    • Pp. 97-98: Theorems 3.3 (2a, 2b, 2d, 2f)
    • Pp. 113-114: Itō Isometry (2a, 2b, 2d, 2f)
    • Pp. 128-130: Questions 6 & 7 (2a, 2b, 2d, 2f)
    • Pp. 132-137: Questions 10-12 (2a, 2b, 2d, 2f)
    • Pp. 146-147: Question 19 (2a, 2b, 2d, 2f)
    • Pp. 186-188: Definition 4.1(b), Definition 4.1(f) and Theorem 4.2 (2a, 2b, 2d, 2f)
    • Pp. 221-227: Questions 1-5 (2a, 2b, 2d, 2f)
    • Pp. 233-242: Questions 12-17 (2a, 2b, 2d, 2f)
  • INV201-104-25: Which Free Lunch Would You Like Today, Sir?
    • Outcomes 3e
  • INV201-105-25: An Introduction to Computational Risk Management of Equity-Linked Insurance, Feng, 2018 (sections 1.2-1.3, 4.7 & 6.2-6.3)
    • Outcomes 3f, 3g
  • INV201-106-25: Variable Annuity Volatility Management: An Era of Risk-Control
    • Outcomes 3f, 3g
  • INV201-108-25: Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk
    • Outcomes 3f, 3g
  • INV201-107-25: It's RILA time: An introduction to registered index-linked annuities (excluding Appendices)
    • Outcomes 3g
  • INV201-109-25: Investment Instruments with Volatility Target Mechanism
    • Outcomes 3h