Fall 2021 - ACMA 440 D100

Overview

• Course Times + Location:

Sep 8 – Dec 7, 2021: Mon, 9:30–10:20 a.m.
Burnaby

Sep 8 – Dec 7, 2021: Wed, 8:30–10:20 a.m.
Burnaby

• Exam Times + Location:

Oct 13, 2021
Wed, 5:30–7:20 p.m.
Burnaby

Nov 17, 2021
Wed, 5:30–7:20 p.m.
Burnaby

Dec 18, 2021
Sat, 8:30–11:30 a.m.
Burnaby

• Prerequisites:

ACMA 340 with a minimum grade of C.

Description

CALENDAR DESCRIPTION:

Advanced actuarial models and their application to insurance and financial risks. Introduction to stochastic calculus: Ito's lemma, risk neutrality. Fundamental theorems of asset pricing. Black-Scholes-Merton partial differential equations. Exotic options. Monte Carlo methods. Advanced option pricing models. Implied volatility. Actuarial applications. Covers part of the syllabus for Exam IFM of the Society of Actuaries and Exam 3F of the Casualty Actuarial Society. Quantitative.

COURSE DETAILS:

Some classes will take place in lieu of the tutorial session. These will be announced during the first lecture of the semester.

Outline:

This course covers financial and actuarial models and their applications to insurance and financial risks. The topics covered include:

• The Black-Scholes-Merton Model : The Lognormal Distribution, Assumptions of the Black-Scholes-Merton Model, The Black-Scholes-Merton Formula, Option Greeks.
• Elementary Stochastic Calculus : Probability Theory, Stochastic Process, Martingale, Markov Process, Brownian Motion, Stochastic Differential Equations, Ito’s Lemma.
• The Black-Scholes-Merton Equation : Differential Equation and Valuation Under Certainty, The Black-Scholes-Merton Equation, Finite Difference Approximation, The Explicit Finite Difference Method, The Implicit Finite Difference Method, The Crank-Nicolson Method
• Mean-Variance Portfolio and Asset Pricing : Mathematics of Portfolios, Diversification, Mean-Variance Theory, Capital Asset Pricing Model, Arbitrage Pricing Theory
• Risk Neutrality and Fundamental Theorems of Asset Pricing : Intuition Behind Risk-Neutral Pricing, Risk-Neutral Pricing and the Binomial Model, Risk-Aversion and Marginal Utility, First-Order Condition for Portfolio Selection, Change of Measure and Change of Numéraire, The Girsanov Theorem, Fundamental Theorems of Asset Pricing
• More on Exotic Options: Asian Options, All-or-Nothing Options, Barrier Options, Monte Carlo Simulation.
• Advanced Option Pricing Models : Measurement and Behaviour of Volatility, Autoregressive Conditional Heteroskedasticity, Generalized ARCH, The Cox Model, The Merton (1976) Model, The Heston (1993) Model, The Bates (1996) Model, The Heston and Nandi (2000) Model
• Implied Volatility and Empirical Issues : Implied Volatility, Volatility Smiles, Hedging in the Presence of Volatility Smiles, Empirical Facts on Equity Volatility Smiles, Model Calibration
• Actuarial Applications : Applications to Life Insurance, Applications to P&C Insurance, Equity-Linked Insurance & Annuities, Pension Funding, Asset-Liability Management.

This course is accredited under the Canadian Institute of Actuaries (CIA) University Accreditation Program (UAP). Details of required courses and grades at Simon Fraser University are available here (https://www.cia-ica.ca/membership/university-accreditation-program-home/accredited-universities/accredited-university-detail?pav_universityid=236ca8c4-60e5-e511-80b9-00155d111030).

In addition to the specific university’s internal policies on conduct, including academic misconduct, candidates pursuing credits for writing professional examinations shall also be subject to the Code of Conduct and Ethics for Candidates in the CIA Education System and the associated Policy on Conduct and Ethics for Candidates in the CIA Education System. For more information, please visit Obtaining UAP Credits (https://www.cia-ica.ca/membership/university-accreditation-program-home/information-for-candidates/obtaining-uap-credits).

• Assignments 10%
• Term Project 10%
• Midterms 40%
• Final Exam 40%

NOTES:

The pass mark is 50%. The final grade will be allocated according to the student’s achievement in the course. Under no circumstances will late assignments be accepted.

All above grading is subject to change.

Students are expected to take responsibility for their learning. To assist students in understanding scholarly expectations,
the following actions are examples of violations of the Student Academic Integrity Policy. Please note that this list is not
exhaustive.

• Plagiarism
• Submitting shared work as individual work (i.e, collusion)
• Submitting an assignment or paper more than once (i.e, cheating)
• Cheating during an exam: Using any device/mobile phone to receive or share information during the exam
• Submitting a purchased assignment or essay (i.e, contract cheating)
• Falsifying documents (e.g., Doctor’s note) to gain an advantage Accessing exam information from an unauthorized source (i.e., pay to pass)

Materials

Derivatives Markets, 3rd ed. Author: McDonald, R.L. (2013). Publisher: Pearson.
Chapters 12-14, 18-25, Appendices B and C.

eBook ISBN: 9780134234960
Book ISBN: 9780321543080

Options, Futures, and Other Derivatives. Hull, J. C. (2006). Pearson. Chapters 14, 15, 19, 20, 28, 31.

eBook ISBN: 9780134234939
Book ISBN: 9780133456318

Stochastic Calculus for Finance II: Continuous-Time Models. Shreve, S. E. (2004). Springer. Chapters 3-5, 11

Hardcover ISBN: 978-0-387-40101-0
Softcover ISBN: 978-1-4419-2311-0

Volatility and Correlation: The Perfect Hedger and the Fox, 2nd ed. Rebonato, R. (2005). Wiley. Chapters  6-9, 13, 14

Book available on-line through the SFU Library

eBook ISBN: 978-0-470-09140-1
Hardcover ISBN: 978-0-470-09139-5

Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit. Brigo, D. & Mercurio, F. (2007). Springer. Chapters 1, 3.

Investment Guarantees: Modeling and Risk Management for Equity-linked Life Insurance. Hardy, M. (2003). Wiley. Chapters 1, 8, 13.

Students with Disabilities:
Students requiring accommodations as a result of disability must contact the Centre for Accessible Learning 778-782-3112 or csdo@sfu.ca

Tutor Requests:
Students looking for a tutor should visit hhttps://www.sfu.ca/stat-actsci/all-students/other-resources/tutoring.html. We accept no responsibility for the consequences of any actions taken related to tutors.