Overview

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. This course is accredited under the University Accreditation Program of the Canadian Institute of Actuaries. 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
• Interest Rate Modelling and Derivatives : Introduction to Interest Rate Derivatives, Interest Rate Derivatives and the BSM Approach, Continuous-Time Short-Rate Models (Rendelman-Bartter Model, Vasicek Model, Cox, Ingersoll and Ross Model), Interest-Rate Trees (Black, Derman and Toy Model, Hull and White 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) for the 2019-2020 academic year. Achievement of the established exemption grade in this course may qualify a student for exemptions from writing certain preliminary exams. Please note, a combination of courses may be required to achieve a single exemption. Please see http://www.cia-ica.ca/membership/uap for full details.

Grading

Materials

REQUIRED READING:

RECOMMENDED READING: