Year 4 (Midterm)
I SCMA459 Investment Science II
Introduction to Derivatives
Forward Contracts
Futures Contracts
Options
Payoffs
Examples
Introduction to Derivative Pricing
Arbitrage opportunity
Forward price
Put-Call parity for European options
Upper and lower bounds on European option prices
Call option
Put option
Upper and lower bounds on American option prices
Call option
Put option
Option Strategies
Single-Period Binomial Model
Notations
Risk-Neutral Probability (Martingale)
Replicating Porfolio
Value of portfolio
Arbitrage portfolio
Attainable payoff
Risk Neutral Pricing Formula
Multi-Period Binomial Model
Risk-Neutral Probability (Martingale)
Risk Neutral Pricing Formula
II SCMA470 Risk Analysis and Credibility
Basic Probability Concepts
Moments
Moment Generating Function (MGF)
Probability Generating Function (PMF)
Model Fitting
Pearson chi-square goodness-of-fit statistic
Loss Distributions
Exponential distribution
Gamma distribution
Lognormal distribution
Pareto distribution
Deductibles and Reinsurance
Deductibles
Excess of Loss Reinsurance
Mixed Distribution
Collective Risk Model
Conditional Expectation and Variance
Compound Distribution
Compound Poisson,
\(\mathcal{CPN}(\lambda,F_X)\)
Compound negative binomial,
\(\mathcal{CNB}(k,p,F_X)\)
Compound binomial,
\(\mathcal{CBN}(n,p,F_X)\)
Effects of Reinsurance
Proportional reinsurance
Excess of loss reinsurance
Approximations
Normal approximation
Translated gamma
Premium Calculation
III SCMA479 Survival Analysis
Introduction to Survival Models
Hazard rate function
Exponential function
Estimating Lifetime Distribution
Study types
Nonparametric method
Empirical df
Greenwood’s formula
Parametric Method
Uncensored data
Censored data
Cox’s Proportional Hazard Model
Parametric Regression Model
Semi Parametric Model: Cox Proportional Hazard Model
Cox Partial Likelihood
IV SCMA477 Life Contingencies II
Benefit Reserves
Recursion Relation
Retrospective Approach
Models with Expenses
Thiele’s Differential Equation
UNOFFICIAL notes
UNOFFICIAL notes
2025-09-22
Year 4 (Midterm)
SCMA 459 Investment Science II
SCMA 470 Risk Analysis and Credibility
SCMA 479 Survival Analysis
SCMA 477 Life Contingencies II