CAS – P Probability
Here, I provide my summary notes of P Probability Exam of CAS. The purpose of the use is non-commercial research and/or private study. Please do not copy or distribute without permission.
Notes:
Chapter 1: Sets, Chapter 2: Combinatorics, Chapter 3: Conditional Probability (Sets), Chapter 4: Bayes’ Theorem, Chapter 5: Random Variable,
Chapter 6: Conditional Probability for Random Variable, Chapter 7: Mean, Chapter 8: Variance and Other Moments, Chapter 9: Percentiles,
Chapter 10: Mode, Chapter 11 and 15: Joint Distribution, Chapter 12 and 27 Marginal Distribution, Chapter 13 and 28: Joint Moments,
Chapter 14 and 29: Covariance, Chapter 15: Conditional Moments, Chapter 16 and 26: Uniform Distribution, Chapter 17: Double Expectation Formulas
Chapter 18 and 19: Binomial and Negative Binominal Distributions, Chapter 20: Poisson Distribution (Discrete),
Chapter 21: Exponential Distribution (Continuous), Chapter 22: Normal Distribution (Continuous), Chapter 23: Central Limit Theorem, Chapter 24: Order Statistics
CAS – Financial Mathematics
Here, I provide written solution to Financial Mathematics (FM) example problems of CAS. The purpose of the use is non-commercial research and/or private study. Please do not copy or distribute without permission.
For official sample questions, please check out the official website of Society of Actuaries and the Casualty Actuarial Society.
Written Solutions:
Questions 1-84, Question 86-117, Question 119-170, Question 171-260, Question 261-309, Question 311-317, Question 319-325, Question 327-385
Duration Mismatch
In theory, durations of assets and liabilities should match. If a company’s duration gap is zero, then the company is not affected by (is immunized against) interest rate risk. For insurance companies, the duration of liabilities is normally provided by actuaries, while duration of assets is handled by the investment department. Duration mismatch, as known as liquidity mismatched, is one of the major Asset-Liability Mismatches besides currency mismatch and interest rate mismatch in Asset and Liability Management (ALM).
Note can be found here: Duration Mismatch
IBNR and Chain Ladder Method
Claim Reserves are composed of Reported but Not Settled (RBNS) Claim Reserve and Incurred but Not Reported (IBNR4) Claim Reserve. Here we focus on using Chain Ladder Method (CLM) to estimate the IBNR claim reserve.
Note can be found here: IBNR and Chain Ladder Method
Interest Rate Curve
Here I provide an excel template for interest rate curve calculation. Raw data is collected from ChinaBond public website. Interest rate calculation is based on “Chinese Government Official Document Guide”. Formulas are all based on “Solvency Supervision Rules No. 3 for Insurance Companies: Life Insurance Contracts Article 19 of the Liability Assessment stipulates”.
Excel template can be downloaded here: Interest_Rate_Curve.xlsx
Benefit Obligation
Here, I provide an excel sample of benefit obligation calculation. In this example, Life table is United States, 2021, Life Table, retirement age is assumed to be 65, there are assumed to be no spouse and childern benefits, and no contribution.
This excel sample does not reflects any company’s real business model, only for vba code illustration.
Excel template can be downloaded here: Obligation_VBA.xlsm
VaR and Expected Shortfall (ES)
Value at risk (VaR) and expected shortfall (ES) provide a number that can summarize the total risk of a portfolio, which can answer the simple question of “how bad can it be tomorrow” or “How much can I loss tomorrow?” In this paper, we provide examples to calculate the 1-day 99% VaR for a portfolio using simulation method and variance-covariance approach. The paper also provides corresponding python, matlab, and R code.
Paper can be downloaded here: VaR and ES