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Showing posts from January, 2018

### Role of Generalised Linear Model in non-life pricing Phase3

Phase1: http://www.actuarysense.com/2018/10/role-of-generalised-linear-model-in-non.html
Phase2: http://www.actuarysense.com/2018/11/role-of-generalised-linear-model-in-non.html So we know that the purpose of GLM is to find the relationship between mean of the response variable and covariates.

Linear Predictor: Let’s denote it with, “η” (eta). So, linear predictor is actually a function of covariates. For example, in the normal linear model where function is Y = B0 + B1x. So linear predictor will be η = B0 + B1x. Always note that linear predictor has to be linear in its parameter. In this case parameters are B0 and B1. But still the question is how I came up with B0 + B1x as a function? First of all, note that broadly there are two types of Covariates. 1. Variables: It takes the numerical value. For example: age of policyholder, years of ex…

### Effective Interest rates vs Nominal rates vs Force of Interest

What exactly is Effective interest rate? The Effective interest rate over a given time period is the amount of interest a single initial investment will earn at the end of time period.
We will clear now it in detail.
1.Effective annual interest had interest paid once at the end of each year. 2.Effective annual Discount had interest paid once at the start of each year.
So, what will happen if interest paid is not once in a measurement period, then there comes a Nominal Rate.
Nominal is used where is interest is paid more (or less) frequently than once per measurement period.
Application of Nominal rate in real life: Bank accounts normally use nominal rates. They quote the annual interest rate but interest is actually added at the end of each month. Thus, here interest is paid more frequently than once per unit time year.
8 points for Interest Rates: Nominal and Effective
1) Here is the notation; i(p) = Nominal rate of interest convertible pthly or compounded pthly (we meant to say that inter…

### Comprehensive Study on Interest Rates and Discount Rates

Comprehensive Study on Interest Rates and Discount RatesFollow us on LinkedIn : Actuary Sense

1. Interest Rates are the Fundamental Part of the Actuarial Work. 2. In What Situations will Banks act as a Borrower?
- accepts money from savers - issues own shares to investors - it sells Fixed interest Securities
So, how does a lender charge interest rates. Let’s see 2 Scenarios: Scenario 1:If you lend money to US government and to a Businessman, then you will probably demand a higher rate of interest from businessman as he is more likely not to repay the loan or interest amount. Scenario 2: If a lender expects higher inflation over the term of loan, it may demand higher rate of interest to increase its real return
INTEREST: 1.Simple Interest: Here the interest once credited, does not itself earn further interest. So, the accumulation factor will be: (1+ni) = here “n” represents no. of years and “i” represents simple interest rate per annum.
This is not the right…

### Key Points of Financial Mathematics- Cashflow Models

1. Net Cashflow = Inflow - Outflow

2. Theory Viewpoint of Continuously Payable Cashflow = We say this thing when cashflows are paid
very Frequently. Ex= daily or weekly.
We do this because mathematics used to investigate these cashflows is sometimes become easier when we use continuous rather than at regular intervals.

3. Where there is uncertainty about Amount or Timing of Cashflows. An actuary can assign probabilities to both the amount and existence of cashflow.

Main difference between CT1 and CT5 is that we calculate Present value in CT1 because we assume that amount will definitely come, so we won't consider probability.
But in CT5 we calculate Expected Present Value because here probabilities are assigned with corresponding future cashflows too.

4. Zero Coupon Bond: When a Bond is issued at a discount and matures at Par Value. The difference between issue price and redemption price is the interest that…

### Pension Plans: DB vs DC

Broadly there are three sources of Retirement Income:    1.Government Programs (such as Social Security Benefits)    2.Employer Programs (such as Pensions)    3.Personal Savings
1.Governmental Programs: Under this program, there are Social security Benefits (Social Security benefits are paid out monthly to retired workers and their spouses who have, during their working years, paid into the Social Security system) Medicare and Medicaid. Difference between Medicare and Medicaid is that, Medicare is a federal program that provides health coverage if you are 65 or older or have a severe disability, no matter your income. Medicaid is a state and federal program that provides health coverage if you have a very low income
2.Employer Contributions: For example: Defined Contribution plans, Defined Benefits plan etc. which we will discussed shortly.

3.Personal Savings: such as Personal investments.
Now Let’s …

### Term structure of interest Rates : Theories Explained

Term Structure of Interest Rates: The term structure of interest rates, also called the yield curve, is a graph that plots the yields of similar-quality bonds against their maturities, from shortest to longest
Important Notes: ·The graph that plots coupon rates against a range of maturities -- that graph is called the spot curve. ·The graph that plots yields against a range of maturities – that graph is called the Yield curve. So, what is the difference between coupon rates and yield rates? - Yield rate is the interest earned by the buyer on the bond purchased, and is expressed as a percentage of the total investment. Coupon rate is the amount of interest derived every year, expressed as a percentage of the bond’s face value.Yield rate and coupon rate are directly correlated. The higher the rate of coupon bonds, the higher the yield rate.
As you know that the interest rate will not remain same as the markets are dynamic and const…

### Derivatives:Forwards and Futures

Before understanding what is derivative, let’s learn what is underlying asset. Underlying asset: Underlying asset can be real asset such as commodities, gold etc or financial assets such as index, interest rates etc.