An annuity refers to a series of equal cash flows that occur periodically such as monthly or annually. For example, an investment that gives you fixed monthly payments for a specified period. There are two types of annuities, namely, regular annuities and annuities due. In a regular annuity, the first cash flow occurs at the […]

# Financial Mathematics

## 30e/360 Day Count Convention (Eurobond Basis)

In different bond markets and instruments there are different day count conventions for calculating accrued interest. These day count conventions depend on the location, currency, market and type of instrument. A day count convention is a fraction with the numerator as 30 or actual number of days to be taken in a month, and the […]

## Role of a Quantitative Modeler

A quantitative modeler is someone who works in finance and uses numerical and quantitative techniques to build complex quantitative models. They are commonly known as quants or quantitative analysts. The typical industries that hire quantitative modelers include investment banking, risk management, portfolio optimization, and derivatives pricing and hedging. Broadly speaking, quantitative modelers apply mathematics in […]

## Calculate Historical Volatility Using EWMA

Volatility is the most commonly used measure of risk. Volatility in this sense can either be historical volatility (one observed from past data), or it could implied volatility (observed from market prices of financial instruments.) The historical volatility can be calculated in three ways, namely: Simple volatility, Exponentially Weighted Moving Average (EWMA) GARCH One of […]

## How to Use the Rule of 72 Formula

In finance, rule of 72 is an important approximation rule that is used to quickly estimate the number of years it will take for an investment double in value at a given interest rate. According to this rule, the interest rate multiplied by the number of years it will take for the investment to double […]

## Correlation and Covariance

Both correlation and covariance are an indicator of the relationship between two variables. They indicate whether the variables are positively or negatively related. The correlation also indicates the degree to which the two variables are related. It’s a translation of covariance into a unit-less measure that we can understand (-1.0 to 1.0). The correlation of […]

## Compute Bond Price with Zero (Spot) Rate Curve Using TI BAII+

This video demonstrates how to compute the theoretical price of a coupon paying bond using spot rates. What is the price of a 2-year bond that pays a 6% semi-annual coupon given a zero rate curve? The calculation is shown using the Texas Instruments BA II Plus Financial Calculator This video is developed by David […]

## Central Limit Theorem (Distribution of Averages)

Assume that there are n independent and identically distributed variables and each of the variables has the same probability distribution as the others and all are mutually independent. The Central Limit Theorem states that the mean of such variables will approach a normal distribution as the number of observations increases. Examples of normally distributed variables […]

## How to Select the Most Appropriate Time Series Model?

Simple Linear and Exponential Growth Models – If an analyst looks at a time series plot graph he/she may see patterns exhibiting possible linear or exponential growth relationship to the dependent variable. Serial correlation of the error terms must not be present and the Durbin Watson test can test for this. Auto-Regressive Models – If […]

## Auto-Regressive Models – Random Walks and Unit Roots

This is the case of an AR time series model where the predicted value is expected to equal the previous period plus a random error: xt = b0 + xt-1 + εt When b0 is not equal to zero, the model is a random walk with a drift, but the key characteristic is a b1 […]