Blog posts

Understanding statistical distributions is key when working with data, as they help describe how values behave in a dataset. Different distributions are useful for modelling different types of real-world scenarios. This guide provides a brief overview of some of the most commonly used statistical distributions, along with their key properties and how to generate random samples from them using Python.

Contents:

1. Normal
2. Uniform
3. Bernoulli
4. Binomial
5. Poisson

Normal distribution

The normal distribution, also called the Gaussian distribution, is symmetric and bell-shaped, commonly used to model natural phenomena where values cluster around a central mean with a given spread.

An arithmetic progression annuity (or arithmetic gradient annuity) is a type of annuity where payments either increase or decrease by a fixed amount each period. This contrasts with a standard annuity, where payments remain constant over time. In this post, we'll explore the formulas for an arithmetic progression annuity and build a cash flow model to help illustrate how it works.

Contents:

1. Key features
2. Present value formula
3. Future value formula
4. Modelling example

Key features

An arithmetic progression annuity has the following key features:

• Initial payment - the first payment, typically denoted \( P \), is a fixed amount.
• Constant change …

In this post, we will tackle the valuation of a call option using two methods: a closed-form formula and a stochastic model. Options are a type of financial instrument that give their owner the right, but not the obligation, to buy or sell an asset at a predetermined price within a certain period. Here, we'll focus on a call option, which is a type of option allowing the holder to purchase the asset at a specific price (known as the strike price) before the option expires. Call options are commonly used in financial markets to bet on the potential increase …

In this post, we will discuss the two main types of loan repayment structures and build sample loan schedules in Python using the cashflower package.

List of content:

1. Repayment structures
2. Equal payment loan schedule
3. Equal principal loan schedule

Repayment structures

There are two main types of loan repayment structures:

• equal payment loan (annuity loan),
• equal principal loan (fixed principal).

Equal payment loan (annuity loan)

The total monthly payment is fixed (the same amount every month). Initially, a larger portion of the payment goes towards interest and a smaller portion towards the principal. Over time, as the outstanding loan balance …