Financial mathematics

2년 전

Financial mathematics, it is understood for this, a branch of mathematics that studies the quantifiable variations that occur in financial capital (contributions in money) during the course of time.

Classifications of financial mathematics
In mathematics, simple and complex financial operations are studied, the definition is as follows:

Simple: Analyze the monies that come from a single capital (Denominated interests).
Complex: Analyze the money that comes from more than one capital (Rented Rents).

Another classification is the application of the operations of the application, where depending on the temporality, there can be two main principles:

Principle of Capitalization: When I have flows to date and I want to know how much I will have in the future
Discount Principle: How much flow will I have in the future and I would like to know how much is worth today.
The purpose of being able to analyze this current, is picked up by the principle that money loses value over time, have you noticed that buying a package of chips was worth $ 200 and now it is worth $ 500 ?, some people consider it as "Inflation ", But it's not necessarily just that. There is also another factor called "Cost of Opportunity", where it says that it is what I sacrifice for having the flows in one concept and not another. Example: "You have $ 100,000 today, of which you can spend it on having a party, or else invest and in two more months, receive $ 105,000", if you choose the first option, the opportunity cost would be to stop winning $ 5,000, if you choose the second option, the opportunity cost consists of not making the celebration. Therefore financial mathematics are born to analyze flows and depending on the decision you want to make, you can add or remove this concept that we will momentarily call "Sum of inflation and opportunity cost".

All of the above, is called "Loss of value in time", and meets certain elementary principles:

Before two capitals of the same amount at different times, the one that is closest time will be preferred.
Before two capitals of different amount but at the same time, the highest amount will be preferred.
All these principles and bases are used to compare flows that by default of time can not be comparable. If you had $ 100,000 today and $ 100,000 in 2 more years, nominally they are still $ 100,000, but the value is higher today, since what you can acquire today is more than you can with the same face value in the future. Therefore, financial mathematics fulfills that role.
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financial mathematics

Financial Mathematics: Simple Financial Operations
Also called interests, they analyze the flows of a single capital, these can be simple or compound, these allow calculating the capital at a future time. In the short term and by mutual agreement, simple capitalization is used, where the basis is that future flows (called interest), do not become part of capital, the formula used is as follows:
M = c + (1 + n.i)

Financial Mathematics: Simple Financial Operations

Where:

M = Amount, which is equivalent to the final value of the capital to be evaluated.

N = Time the evaluation will last.

I = applicable interest rate.

Financial Mathematics: Complex Financial Operations
Also called rent, this concept analyzes multiple capitals and multiple time scenarios, given the complexity, this topic will be touched on another blog, but today we will indicate some topics to consider for this type of operations:

Income can be analyzed as temporary (at a certain period) or perpetual (without a defined period).
The rent can be analyzed under the modality of expired (that the payment or collection is made after a specified date) or anticipated (which is done prior to a date indicated).
The payment can be immediate or deferred (that the obligation or the right is known and it is registered today despite the fact that the payment or collection will be seen in the future).

Financial mathematics is the basis of finance in general.
Without financial mathematics there would be no valuable tools, such as the NPV, the IRR, the amortization tables for bank loans among others.

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I am being critical of the contents of this post. This post covers mostly on Time Value of Money, mathematics on compound interest on invested money and loans. This material is the basic part of financial mathematics.

Yes, financial mathematics is complex but the contents here does not touch on probability and statistics for finance/financial engineering. Financial mathematics covers more of:

  • Random Walks
  • Brownian Motion
  • Ito/Stochastic Calculus
  • Partial Differential Equations
  • Black-Scholes Model