*Disclaimer: The analysis presented in this article is aimed at implementing time series models on financial time series data for educational purposes only and therefore, does not constitute financial and/or investment advice. I have no positions in any of the stocks mentioned in this article and no business relationship with any company whose stock is mentioned in this article.*

The technology industry has seen a massive increase in growth over the past decade from the continuous development of technologies with increased capabilities. One of the key players in this industry is Nvidia. Known for popularizing the term “graphics processing unit”…

A technical guide to understanding modern portfolio optimization theory

- The main purpose of portfolio optimization is to maximize returns and minimize the risk of a portfolio of assets according to modern portfolio theory (Markowitz, 1952)
- For investors and asset managers, knowing how much capital needs to be allocated to a particular asset or a basket of assets can statistically make or break a portfolio
- Modern portfolio theory (Markowitz, 1952) simply formalizes and extends the concept of portfolio diversification

Portfolio optimization is the process of selecting proportions of various assets to include in a portfolio, in such a way as to…

Understand dynamics that exist between the stock market and the volatility index (VIX)

- Forecasting the price of an asset is extremely complex due to the fact that there are a plethora of endogenous and exogenous factors that could massively affect it
- Instead, investors should take a closer look at volatility which is a lot easier to forecast with a certain degree of confidence due to its mean-reverting nature
- I personally use the volatility index to strategically forecast potential market pullbacks and structure intelligent trades

Volatility in the stock market could be simply be defined as the degree of variance of…

Let’s explore the fundamental disconnect that exists between the stock market and the overall economy

- There is no direct correlation between the economy and the stock market in general
- The stock market is forward-looking while the economy is backward-looking
- The stock market doesn’t represent the economy

Learn how to use statistical methods to assess the financial risk and financial returns of an investment

- Maximizing returns while minimizing the risk associated with an investment is one of the most important tenets of quantitative finance
- An analysis of an investment return distribution is the starting point of any portfolio risk management process
- Analyzing returns distribution allows us to visualize the frequency of a given range of returns
- Risk management has become crucial for every financial institution (especially after the financial crisis in ‘08)

In quantitative finance, investment risk or financial risk can have a variety of definitions:

- The…

- Anyone can learn quantitative trading. You don’t need to have a PhD in Quantum Astrophysics to create quantitative trading systems or perform quantitative research
- The process of identifying a suitable trading strategy is identical to the scientific method: It requires creating hypotheses and making assumptions based on data to identify a statistical edge.
- Quantitative research (data mining, hypothesis testing…) always precedes backtesting trading strategies

As a trading enthusiast, I have always wondered if the best quant traders possessed predetermined trading strategies that they could use to consistently generate superior returns. I thought trading was as straightforward as solving an equation…

- Monte Carlo simulation is one of the most important algorithms in quantitative finance
- Monte Carlo simulation can be utilized as an alternative tool to price options ( the most popular option pricing model is based on the Black-Scholes-Merton formula)

Before demonstrating the implementation of the Monte Carlo algorithm, it’s important to fully comprehend the science behind it. Simply put, Monte Carlo simulation generates a series of random variables that have similar properties to the risk factors which the simulation is trying to simulate.

The simulation produces a large number of possible outcomes along with their probabilities. …

**Summary**

- Implied volatility is a key component when determining the theoretical price of a European call option
- Unlike price, implied volatility cannot be instantaneously measured. It’s an average and needs to be estimated overtime
- The Black-Scholes-Merton (1973) option pricing formula is used to determine implied volatility (implied volatility is not an input parameter for the formula, but the result of an optimization procedure given that formula)

Let’s take a look at the famous option pricing formula offered by Black-Scholes-Merton (1973):

Applied Mathematics | Quantitative Finance