In the Classroom, a new video has been added to the online course 5.20. This is a quantitative finance (energy) course with a focus on Option Contracts for crude oil. This video explains the concept of risk free rate in this context. We need to learn what the risk free rate is because later in the code (in a future video) we will use the risk-free rate for finding the price of the option contract. Every option contract has a 'price' which is known as the 'premium', which we evaluate (later on) using Black Scholes. An input parameter in Black Scholes is the risk-free rate. The video explains that to find the risk-free rate we need to first check what our Option Contract is priced at. So, it is priced in US dollars because the Crude Oil is priced in US dollars. Therefore we look at the United States. Then we need to find the time-to-maturity. In our case, the Option expires 1 month from today. This is the example in our code. With this information , we use our financial source like Bloomberg. And we check the 1-month yield of the U.S, Treasury Bill. The US Government has zero risk of default (going bankrupt). Ofcourse In the real world, nothing is truly zero risk. But this is the assumption, which is widely accepted in finance. A numerical example explains what our return will be one month after we invest in this zero-risk investment vehicle.

A new video has been uploaded in the Online Course 5.20 in the Classroom. This course focuses on option contracts for crude oil, where the underlying asset is the spot price. An option contract is signed between two parties/ companies . Every option contract applies to an asset . This asset is known as “underlying”. So this course is about option contracts that have the crude oil as their underlying asset. The company that owns the option contract can exercise it until it expires. There is no obligation to exercise it. This is why it is called “option contract”. The company will exercise it only if it makes economic sense ie if it makes a profit. The video focuses on the “volatility” concept of option contracts . The video explains that the spot price of crude oil follows a probability distribution called : lognormal distribution. The attached plot, explained in the video, visualizes this concept. It shows how higher volatility (the red line) creates a much wider range of possible spot price outcomes compared to lower volatility (the green line). So a higher volatility means that in the future , the spot price of crude oil is more uncertain than if the volatility was lower. So volatility is similar to uncertainty . And it is visualized as a probability distribution that is wider. This plot shows the spot price of crude oil one year from today. One year from today this price is uncertain . The spot price of oil follows the log normal distribution . This distribution has a different shape depending on the volatility . Here we look at values for volatility of 10%, 30% and 50%. This is a fundamental plot and analysis for any quantitive finance / energy career . This specific plot has been part of multiple interviews for years . This plot is analyzed in the video using simple language. If you have any questions please contact me. I want this concept to be as clear as possible .

A new video has been added to the online course 5.20 in the Classroom. This video explains what an option chain is. An option is a contract that gives its owner the right to buy or sell an asset (it is called 'underlying asset') such as WTI crude oil (in this example) at a fixed price (called 'strike price') by a certain date when the option expires. The underlying asset is WTI Crude in this case . WTI stands for West Texas Intermediate. It is the main crude oil benchmark in the United States. When you hear "oil prices" in American news, they're usually referring to WTI. Crude oil is unrefined petroleum extracted from the ground. Its spot price is $78.5/barrel. The spot price changes every second. An option chain is a set of options having the same underlying asset. In this case, the chain has a set of 5 call options has the same underlying asset i.e. WTI Crude. So in this video WTI crude oil is trading at $78.50 per barrel. We have five options with different strike prices: $70, $75, $80, $85, and $90. I explain what these numbers mean and how they form an option chain.

If you are developing optimisation models, I'm curious what solvers do you prefer for your mathematical optimization models. Whether you're doing linear programming, mixed-integer, or nonlinear optimization.

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