# Value at Risk - Ch.12: Monte Carlo Methods

#1

Reading Source: Textbook - Value at Risk

Topics Covered in this Reading:

• Why Monte Carlo Simulations?
• Simulations with One Random Variable
• Simulating a Price Path
• Creating Random Numbers
• The Bootstrap
• Computing VaR
• Risk Management and Pricing Methods
• Speed Versus Accuracy
• Accuracy
• Acceleration Methods
• Simulations with Multiple Variables
• From Independent to Correlated Variables
• Number of Risk Factors
• Deterministic Simulation
• Choosing the Model

Value at Risk - Ch.12: Monte Carlo Methods
#3

Hi, I’m having trouble understanding the “curse of dimensionality”, and how Monte Carlo simulation helps address this issue.

Any thoughts? Are there any legitimate reasons for us to not use Monte Carlo methods?

#4

Hi Shy_Guy,

I think this website might help:
https://www.lumina.com/blog/how-monte-carlo-simulation-fights-the-curse-of-dimensionality

My understanding is as follows.

The curve of dimensionality occurs when you’re trying to solve mathematical equations with many variables. As the number of variables increases, the equation becomes significantly more complex and solving the equation can become near impossible.

Monte Carlo simulation takes an entirely different approach to solve the equation - Because it’s essentially a giant approximation. The benefit is that it can work even when there’s a significant amount of variables.

I think a big issue with Monte Carlo simulation is that it requires significant computing power, which could be quite costly.

However, as mentioned in the reading, when using Monte Carlo simulation we need to consider the tradeoff between speed and accuracy.

Hope this helps!

#5

Very helpful

#6

Hi, when computing VAR using Monte Carlo, we want to create random variables Ɛ so that we can calculate stock prices. We then use the Cholesky Decomposition to generate correlated variables. Do we want correlated variables? What is the difference between correlated and uncorrelated variables in terms of generating a stock price?

#7

@beyoncepadthai

I have come across this idea somewhere, but I can’t remember where.

I think in REALITY, stock prices do have correlation. So, if I know the change in the stock price, Ɛ, today… there would be a correlation on the change in the stock price tomorrow. It is unlikely to be completely uncorrelated. For example, the odds of a stock increasing by 30% today and decreasing by 25% tomorrow is probably unlikely. But I think this remains a topic of research.

So perhaps in REALITY, if we were trying to model stock prices, we may want some level of correlation in the day-over-day stock price changes, but I think this can get complex, so it may be often ignored.

Can anyone remember what the correlation between day-over-day stock price changes is? I thought it was like autocorrelation or something