In many places we can see the figure of the Monte Carlo simulation, predicting stock prices, predicting the biggest losses of stocks, predicting the price of structural bonds.
First of all, the Monte Carlo simulation is a statistical method that is used to simulate large amounts of data. If you look directly at this sentence, you will be immediately blown away, shouting statistical methods, why do you simulate large amounts of data?
The first is why: why is it called a Monte Carlo simulation?
The Monte Carlo simulation was a statistical method proposed by American mathematicians such as John Newman and Ulam during World War II to solve the problem of neutron random scattering of fissile materials in the development of atomic bombs. The method was given the codename Monte Carlo because the work at that time was classified. Monte Carlo was a very famous casino in Monaco at the time, and gambling was based on probability, so it was named after the casino and is easy to remember.
The second reason is: what exactly is the Monte Carlo simulation and why is it used in finance?
If the closing price of the company's stock was 10 bucks last night, would you like to know what the price of the company's stock will be 100 days from now?
Today's stock price is equal to yesterday's stock price + 0.2
Or let me be a little bit academic, using a little formula, that is St = St-1 + 0.2, which means that today is twice as much as yesterday, and I know yesterday's closing price, so I can know today's closing price, and then I can find the closing price after 100 days.
Let's not forget that stocks jump up and down like monkeys, so there's a big surprise every day, which we call stock price fluctuations. I don't know how big the stock price fluctuates every day, so it's random, so it's natural to think there's a random item in this push:
Today's stock price is equal to yesterday's stock price plus today's stock price fluctuation.
The mathematical representation is that St = St-1 + e, and e represents the fluctuation of the daily stock price, which is a random number, and the so-called random number is the value of the uncertain number. Now we just need to use a statistical method that is best understood, which is the method of issuing a random number, and I can move forward. For example, if the initial stock price of a million shares is S0 = 10, if at this point I issue the first random number, e1 = 0.3, then S1 = 10.3, I move forward one step, I issue another random number e2 = -0.4, S2 = 9.9, and by the same method, I move forward one million shares after 100 days, and I have a better way of finding the price of a million shares, and that's a good way to find this 100-day stock price movement.
So I'm going to simulate a path that's not very reliable, which is fine, I'm going to simulate a path that's not very reliable, I'm going to simulate a path that's 1,000, and then on the 100th day, I'm going to take a knife, and I'm going to find that there's 1,000 data, and there's a lot of data, and the simplest way that I can do that is I'm going to find an average, and that's a fairly reliable estimate of the value of the stock.
Of course, the distribution of random numbers is not completely irregular, and it is common for Monte Carlo simulations to assume the distribution of random numbers based on the characteristics of historical data. For example, if we find that stock price fluctuations still correspond to the most common distribution (the normal distribution), then we generally assume that e also obeys the normal distribution, so that we can tell the computer how to distribute random numbers.
Third, why is the Monte Carlo simulation so innovative in financial research?
The greatest thing about Monte Carlo simulations is that they make a social science problem look like a natural science. The most important thing to study in the natural sciences, like chemistry and physics, is data, because you can lock yourself in a lab, and you have that little car crash 10,000 times, and you have 10,000 data, and the smallest changes in the variables can be studied in a comprehensive way. But finance is not a social science that can do experiments, and 100 days go by, and only 100 days go by, and you can't go back again, because time can't go back again.
Of course, we can also see from the above analysis that it has the advantage that it is not limited to historical data, because the data it gets is simulated, not historical data, so the analysis can be more comprehensive. For example, if you do research with only historical data, it is impossible to predict that there will be a subprime crisis, because it has never happened in history, but with the simulation method you can get a lot of data that has not happened in history, you can make a more comprehensive prediction.
This is our introduction to the Monte Carlo simulation, of course with the development of information technology and the comprehensiveness of the division of labor, we financial analysts often do not need to model ourselves, but we still need to have some knowledge of the principles of the model in order to know the scope of each model's inapplicability, where the risks are, in order to make better predictions about the future.
Translated from the German