@quantfinancetogo: ➡️ Quantitative Finance from Scratch, part 17: the Monte Carlo simulation. The future is uncertain, so a Monte Carlo simulation makes many random assumptions about it. Every run draws another scenario, every scenario becomes a path, and from all the paths you read off what matters: the typical outcome, a good case, a bad case and the chance of a loss. Our example is simulated with assumed numbers: $10,000 over 30 years, an average return of 8% a year and swings of 20% a year, each year's growth drawn from a bell curve. 10,000 runs give 10,000 possible futures: Typical (the median): $60,814 Bad case: 1 in 10 ends below $14,636 Good case: 1 in 10 ends above $246,456 Chance of a loss after 30 years: 5% (500 of 10,000 paths) Average: $111,469, above the median because a few lucky paths pull it up (volatility drag, part 9) More runs give more precise numbers, with the square root rule from part 3: 100 times the runs, 10 times the precision. Where it is used: the Basel market risk rules let supervisors permit bank risk models based on Monte Carlo simulation. It is also used to value complex options and for retirement modeling. Sources: N. Metropolis and S. Ulam, "The Monte Carlo Method", Journal of the American Statistical Association 44(247), pages 335 to 341 (1949). N. Metropolis, "The Beginning of the Monte Carlo Method", Los Alamos Science, Special Issue 1987, pages 125 to 130. This video is for education only, and nothing in it is financial advice. #quantfinance #montecarlo #simulation #finance #python

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Thursday 08 October 2026 12:27:57 GMT