Topic · Mathematics
← All topicsNumerical Methods
31 articles · 5 checkpoints · 20 deeper reads · 6 reference notes
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Computers don't store real numbers, they store close approximations with a fixed number of significant digits. That gap is invisible almost all the time, until it silently breaks a P&L reconciliation or a risk check.
Computers can't generate true randomness on demand, so every Monte Carlo simulation runs on numbers that only look random. Understanding how the illusion is built explains both why it usually works and the specific ways it can quietly fail.
How a computer finds the implied volatility that makes an option price match the market, or any other input that makes a formula hit a target, without ever solving an equation algebraically.
Two tricks for squeezing a more accurate answer out of the same Monte Carlo simulation budget, by using the randomness you already generated more cleverly instead of running more paths.
The simplest way to turn a stochastic differential equation into code: chop time into small steps, and at each one nudge the price by its drift plus a scaled random shock. Simple to implement, and simple to get subtly wrong.
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