🧮 Title: Pricing Options with Randomness: Monte Carlo Methods in Quantitative Finance Introduction: Why do we need Monte-Carlo methods? Option pricing lies at the heart of modern quantitative finance. While classical models such as the Black-Scholes formula provide closed-form solutions for simple European options, many real-world derivatives are far more complex. Examples include path-dependent options (Asian and barrier options), multi-asset options, and options with stochastic volatility or jumps. For such problems, analytical solutions are often unavailable. This is where Monte-Carlo methods become a powerful and flexible numerical tool. What is the Monte-Carlo method? The Monte Carlo method is a simulation-based numerical technique that uses randomness to approximate solutions to complex mathematical problems. In option pricing, Monte-Carlo methods work by Simulating many possible future paths of the underlying asset price. Computing the option payoff for each simulated path...