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Paper / 2025SMQ / 232932269188713

Confidence intervals for empirical convergence rates of randomised quasi-Monte Carlo, with applications to option pricing

Giacomo Case

monte carlo simulation / numerical methodsResource overview

Confidence intervals for empirical convergence rates of randomised quasi-Monte Carlo, with applications to option pricing

Paper2025

by Giacomo Case

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Suggested foundations for monte carlo and numerical simulation and options and derivatives pricing. Specialist prerequisites vary by paper.

Laws of Large Numbers and the Central Limit Theorem
Understand convergence, sampling error and confidence intervals.
Random Number Generation
Generate reproducible samples and distinguish randomness from model assumptions.
The Binomial Model
Build replication and risk-neutral probabilities in a tractable model.
Market Model and Risk-Neutral Valuation
Distinguish pricing probabilities from physical forecasts.

Monte Carlo Option Pricing
Turn a discounted payoff into an estimator.
Correlated Randoms and Low-Discrepancy Sequences
Study dependence and alternatives to independent sampling.
The Black-Scholes PDE, Formula and Implied Volatility
Connect the pricing equation, closed-form value and implied volatility.

From martingales to option pricing
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.