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All modules
11
Quant · 3 submodules · 7 lessons · 2h 32m

Monte Carlo Methods

GBM paths, European MC pricing, standard errors, antithetics — hand-held from first path to confidence intervals.

Submodule 11.1

GBM Simulation

Path generation under risk-neutral measure.

  1. 1

    GBM Intuition

    SDE idea in words and the exact terminal solution.

    18 min
  2. 2

    Simulate Terminal Spots

    MC estimate of E[S_T] vs theory.

    24 min
  3. 3

    Multi-Step Paths

    Build a full path vector for path-dependent payoffs later.

    20 min

Submodule 11.2

Pricing & Errors

Discounted payoffs and stderr.

  1. 1

    MC European Call

    Price with discounted mean payoff + standard error.

    28 min
  2. 2

    Compare MC to Black-Scholes

    Cross-check methods; discuss bias vs variance.

    18 min

Submodule 11.3

Variance Reduction

Antithetics and ideas beyond.

  1. 1

    Antithetic Variates

    Pair Z and -Z to cut variance.

    22 min
  2. 2

    Module 10 Lab: MC Report Card

    Print BS, MC, se, CI, and error vs BS.

    22 min