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Quantitative MethodsModule 6 of 11

Simulation Methods

4

Concepts

2

Formulas

1

Decisions

3

Quiz Questions

Key Concepts

4 concepts covered in this module.

Lognormal Distribution

If ln(X) is normally distributed, X follows a lognormal distribution. Bounded below by 0 — natural for asset prices.

Continuous Compounding

If rcc is normally distributed, then the price relative (1+R) is lognormally distributed.

Monte Carlo Simulation

Uses random number generation to simulate thousands of scenarios. Useful when analytical solutions are impossible.

Bootstrapping

Resampling with replacement from historical data. Does not assume any particular distribution.

Formulas

2 essential formulas for this module.

Lognormal Price

ST = S0 × ercc×T

Where: rcc = continuously compounded return, T = time

CC Return from Prices

rcc = ln(ST / S0)

Where: ln = natural logarithm

Decision Frameworks

1 decision frameworks to guide your analysis.

When to use Monte Carlo vs Bootstrapping?

  • Monte Carlo: when you have a model/distribution to simulate from
  • Bootstrapping: when you want to let historical data speak without distributional assumptions

Mind Map

Visual overview of how concepts connect in this module.

Simulation Methods
Lognormal Distribution
ln(X) ~ Normal
Bounded below by 0
Right-skewed
Models asset prices
Monte Carlo
Random number generation
Thousands of trials
Model-dependent
VaR, option pricing
Bootstrapping
Resample with replacement
No distribution assumed
From historical data
Standard error estimation

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Portfolio Mathematics

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Estimation and Inference