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QUANT 9) - Coggle Diagram
QUANT 9)
9.1: Historical Simulation
Simulation def
A
parametric/closed-form approach
(ex: like using a forumla) is faster and simpler — so it's always the default unless the situation has a feature a formula can't handle -> then we use a SIMULATION
Historical Simulation
Advantages
edge = tractability/simplicity; its weakness = totally data-dependent, no ability to flex assumptions.
Applying the 4-Step Process to Historical Simulation
Application: Value at Risk (VaR) for a Long-Only Portfolio
Parametric vs. Historical VaR
with Monte Carlo, draws random numbers from a distribution the analyst chooses
Historical simulation draws its scenarios directly and only from the observed dataset, will systematically understate the portfolio's true tail risk.
Why Daily VaR Assumes a Mean Return of Zero
Basics
: pull directly from actual observed data rather than an assumed distribution
Data Deficiency Issues
Sources of Missing/Unreliable Data
historical simulation can understate risk when the data window is calm
Compensating for Data Gaps
Special Case: Fixed-Income Instruments
Why Fixed Income Needs a Different Approach
Duration and Price Volatility
9.3: Monte Carlo Simulation
Application 1: Estimating Portfolio Performance
Application 2: Valuing Financial Instruments
Benchmark Case: European Call Options
Path-Dependent Options — Asian-Style Options
Other Complex Instruments
Mortgage-backed securities (MBS)
Convertible bonds
Multivariate Monte Carlo Simulation
The Cholesky Decomposition
Basics
Monte Carlo simulation is usually conducted by simulating scenarios from an analytical distribution, such as a normal distribution.
Monte Carlo simulation doesn't sample from the past — it draws random numbers from a distribution the analyst chooses. That means she isn't limited by what actually happened in her 2-year window; she can explicitly build in a harsher assumption
9.2: Bootstrap Resampling
Bootstrapping vs. Historical Simulation
Fundamental Difference: Treatment of Data
Shared Traits with Historical Simulation
Historical simulation may be preferred over Monte Carlo simulation because Is regarded as being more intuitive and easier to explain.
Historical data
Strengths and Weaknesses of Bootstrapping
edge = flexibility/adaptability to new scenarios; its weakness = depends on assumption accuracy
Basics
pull directly from actual observed data rather than an assumed distribution
involves generating random samples from a given dataset
Resampling