Monte Carlo-simulatie

Je kunt een Monte Carlo-simulatie gebruiken van de assets in de beleggingsportefeuille van investment banks uit 2005–2010 om de 95%-VaR te bepalen.

De gemiddelde assetverliezen staan in de Numpy-array mu. De efficiënte covariantiematrix is e_cov (let op: we gebruiken hier de dagelijkse, niet de geannualiseerde variant zoals in eerdere oefeningen). Je gebruikt deze om voorbeeldpaden te maken voor assetverliezen over één dag, om zo het dagelijkse portefeuilleverlies te simuleren.

Met de covariantiematrix e_cov kunnen assetpaden onderling gecorreleerd zijn, wat een realistische aanname is.

De simulatie total_steps staat op 1440, zoals in de video. Het aantal runs N staat op 10000.

Voor elke run bereken je de cumulatieve losses, en pas je vervolgens de functie np.quantile() toe om de 95%-VaR te vinden.

Portefeuille-weights en de norm-verdeling uit scipy.stats zijn beschikbaar.

Deze oefening maakt deel uit van de cursus

Kwantitatief risicobeheer in Python

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Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Initialize daily cumulative loss for the 4 assets, across N runs
daily_loss = np.zeros((____ , N))

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Deze oefening maakt deel uit van de cursus

Kwantitatief risicobeheer in Python

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Begin de cursus gratis

Risk management begins with an understanding of risk and return. We’ll recap how risk and return are related to each other, identify risk factors, and use them to re-acquaint ourselves with Modern Portfolio Theory applied to the global financial crisis of 2007-2008.

Exercise 1: Welcome!Exercise 2: Portfolio returns during the crisis Exercise 3: Asset covariance and portfolio volatility Exercise 4: Risk factors and the financial crisis Exercise 5: Frequency resampling primer Exercise 6: Visualizing risk factor correlation Exercise 7: Least-squares factor model Exercise 8: Modern portfolio theory Exercise 9: Practice with PyPortfolioOpt: returns Exercise 10: Practice with PyPortfolioOpt: covariance Exercise 11: Breaking down the financial crisis Exercise 12: The efficient frontier and the financial crisis

Now it’s time to expand your portfolio optimization toolkit with risk measures such as Value at Risk (VaR) and Conditional Value at Risk (CVaR). To do this you will use specialized Python libraries including pandas, scipy, and pypfopt. You’ll also learn how to mitigate risk exposure using the Black-Scholes model to hedge an options portfolio.

Exercise 1: Measuring Risk Exercise 2: VaR for the Normal distribution Exercise 3: Comparing CVaR and VaR Exercise 4: Which risk measure is "better"?Exercise 5: Risk exposure and loss Exercise 6: What's your risk appetite?Exercise 7: VaR and risk exposure Exercise 8: CVaR and risk exposure Exercise 9: Risk management using VaR & CVaR Exercise 10: VaR from a fitted distribution Exercise 11: Minimizing CVaR Exercise 12: CVaR risk management and the crisis Exercise 13: Portfolio hedging: offsetting risk Exercise 14: Black-Scholes options pricing Exercise 15: Options pricing and the underlying asset Exercise 16: Using options for hedging

In this chapter, you’ll estimate risk measures using parametric estimation and historical real-world data. You'll then discover how Monte Carlo simulation can help you predict uncertainty. Lastly, you’ll learn how the global financial crisis signaled that randomness itself was changing, by understanding structural breaks and how to identify them.

Exercise 1: Parametrische schatting Exercise 2: Parameterschatting: Normaal Exercise 3: Parameterschatting: Scheve Normaalverdeling Exercise 4: Historische en Monte Carlo-simulatie Exercise 5: Historische simulatie Exercise 6: Monte Carlo-simulatie

Huidige oefening

Exercise 7: Structurele breuken Exercise 8: Crisis structurele breuk: I Exercise 9: Structurele breuk tijdens de crisis: II Exercise 10: Crisis structurele breuk: III Exercise 11: Volatiliteit en extreme waarden Exercise 12: Volatiliteit en structurele breuken Exercise 13: Extreme waarden en backtesten

It's time to explore more general risk management tools. These advanced techniques are pivotal when attempting to understand extreme events, such as losses incurred during the financial crisis, and complicated loss distributions which may defy traditional estimation techniques. You’ll also discover how neural networks can be implemented to approximate loss distributions and conduct real-time portfolio optimization.

Exercise 1: Extreme value theory Exercise 2: Block maxima Exercise 3: Extreme events during the crisis Exercise 4: GEV risk estimation Exercise 5: Kernel density estimation Exercise 6: KDE of a loss distribution Exercise 7: Which distribution?Exercise 8: CVaR and loss cover selection Exercise 9: Neural network risk management Exercise 10: Single layer neural networks Exercise 11: Asset price prediction Exercise 12: Real-time risk management Exercise 13: Wrap-up and Future Steps