Valori estremi e backtesting

I valori estremi sono quelli che superano una soglia e servono a verificare se misure di rischio come il VaR riflettono correttamente il rischio di perdita.

Esplorerai i valori estremi calcolando il VaR al 95% del portafoglio a pesi uguali di investment bank per il 2009-2010 (ricorda che questo è equivalente a una simulazione storica dal 2010 in poi) e poi facendo backtesting sui dati del 2007-2008.

Le perdite di portafoglio 2009-2010 sono disponibili in estimate_data, da cui calcolerai la stima del VaR al 95%. Quindi trova i valori estremi che superano la stima del VaR, usando le perdite di portafoglio 2007-2008 in backtest_data.

Confronta la frequenza relativa dei valori estremi con il VaR al 95% e, infine, visualizza i valori estremi con uno stem plot.

Questo esercizio fa parte del corso

Gestione quantitativa del rischio in Python

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Istruzioni dell'esercizio

Calcola il VaR al 95% su estimate_data usando np.quantile().
Trova gli extreme_values da backtest_data usando VaR_95 come soglia di perdita.
Confronta la frequenza relativa di extreme_values con la stima VaR_95. Coincidono?
Mostra uno stem plot di extreme_values, evidenziando come le grandi deviazioni si siano raggruppate durante la crisi.

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# Compute the 95% VaR on 2009-2010 losses
VaR_95 = ____.____(estimate_data, 0.95)

# Find backtest_data exceeding the 95% VaR
extreme_values = backtest_data[____ > VaR_95]

# Compare the fraction of extreme values for 2007-2008 to the Var_95 estimate
print("VaR_95: ", VaR_95, "; Backtest: ", len(____) / len(backtest_data) )

# Plot the extreme values and look for clustering
plt.stem(extreme_values.index, ____)
plt.ylabel("Extreme values > VaR_95"); plt.xlabel("Date")
plt.show()

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Questo esercizio fa parte del corso

Gestione quantitativa del rischio in Python

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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: Stima parametrica Exercise 2: Stima dei parametri: Normale Exercise 3: Stima dei parametri: Normale asimmetrica Exercise 4: Simulazione storica e Monte Carlo Exercise 5: Simulazione storica Exercise 6: Simulazione Monte Carlo Exercise 7: Rotture strutturali Exercise 8: Interruzione strutturale della crisi: I Exercise 9: Rottura strutturale della crisi: II Exercise 10: Rottura strutturale della crisi: III Exercise 11: Volatilità e valori estremi Exercise 12: Volatilità e break strutturali Exercise 13: Valori estremi e backtesting

Esercizio in corso

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