Penetapan harga opsi Black-Scholes

Opsi adalah derivatif yang paling luas digunakan di dunia untuk membantu mengelola risiko harga aset. Pada latihan ini Anda akan menetapkan harga opsi call Eropa pada saham IBM menggunakan rumus penetapan harga opsi Black-Scholes. Data IBM_returns telah dimuat di workspace Anda.

Pertama, Anda akan menghitung volatilitas sigma dari IBM_returns, sebagai simpangan baku yang dianualkan.

Selanjutnya Anda akan menggunakan fungsi black_scholes(), yang dibuat untuk latihan ini dan latihan berikutnya, untuk menilai opsi pada dua tingkat volatilitas yang berbeda: sigma dan dua kali sigma.

Harga strike K, yaitu harga di mana investor memiliki hak (namun bukan kewajiban) untuk membeli IBM, adalah 80. Suku bunga bebas risiko r adalah 2% dan harga spot pasar S adalah 90.

Anda dapat menemukan kode sumber fungsi black_scholes() di sini.

Latihan ini adalah bagian dari kursus

Manajemen Risiko Kuantitatif dengan Python

Petunjuk latihan

Hitung volatilitas IBM_returns sebagai simpangan baku sigma yang dianutkan (Anda menganualkan volatilitas di Bab 1).
Hitung harga opsi call Eropa Black-Scholes value_s menggunakan fungsi black_scholes() yang tersedia, ketika volatilitas adalah sigma.
Selanjutnya temukan harga opsi Black-Scholes value_2s ketika volatilitas menjadi 2 * sigma.
Tampilkan value_s dan value_2s untuk meninjau bagaimana harga opsi berubah seiring peningkatan volatilitas.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Compute the volatility as the annualized standard deviation of IBM returns
sigma = np.sqrt(____) * IBM_returns.____

# Compute the Black-Scholes option price for this volatility
value_s = black_scholes(S = 90, X = 80, T = 0.5, r = 0.02, 
                        sigma = ____, option_type = "call")

# Compute the Black-Scholes option price for twice the volatility
value_2s = ____(S = 90, X = 80, T = 0.5, r = 0.02, 
                sigma = ____, option_type = "call")

# Display and compare both values
print("Option value for sigma: ", ____, "\n",
      "Option value for 2 * sigma: ", ____)

Edit dan Jalankan Kode

Latihan ini adalah bagian dari kursus

Manajemen Risiko Kuantitatif dengan Python

SkillTag.level.advancedSkillTag.label

4.8+

Mulai Kursus 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: Mengukur Risiko Exercise 2: VaR untuk distribusi Normal Exercise 3: Membandingkan CVaR dan VaR Exercise 4: Ukuran risiko mana yang "lebih baik"?Exercise 5: Eksposur risiko dan kerugian Exercise 6: Seberapa besar selera risiko Anda?Exercise 7: VaR dan eksposur risiko Exercise 8: CVaR dan eksposur risiko Exercise 9: Manajemen risiko menggunakan VaR & CVaR Exercise 10: VaR dari distribusi terestimasi Exercise 11: Meminimalkan CVaR Exercise 12: Manajemen risiko CVaR dan krisis Exercise 13: Lindung nilai portofolio: mengimbangi risiko Exercise 14: Penetapan harga opsi Black-Scholes

Latihan Saat Ini

Exercise 15: Penetapan harga opsi dan aset dasar Exercise 16: Menggunakan opsi untuk lindung nilai

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: Parametric Estimation Exercise 2: Parameter estimation: Normal Exercise 3: Parameter estimation: Skewed Normal Exercise 4: Historical and Monte Carlo Simulation Exercise 5: Historical Simulation Exercise 6: Monte Carlo Simulation Exercise 7: Structural breaks Exercise 8: Crisis structural break: I Exercise 9: Crisis structural break: II Exercise 10: Crisis structural break: III Exercise 11: Volatility and extreme values Exercise 12: Volatility and structural breaks Exercise 13: Extreme values and backtesting

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