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Questions and Answers
What is implied volatility primarily based on?
What is implied volatility primarily based on?
Which of the following statements is true regarding historical volatility?
Which of the following statements is true regarding historical volatility?
What are the considerations for sample length in estimating historical volatility?
What are the considerations for sample length in estimating historical volatility?
Why can volatility not be directly observed?
Why can volatility not be directly observed?
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How does sample frequency affect volatility estimates?
How does sample frequency affect volatility estimates?
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What may cause structural changes in volatility?
What may cause structural changes in volatility?
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Why might short sample periods be beneficial in volatility estimation?
Why might short sample periods be beneficial in volatility estimation?
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What is a potential downside of using long sample lengths for volatility estimation?
What is a potential downside of using long sample lengths for volatility estimation?
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What is the primary advantage of using daily data for estimating volatility?
What is the primary advantage of using daily data for estimating volatility?
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Why is it recommended to use multiples of three months when estimating volatility?
Why is it recommended to use multiples of three months when estimating volatility?
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Which sampling frequency is recommended for longer forecasting horizons?
Which sampling frequency is recommended for longer forecasting horizons?
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What is considered a benchmark estimator for measuring volatility?
What is considered a benchmark estimator for measuring volatility?
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What is the key challenge when estimating volatility measures?
What is the key challenge when estimating volatility measures?
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Which volatility measure is often referred to as historical volatility?
Which volatility measure is often referred to as historical volatility?
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What is a disadvantage of using daily data for volatility estimation?
What is a disadvantage of using daily data for volatility estimation?
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What does the drift term, μ, represent in the context of geometric Brownian motion?
What does the drift term, μ, represent in the context of geometric Brownian motion?
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What condition must be met for the classical estimator to be unbiased?
What condition must be met for the classical estimator to be unbiased?
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What does the average of all the squared returns measure?
What does the average of all the squared returns measure?
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Why do we tend to underestimate volatility when only considering opening and closing prices?
Why do we tend to underestimate volatility when only considering opening and closing prices?
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What does Parkinson suggest to improve the estimation of volatility?
What does Parkinson suggest to improve the estimation of volatility?
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Which of the following statements about the classical estimator is true?
Which of the following statements about the classical estimator is true?
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What happens to a stock price during the time when the market is closed?
What happens to a stock price during the time when the market is closed?
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How is the fraction of the day calculated if the market is open from 8 to 5?
How is the fraction of the day calculated if the market is open from 8 to 5?
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What is the relationship between the opening and closing prices and actual volatility when the market closes?
What is the relationship between the opening and closing prices and actual volatility when the market closes?
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What is the primary advantage of range-based measures in financial data analysis?
What is the primary advantage of range-based measures in financial data analysis?
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How does the ARCH model determine volatility?
How does the ARCH model determine volatility?
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What does the term 'heteroscedastic' refer to in financial modeling?
What does the term 'heteroscedastic' refer to in financial modeling?
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In the given time series model Rt = a + εt, what do the variables represent?
In the given time series model Rt = a + εt, what do the variables represent?
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What does the symbol σ² represent in the context of the time series model?
What does the symbol σ² represent in the context of the time series model?
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Which model is defined by the equation σt² = ω + β.εt-1²?
Which model is defined by the equation σt² = ω + β.εt-1²?
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What does the coefficient β in the ARCH model indicate?
What does the coefficient β in the ARCH model indicate?
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What does a sum of $a + b$ close to 1 indicate in terms of volatility shocks?
What does a sum of $a + b$ close to 1 indicate in terms of volatility shocks?
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What aspect of volatility do GARCH models specifically address?
What aspect of volatility do GARCH models specifically address?
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What condition must be met regarding the parameters 'a' and 'b' in a volatility model?
What condition must be met regarding the parameters 'a' and 'b' in a volatility model?
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What is a characteristic of the unconditional distribution of a GARCH(1,1) process?
What is a characteristic of the unconditional distribution of a GARCH(1,1) process?
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Which of the following best describes the GARCH-in-mean model?
Which of the following best describes the GARCH-in-mean model?
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What happens when $a + b = 1$ in a volatility model?
What happens when $a + b = 1$ in a volatility model?
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What does the unconditional kurtosis K of a GARCH(1,1) process represent?
What does the unconditional kurtosis K of a GARCH(1,1) process represent?
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What implication does a situation where $a + b < 1$ have for volatility?
What implication does a situation where $a + b < 1$ have for volatility?
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What does the presence of volatility clusters in financial returns indicate?
What does the presence of volatility clusters in financial returns indicate?
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What does the unconditional variance formula $ au^2 = rac{ au}{1 - eta}$ represent?
What does the unconditional variance formula $ au^2 = rac{ au}{1 - eta}$ represent?
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What is the key distinction between the ARCH and GARCH models?
What is the key distinction between the ARCH and GARCH models?
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Why is a GARCH(1,1) model often sufficient for financial time series?
Why is a GARCH(1,1) model often sufficient for financial time series?
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In GARCH models, what does the term $σ^2_{t-1}$ represent?
In GARCH models, what does the term $σ^2_{t-1}$ represent?
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How is the conditional variance modeled in a GARCH process?
How is the conditional variance modeled in a GARCH process?
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What does the component 'ω' represent in the GARCH formula?
What does the component 'ω' represent in the GARCH formula?
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Which of the following statements about the ARCH process is true?
Which of the following statements about the ARCH process is true?
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What is the primary focus of the GARCH model in financial analytics?
What is the primary focus of the GARCH model in financial analytics?
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Study Notes
Historical Volatility Estimation
- Volatility is crucial for investment decisions, performance evaluation, and risk management.
- Two methods exist for forecasting volatility:
- Implied volatility: derived from observed option prices, not guaranteed to reflect future market behavior.
- Historical volatility: uses historical price data to predict future volatility, relies on the assumption that the past is indicative of the future.
- Estimating historical volatility is challenging because volatility is a latent factor, not directly observable.
- Several factors influence the estimate, including:
- Sample length: longer samples increase accuracy but may not reflect current market dynamics.
- Sample frequency: daily, weekly, or monthly data impact the estimate.
- Pricing measure (different measures of price data): which assumptions are applied to the price process.
- Choosing sample length balances accuracy and timeliness.
- Short samples reflect time variations but may lack accuracy.
- More accurate estimates may not be current.
- Volatility clustering and structural changes can affect the stability of historical data.
- Long samples lose accuracy when volatility is clustered in different periods, or significant market changes occur.
- Short samples offer better accuracy, but focus on short-term volatility variations.
- Volatility measures include standard deviation of returns or range-based methods.
Sampling Frequency
- Daily data offers high observations, but can include holiday or vacation impacts.
- Weekly/monthly data reduce holiday/vacation variations, but reduce the overall observations during the sampling period.
Volatility Measure: Price Ranges
- The choice of volatility measure critically affects the estimate.
- Historical volatility is often represented as the standard deviation of past returns.
- Other measures such as range-based estimators (considering high-low prices) and squared return are also used.
- Range-based estimators (using opening/closing, high/low) may understate actual volatility, because the range of price changes is more constrained.
GARCH Models
- Volatility clusters and its dynamic behavior are important for understanding financial markets
- Volatility is commonly modeled using GARCH models because volatility is often not constant.
- Alternative models are EGARCH and GJR-GARCH, which account for asymmetric volatility reactions to positive and negative shocks.
- GARCH-in-Mean models link volatility to mean (average return).
Utility and Indifference Curves
- Investors choose among investment opportunities based on risk-return preferences.
- Expected return and risk are key consideration factors.
- A utility function is used to rank different investment opportunities.
- Investors maximize utility when optimizing choices.
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Description
This quiz explores the concept of historical volatility in investment decisions. It covers methods for forecasting volatility, particularly historical and implied volatility. Additionally, it discusses the factors affecting historical volatility estimates, including sample length and frequency.
