Lecture 4: Volatility Flashcards
Fill in the blank words in the following definition of volatility:
Volatility: A variable’s volatility, σ, is the standard deviation of the return provided by the variable per unit of ___ when the return is expressed using _____ _______.
Volatility: A variable’s volatility, σ, is the standard deviation of the return provided by the variable per unit of TIME when the return is expressed using CONTINUOUS COMPOUNDING.
The time unit in volatility differs with respect to when the volatility measure is used for option pricing vs. risk management.
In risk management, the unit of time equals _____
In option pricing, the unit of time equals ____
In risk management, the unit of time equals ONE DAY
In option pricing, the unit of time equals ONE YEAR
The 1.96 equals the _____-quantile on a normal distribution: i.e., we are _____% certain that a standard normally distributed stochastic variable will be less than 1.96. This constant is multiplied by the one-day one-standard deviation price movement of $1.
Fill in the (same) number in the blanks
The 1.96 equals the 97.5%-quantile on a normal distribution: i.e., we are 97.5% certain that a standard normally distributed stochastic variable will be less than 1.96. This constant is multiplied by the one-day one-standard deviation price movement of $1.
When the confidence level increases, the interval of future values will (increase/decrease)
Note that if the confidence level increase (e.g., to 99%), the interval would increase likewise. This is because we require the interval to be 99% certain
–> (high certainty, higher interval)
When a return is continuous compounded, the cont. compounded return is equal to the log return of the relative change of price over the period.
True/ False
True
When converting daily volatility to annual and vice versa, the number of days used (T-variable) denotes the number of days per year. What number is most accurate?
A) business days = 252 days
B) calendar days = 365 days
A) business days = 252 days
Two approaches to volatility estimation exist. Which?
Implied volatility
Historical data volatility
Implied volatility prescribes the use ___ ____ on options, and is the volatility applied by the __-__ ______. Thus, the implied volatility is simply the volatility that results in the option being traded at the _____ _____ _______
Fill in the blanks.
Implied volatility prescribes the use MARKET DATA on options, and is the volatility applied by the B-S MODEL. Thus, the implied volatility is simply the volatility that results in the option being traded at the CURRENT PRICE OBSERVED
VIX-index is published at CBOE, and equals the implied volatility of 30-day options on S&P500. It represents a measure of the market’s expectation of stock market volatility over the next 30-day period.
This index is also known as _____?
Fear-index
When a positive return today leads to an increased probability of a positive return tomorrow –> this is an example of _____ ______
Momentum effect: positive correlation between returns today and returns tomorrow
When relaxing the assumption of constant volatility over time, one can take time-variation into account by two ways. Which?
Hint: something about weights assigned to observations
1) putting equal weight on each observation, and then calculate historical volatility
2) putting more weight on more recent observations - e.g., the exponential weighted moving average (EWMA) model
In the exponential weighted moving average (EWMA) model, the lambda is known as the smoothing parameter (weight put on the volatility estimate from the day before). Note: 0 ≤ λ ≤ 1
A high lambda implies a (slower/faster) decay in the series - i.e., that more datapoints are required, which in turn are assigned weights that decrease (slower/ faster).
Choose the right words
A high lambda implies a slower decay in the series - i.e., that more datapoints are required, which in turn are assigned weights that decrease slower.
I.e., relatively low difference between the weight assigned to recent and older data
A low lambda implies a (slower/faster) decay in the series - i.e., that fewer datapoints are required, which in turn are assigned weights that decrease (slower/ faster).
Note: 0 ≤ λ ≤ 1
Choose the right words
A low lambda implies a faster decay in the series - i.e., that fewer datapoints are required, which in turn are assigned weights that decrease faster.
I.e., huge weight is put on the latest observations, and very low weight is put on older data
What is the rationale for assigning higher weights to more recent observations under the EWMA model?
Under the notion that more recent movements in the market have some influence on the movements to be observed (e.g., momentum), higher weights should be assigned to more recent observations.
