Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Quantitative Risk Management: Volatility Modeling

In course

FIN-609: Asset Pricing (2011 - 2024)

This course provides an overview of the theory of asset pricing and portfolio choice theory following historical developments in the field and putting emphasis on theoretical models that help our understanding of financial decision making and financial mar ...

Description

This lecture by the instructor covers the modeling of volatility in quantitative risk management. Topics include ARMA processes, ARCH and GARCH models, causal representation, and volatility forecasting. The lecture delves into the estimation of parameters, stationarity, and conditional risk measurement.

Instructor

Semyon Malamud

Official source

Ontological neighbourhood

Economics

Microeconomics: Financial economics

Related concepts (32)

Volatility (finance)

In finance, volatility (usually denoted by σ) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option).

Stochastic volatility

In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others.

Volatility smile

Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.

Implied volatility

In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of said option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Related lectures (33)

Quantitative Risk Management: Volatility Modeling

Covers volatility modeling in quantitative risk management, including ARMA, ARCH, GARCH models, and forecasting.

Long Memory and ARCH: Time Series Math 342

Explores long memory in time series and Autoregressive Conditional Heteroskedasticity processes in financial data.

Financial Time Series: GARCH Processes

Covers GARCH processes for financial time series analysis.

Financial Time Series: Stylized Facts and Models

Explores financial time series, including ARMA and GARCH processes, emphasizing risk estimation.

ARCH and GARCH Models: Volatility Forecasting