We consider a simple uncertain-volatility model for the asset price underlying a given option market. The asset price volatility is assumed to follow a discrete (actually finite) Markov chain σ, which changes value on some fixed future times. The volatility chain is independent of the Brownian motion governing the future evolution of the asset. Modeling the volatility evolution in this way is e...

We introduce a functional volatility process for modeling volatility trajectories for high frequency observations in financial markets and describe functional representations and data-based recovery of the process from repeated observations. A study of its asymptotic properties, as the frequency of observed trades increases, is complemented by simulations and an application to the analysis of i...

This paper examines the price volatility in the silver spot (cash) market. A host of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are used to analyze and gain a better understanding of the volatility of silver prices. We find the TGARCH (1,1) model indicates that both positive and negative shocks do not have a significant effect on volatility in the silver spot marke...

This paper focuses on the performance of various GARCH models in terms of their ability of delivering volatility forecasts for stock return data. Volatility forecasts obtained from a variety of mean and variance specifications in GARCH models are compared to a proxy of actual volatility calculated using daily data. In-sample tests suggest that a regression of volatility estimates on actual vola...

We see that the price of an european call option in a stochastic volatility framework can be decomposed in the sum of four terms, which identify the main features of the market that affect to option prices: the expected future volatility, the correlation between the volatility and the noise driving the stock prices, the market price of volatility risk and the difference of the expected future v...

We apply the ACD-ICV method proposed by Tse and Yang (2011) for the estimation of intraday volatility to estimate monthly volatility, and empirically compare this method against the realized volatility (RV) and generalized autoregressive conditional heteroskedasticity (GARCH) methods. Our Monte Carlo results show that the ACD-ICV method performs well against the other two methods. Evidence on t...

This study investigates whether intraday returns contain important information for forecasting daily volatility. Whereas in the existing literature volatility models for daily returns are improved by including intraday information such as the daily high and low, volume, the number of trades, and intraday returns, here the volatility of intraday returns is explicitly modelled. Daily volatility f...

Time-varying volatility is common in macroeconomic data and has been incorporated into macroeconomic models in recent work. Dynamic panel data models have become increasingly popular in macroeconomics to study common relationships across countries or regions. This paper estimates dynamic panel data models with stochastic volatility by maximizing an approximate likelihood obtained via Rao-Blackw...

Stock market volatility is the systematic risk faced by investors who hold a market portfolio (e.g., a stock market index fund). Schwert (1989b) has undertaken an extensive study of stock market volatility, using historical data back to the 19th century. Some of his major findings are illustrated in Figure 1, which plots quarterly stock market volatility for the post-World War II period.1 The f...