Multiple time scales and the empirical models for stochastic volatility
arXiv:physics/0611048 · doi:10.1016/j.physa.2006.12.015
Abstract
The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic. To this end we consider the volatility at both short (a few days) and long (a few months)time scales as a Markovian process and estimate for it the coefficients of the Kramers-Moyal expansion using the data for Dow-Jones Index. It has been found that the empirical data allow to take only the first two coefficients of expansion to be non zero that define form of the volatility stochastic differential equation of Ito. It proved to be that for the long time scale the empirical data support the ExpOU model. At the short time scale the empirical model coincides with ExpOU model for the small volatility quantities only.
19 pages, 6 figures
References in corpus (13)
- The statistical properties of the volatility of price fluctuations
- Volatility distribution in the S&P500 Stock Index
- How to quantify deterministic and random influences on the statistics of the foreign exchange market
- Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact
- Volatility in Financial Markets: Stochastic Models and Empirical Results
- Markov properties of high frequency exchange rate data
- Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes
- Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model
- Stochastic volatility and leverage effect
- A correlated stochastic volatility model measuring leverage and other stylized facts
- A comparison between several correlated stochastic volatility models
- Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Months
- Common Underlying Dynamics in an Emerging Market: From Minutes to Months