Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence
2. ENGINEERING AND TECHNOLOGY
We consider an approach to analysing the Stochastic Volatility of a financial time series using the Generalised Kolmogorov-Feller Equation (GKFE). After reviewing the computation of the Stochastic Volatility using a phase only condition, a Green’s function solution to the GKFE equation is derived which depends upon the ‘memory function’ used to construct the GKFE. Using the Mittag-Leffler memory function, we derive an expression for the Impulse Response Function associated with a short time window of data which is then used to derive an algorithm for computing a new index using a standard moving window process. It is shown that application of this index to both a financial time series and its corresponding Stochastic Volatility provides a correlation between the start, direction and end of a trend depending on the sampling rate of the time series and the look-back window that is used.
Blackledge, J., Lamphiere, M., Murphy, K., Overton, S., Panahi, A. (2012) :Stochastic Volatility Analysis using the Generalised Kolmogorov-Feller Equation. Stochastic Volatility Analysis using the Generalised Kolmogorov-Feller Equation. The 2012 International Conference of Financial Engineering, London, 2012. doi:10.21427/D7R637