Financial and actuarial mathematics
Fractal activity time risky assets models with dependence
It is well documented that the Black-Scholes models and associated arbitrage-free asset pricing methodology, which plays a central role in financial theory, has significant shortcomings. The following features of stock returns are well documented in financial econometrics:
- the log-returns process is uncorrelated;
- long-range dependence is present in the absolute and squared returns;
- returns have leptokurtic empirical distributions, i.e., hither-peaked and heavier-tailed then Gaussian distribution.
Work presently concentrates on a proposed fractal activity of time geometric Brownian motion (FATGBM) as a model for risky assets in an attempt to meet the aforementioned features. Heyde and Leonenko (2005) proposed a fractal activity time geometric Brownian motion (FATGBM) as a model for risky assets. This model has some similarities with stochastic volatility model of Barndorff-Nielsen and Shephard. The FATGBM model supports the desired features of log returns (log price increments) that are observed in practice by Clive W. Granger (the Nobel Price in Economics, 2003). In the papers by Prof. Leonenko and his co-authors by using the conception of skew -correcting martingales the pricing theory for FATGBM is developed and an exact contractions of the fractal activity time process is proposed with both monofractal and multifractal characteristics.
Cardiff Investigators
- Prof. Nikolai Leonenko
- Mr Alex Kerss
Collaborators
Prof. Chris Heyde,
Dr. Alla Sikorskii,
Dr. Emanuele Taufer,
Dr. Marco Bee,
Dr. Stuart Petherick
Selected publications
- Leonenko N.N, Petherick, S., Sikorskii A. (2012) Normal Inverse Gaussian model for risky asset with dependence, Statistic and Probability Letters, 82, 109-115
- Leonenko N.N, Petherick, S., A. Sikorskii (2012) Fractal activity time models for risky asset with dependence and generalized hyperbolic distributions, Stochastic Analysis and Application, in press
- Leonenko N.N, Petherick, S., A. Sikorskii (2011) The Student subordinated models with dependence for risky asset returns, Communications in Statistics - Theory and Methods, 40, 3509-3523
- Taufer, E., Leonenko, N.N., Bee, M. (2011) Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models, Computational Statistics and Data Analysis, 55, 2525-2539
- Leonenko N.N, Petherick, S., Taufer, E. (2011) Multifractal scaling for risky asset modelling, Fractals, submitted
- Heyde, C.C., Leonenko, N.N., (2005) Student processes. Adv. in Appl. Probab. 37, N 2, 342-365