The Student Subordinator Model with Dependence for Risky Asset Returns

Abstract

A new, tractable model of the stock price due to Heyde (1999) (see also Heyde and Leonenko, 2005) is elaborated here and used for asset price movement. The model is driven by a Brownian motion, which has a "fractal clock" rather than a calendar clock. We incorporate the Student's t-distribution, and a special dependence structure is introduced through the construction of this fractal time. The Student model described has desired features supported by real financial data.

Student-like models for risky asset with dependence

“…The proposed models with properties i)-v) are different from the models in existing literature ( [1], [6], [8], [9], [10], [14], [15], [16], [19], [20], [21]). For instance, the models based on the Ornstein-Uhlenbeck processes and their superpositions ( [19], [21]) do not satisfy the property i), while the model proposed in [6] uses the Student distribution with time-dependent parameters. The model in [8], [15] uses the Student distribution with only two parameters.…”

“…For modeling the increments over time τ t with a stationary OU processes with Inverse Gamma, Inverse Gaussian or Tampered Stable distribution, see Leonenko et al [16;19]. These constructions modeled the returns by stochastic processes with Student, Normal Inverse Gaussian or Normal Tempered Stable distribution correspondingly.…”

SupOU-based and Related Fractal Activity Time Models for Risky Assets with Dependence

“…Heyde, 2009; C.C. Heyde & Leonenko, 2005;Leonenko, Petherick, & Sikorskii, 2011;Seneta, 2004). More importantly, financial prices seasonality and business cycles can be well explained under using the fractal active time T t with dependence structures.…”

“…More importantly, financial prices seasonality and business cycles can be well explained under using the fractal active time T t with dependence structures. Regarding model calibration and application, Kerss et al (2014); Leonenko et al (2011) pointed out that the marginal distribution of R t and its dependence structure can be fitted separately. With all these nice mathematical properties, FATGBM models have advantages in derivative pricing and trading.…”

Fractal Activity Time Models for Risky Asset with Dependence and Generalized Hyperbolic Distributions

“…Earlier, the model with Student's t distribution was discussed by Heyde and Leonenko [20] for t with inverse Gamma distribution and specified autocovariance function so that the process t exhibits long-range dependence. Parameter estimation for this model is presented in [25].…”