Sensitivity Analysis and Density Estimation for the Hobson-Rogers Stochastic Volatility Model

We study a small open economy with labor, capital accumulation, random death, taxation and a government budget balanced in the long run. We offer methods that provide ordinary differential equations for means and analytical expressions for densities. The latter is achieved by solving stochastic differential equations analytically and deriving the density from this solution. Starting from any distribution, the aggregate distribution converges, both on a transition path towards a steady state and on a transition path towards balanced growth, to a Pareto-distribution. We provide an intuitive economic interpretation for a stationary long-run density with an infinite mean in an economy on a balanced growth path. We also show how government tax policy can lead to non-monotonic links between the equilibrium growth rate of the economy and risk aversion of households.

show abstract

“…3.7). They are also applied in finance papers like Cox and Ross (1976), Aoki (1995), Kawai (2009) or Eberlein and Glau (2014).…”

Section: Related Literaturementioning

confidence: 99%

The dynamics of Pareto distributed wealth in a small open economy

2022

View full text Add to dashboard Cite

show abstract

“…3.7). They are also applied in …nance papers like Cox and Ross (1976), Aoki (1995), Kawai (2009), or Eberlein and Glau (2014).…”

Section: Related Literaturementioning

confidence: 99%

The Dynamics of Pareto Distributed Wealth in a Small Open Economy

2021

View full text Add to dashboard Cite

We study a small open economy displaying Pareto-distributed wealth resulting from random death. The government runs a distribution scheme on inheritance. We present the mathematical background that allows to study the dynamics of means. We end up with ordinary differential equations for the mean of age and of individual and government wealth. We also study distributional dynamics analytically. Starting from any distribution of age and wealth, the aggregate distribution converges, both on a transition path towards a steady state and on a transition path towards balanced growth, to an exponential distribution of age and a Paretodistribution of wealth. The findings are illustrated for different distribution schemes.

show abstract

“…One of the models that better fits market data is the so-called Hobson-Rogers model, introduced in Hobson and Rogers (1998) and studied with respect to various features in Antonelli and Prezioso (2008), Blaka Hallulli and Vargiolu (2007), Chiarella and Kwon (2000), Di Francesco and Pascucci (2004), Figà-Talamanca and Guerra (2006), Pascucci (2008, 2009), Kawai (2009), Platania (2003), Sekine (2008). The Hobson-Rogers model consists in the following (we only present the version with a single offset function).…”

Section: Introductionmentioning

confidence: 99%

Robustness for path-dependent volatility models

Rosestolato

Vargiolu

Villani³

2012

Decisions Econ Finan

View full text Add to dashboard Cite

In this paper, we consider a generalisation of the Hobson–Rogers model proposed by Foschi and Pascucci (Decis Econ Finance 31(1):1–20, 2008) for financial markets where the evolution of the prices of the assets depends not only on the current value but also on past values. Using differentiability of stochastic processes with respect to the initial condition, we analyse the robustness of such a model with respect to the so-called offset function, which generally depends on the entire past of the risky asset and is thus not fully observable. In doing this, we extend previous results of Blaka Hallulli and Vargiolu (2007) to contingent claims, which are globally Lipschitz with respect to the price of the underlying asset, and we improve the dependence of the necessary observation window on the maturity of the contingent claim, which now becomes of linear type, while in Blaka Hallulli and Vargiolu (2007), it was quadratic. Finally, in this framework, we give a characterisation of the stationarity assumption used in Blaka Hallulli and Vargiolu (2007), and prove that this model is stationary if and only if it is reduced to the original Hobson-Rogers model. We conclude by calibrating the model to the prices of two indexes using two different volatility shapes

show abstract

Sensitivity Analysis and Density Estimation for the Hobson-Rogers Stochastic Volatility Model

Cited by 4 publications

References 12 publications

The dynamics of Pareto distributed wealth in a small open economy

The dynamics of Pareto distributed wealth in a small open economy

The Dynamics of Pareto Distributed Wealth in a Small Open Economy

Robustness for path-dependent volatility models

Contact Info

Product

Resources

About