Related papers: A correlated stochastic volatility model measuring…
We consider the stochastic volatility model obtained by adding a compound Hawkes process to the volatility of the well-known Heston model. A Hawkes process is a self-exciting counting process with many applications in mathematical finance,…
We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…
We investigate quantitatively the so-called leverage effect, which corresponds to a negative correlation between past returns and future volatility. For individual stocks, this correlation is moderate and decays exponentially over 50 days,…
In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dY_{s}^{(1)}$% , where $u$ is a $\beta$-H\"older continuous process with $\beta > 1-H$ and…
This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts…
Our article considers a regression model with observed factors. The observed factors have a flexible stochastic volatility structure that has separate dynamics for the volatilities and the correlation matrix. The correlation matrix of the…
In this paper we show that Hilbert space-valued stochastic models are robust with respect to perturbation, due to measurement or approximation errors, in the underlying volatility process. Within the class of stochastic volatility modulated…
There are two possible ways of interpreting the seemingly stochastic nature of financial markets: the Efficient Market Hypothesis (EMH) and a set of stylized facts that drive the behavior of the markets. We show evidence for some of the…
We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
We study stochastic model reduction for evolution equations in infinite dimensional Hilbert spaces, and show the convergence to the reduced equations via abstract results of Wong-Zakai type for stochastic equations driven by a scaled…
Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in log normalized returns, the…
Building on a prominent agent-based model, we present a new structural stochastic volatility asset pricing model of fundamentalists vs. chartists where the prices are determined based on excess demand. Specifically, this allows for…
We propose a new volatility model based on two stylized facts of the volatility in the stock market: clustering and leverage effect. We calibrate our model parameters, in the leading order, with 77 years Dow Jones Industrial Average data.…
We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein-Uhlenbeck process with Levy noise and bounded drift. We…
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with…
This paper outlines an agent-based model of a simple financial market in which a single asset is available for trade by three different types of traders. The model was first introduced in the PhD thesis of one of the authors, see reference…
An extensive empirical literature documents a generally negative correlation, named the "leverage effect," between asset returns and changes of volatility. It is more challenging to establish such a return-volatility relationship for jumps…
In this paper we propose a novel pricing-hedging framework for volatility derivatives which simultaneously takes into account rough volatility and volatility jumps. Our model directly targets the instantaneous variance of a risky asset and…
We present an agent based model of a single asset financial market that is capable of replicating several non-trivial statistical properties observed in real financial markets, generically referred to as stylized facts. While previous…