A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper shows robustness of Hilbert space-valued stochastic volatility models to perturbations.
Study provides LDP for non self-similar stochastic volatility models.
Entropy-minimal measure calculated for a stochastic volatility model.
A new fast method simulates stochastic volatility models.
Approximates derivative pricing under fractional stochastic volatility.
We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these featu…
We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of equivalent martingale measure in the market model. The option is priced with respec…
Two new models for volatility in Markov-switching environments capture financial time-series properties.
Develops a new stochastic volatility model for temperature derivatives.
A new volatility model calibrates SPX & VIX smiles with 6 parameters.
We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation scheme is implemented. We determine the estimates for the option price for prede…
We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbec…
The correlated stochastic volatility models constitute a natural extension of the Black and Scholes-Merton framework: here the volatility is not a constant, but a stochastic process correlated with the price log-return one. At present, several stochastic volatility models are discussed in the literature, differing in t…
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is…
New rough stochastic volatility models using log-modulated fractional Brownian motion.
Extends Alòs' formula to Barndorff-Nielsen and Shephard model.
In this paper, we study the valuation of American type derivatives in the stochastic volatility model of Barndorff-Nielsen and Shephard (2001). We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condi…
We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear mean reversion. Using large deviations techniques, we determine the asymptotic sh…
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
Modeling joint log-volatility dynamics with multivariate fractional Ornstein-Uhlenbeck process.
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic …
We compare the most common SV models such as the Ornstein-Uhlenbeck (OU), the Heston and the exponential OU (expOU) models. We try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect, and thus outline the limitations of each model. We add empirical research on ma…
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we …
The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.
The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The form of the density function of the random variable, which expresses the average of…
Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1- GARCH, and 3/2 - the 3/2 model. Some other models were discovered in \cite{Labordere2009…
Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been propos…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a diffusion process of Ornstein-Uhlenbeck type with unknown drift. We use the dynami…
The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question …
The paper explores how score-driven models can approximate rough volatility.
Paper tackles rough volatility estimation from high-frequency data.
We compute and discuss the Esscher martingale transform for exponential processes, the Esscher martingale transform for linear processes, the minimal martingale measure, the class of structure preserving martingale measures, and the minimum entropy martingale measure for stochastic volatility models of Ornstein-Uhlenbe…
A new model captures forward curve dynamics with stochastic volatility.
In a series of recent papers Barndorff-Nielsen and Shephard introduce an attractive class of continuous time stochastic volatility models for financial assets where the volatility processes are functions of positive Ornstein-Uhlenbeck(OU) processes. This models are known to be substantially more flexible than Gaussian …
This paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigro…
The study identifies volatility models from path geometry using signature-based methods.
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range correlation properties in order to capture such a situation, and we consider Europ…
Model captures SPX and VIX volatility surfaces and skew-stickiness ratio.
The paper models exchange rate risk premium using mean-reverting dynamics.
The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-M…
Approximates option prices in Barndorff-Nielsen and Shephard models using Taylor expansion.
Reducing volatility proxy improves apparent market correlation dynamics.
We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and Lévy semistationary (LSS) processes, which is a class of processes that have been…
We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric Brownian motion, whose diffusion coefficient is expressed through an exponential funct…
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
Classical (Itô diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Lévy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \cite{Tank} for an overvi…
New models optimize quotes for automated market makers considering various price dynamics and demand variability.