arXiv research

The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.

In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and calibration of implied volatility is the addition of a few other factors to the volatil…

This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To capture the multiscale volatility of the financial market, our model adds a fast sca…

Optimizes trading strategies with price impact, predictable returns, and stochastic volatility.

In this paper we present a new method to compute the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility of Fouque \textit{et al.} (2011, CUP). It provides an alternative method to the singular perturbation technique presented in Hikspoors and Jaimungal (2…

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and Sølna (2011, CUP) analyzes models in which the volatility of the underlying i…

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 stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump Lévy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale $\frac{t}{\varepsilon}$ than the assets, and we study the asymptotics as $\varepsilon\t…

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What it is well known is that absolute returns have memory on a long time range, this phenomenon i…

This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process, in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented frequency-by-frequency and the concept of the multiscale ratio is introduced to quantify t…

We perform a scaling analysis on NYSE daily returns. We show that volatility correlations are power-laws on a time range from one day to one year and, more important, that they exhibit a multiscale behaviour.

We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential Lévy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time through common driving factors -- one fast-varying and one slow-varying. Using Four…

Paper introduces MN-DAG for modeling evolving causal relationships in multivariate time series.

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent. Additionally, the process underlying the derivative may exhibit killing (i.e. jum…

We propose a simple stochastic model of market behavior. Dividing market participants into two groups: trend-followers and fundamentalists, we derive the general form of a stochastic equation of market dynamics. The model has two characteristic time scales: the time of changes of market environment and the characterist…

TimeMixer predicts global financial asset volatility, excelling in short-term forecasts.

Method learns dynamics of slow variables from stochastic data.

A framework learns multiscale dynamics from single trajectories using normalizing flows.

Classic contextual bandit algorithms for linear models, such as LinUCB, assume that the reward distribution for an arm is modeled by a stationary linear regression. When the linear regression model is non-stationary over time, the regret of LinUCB can scale linearly with time. In this paper, we propose a novel multisca…

Authors improve accuracy analysis for portfolio optimization with multiple timescale factors.

A new sampling method estimates scores without training or nested MCMC.

Deep learning predicts currency volatility accurately.

In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent deriv…

This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale behaviors, then in a large learning rate regime which only resolves the macroscopic but n…

Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization problem in a Markovian setting under each single scale, the slow one in [Fouque and…

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challen…

MGD combines maximum entropy and diffusion methods for efficient sampling.

Generative models improve for multiscale scientific data with new noise and interpolation techniques.

This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the influence of different timescales on volatility forecasts. The decomposition of …

The article reviews how to set stochastic volatility model parameters.

WALNUTS improves sampling efficiency and robustness for multi-scale distributions.

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do…

Develops a martingale expansion for stochastic volatility models.

We study, both analytically and numerically, an ARCH-like, multiscale model of volatility, which assumes that the volatility is governed by the observed past price changes on different time scales. With a power-law distribution of time horizons, we obtain a model that captures most stylized facts of financial time seri…

MER algorithm speeds up VI solving with Markovian data.

In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…

New gradient methods solve multiscale optimization problems efficiently.

Entropy-minimal measure calculated for a stochastic volatility model.

Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.

Study on Kyle's model with stochastic liquidity impacts asset volatility.

The paper shows robustness of Hilbert space-valued stochastic volatility models to perturbations.

Stochastic volatility models describe stock returns $r_t$ as driven by an unobserved process capturing the random dynamics of volatility $v_t$. The present paper quantifies how much information about volatility $v_t$ and future stock returns can be inferred from past returns in stochastic volatility models in terms of …

The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the exist…

Continuous-time PCD for MLE with explicit error bounds.

Derives short-term option pricing asymptotics in local-stochastic volatility models.

Approximates derivative pricing under fractional stochastic volatility.

Study large deviations in fractional volatility models with non-Gaussian volatility.

Paper improves stochastic collocation for local volatility models.