Related papers: Saddle-Point Approach to Large-Time Volatility Smi…
A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The…
This study investigates the short-term asymptotic behavior of the implied volatility surface (IVS), with a particular focus on the at-the-money (ATM) skew and curvature, which are key determinants of the IVS shape and whose are widely…
Volatility for financial assets returns can be used to gauge the risk for financial market. We propose a deep stochastic volatility model (DSVM) based on the framework of deep latent variable models. It uses flexible deep learning models to…
We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…
Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global structure, metastability, and possible collective mechanisms of…
We introduce a multi-factor stochastic volatility model based on the CIR/Heston volatility process that incorporates seasonality and the Samuelson effect. First, we give conditions on the seasonal term under which the corresponding…
For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…
We address the problem of causal effect estimation where hidden confounders are present, with a focus on two settings: instrumental variable regression with additional observed confounders, and proxy causal learning. Our approach uses a…
Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While L\'evy processes provide a natural mathematical framework for…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant…
We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…
Affine Diffusion dynamics are frequently used for Valuation Adjustments (xVA) calculations due to their analytic tractability. However, these models cannot capture the market-implied skew and smile, which are relevant when computing xVA…
Stochastic volatility models describe asset prices $S_t$ as driven by an unobserved process capturing the random dynamics of volatility $\sigma_t$. Here, we quantify how much information about $\sigma_t$ can be inferred from asset prices…
We propose an affine extension of the Linear Gaussian term structure Model (LGM) such that the instantaneous covariation of the factors is given by an affine process on semidefinite positive matrices. First, we set up the model and present…
Several studies explore inferences based on stochastic volatility (SV) models, taking into account the stylized facts of return data. The common problem is that the latent parameters of many volatility models are high-dimensional and…
In this work, we consider a time-varying stochastic saddle point problem in which the objective is revealed sequentially, and the data distribution depends on the decision variables. Problems of this type express the distributional…
The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be…