Related papers: Skew and implied leverage effect: smile dynamics r…
Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility…
We present a stochastic-local volatility model for derivative contracts on commodity futures able to describe forward-curve and smile dynamics with a fast calibration to liquid market quotes. A parsimonious parametrization is introduced to…
The main goal of this paper is an application of Bayesian model comparison, based on the posterior probabilities and posterior odds ratios, in testing the explanatory power of the set of competing GARCH (ang. Generalised Autoregressive…
Given a surface $M$ and a Borel probability measure $\nu$ on the group of $C^2$-diffeomorphisms of $M$, we study $\nu$-stationary probability measures on $M$. We prove for hyperbolic stationary measures the following trichotomy: either the…
We introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each asset volatility smile is modeled according to a density-mixture dynamical model while the same property…
The leverage effect refers to the well-established relationship between returns and volatility. When returns fall, volatility increases. We examine the role of the leverage effect with regards to generating density forecasts of equity…
We prove that a wide class of correlated stochastic volatility models exactly measure an empirical fact in which past returns are anticorrelated with future volatilities: the so-called ``leverage effect''. This quantitative measure allows…
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power…
Monitoring downside risk and upside risk to the key macroeconomic indicators is critical for effective policymaking aimed at maintaining economic stability. In this paper I propose a parametric framework for modelling and forecasting…
We find statistical evidence for a mismatch between the (global) spatial curvature parameter $K$ in the geodesic equation for incoming photons, and the corresponding parameter in the Friedmann equation that determines the time evolution of…
The continuous observation of the financial markets has identified some stylized facts which challenge the conventional assumptions, promoting the born of new approaches. On the one hand, the long-range dependence has been faced replacing…
Stochastic mirror descent (SMD) is a fairly new family of algorithms that has recently found a wide range of applications in optimization, machine learning, and control. It can be considered a generalization of the classical stochastic…
With the daily and minutely data of the German DAX and Chinese indices, we investigate how the return-volatility correlation originates in financial dynamics. Based on a retarded volatility model, we may eliminate or generate the…
The stochastic volatility inspired (SVI) model is widely used to fit the implied variance smile. Presently, most optimizer algorithms for the SVI model have a strong dependence on the input starting point. In this study, we develop an…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent $\frac{1}{H+3/2}$ rule (where $H$ denotes the Hurst…
We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…
Language model families exhibit striking disparity in their capacity to benefit from reinforcement learning: under identical training, models like Qwen achieve substantial gains, while others like Llama yield limited improvements.…
When developing risk prediction models, shrinkage methods are recommended, especially when the sample size is limited. Several earlier studies have shown that the shrinkage of model coefficients can reduce overfitting of the prediction…
We present a stochastic volatility market model where volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. With this model we exactly measure the leverage effect and other stylized facts, such as mean…