Related papers: Small Volatility Approximation and Multi-Factor HJ…
We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility…
We suggest two classes of multivariate GARCH--models which are both easy to estimate and perform well in forecasting the covariance matrix of more than one hundred stocks. We apply methods from random matrix theory (RMT) to determine the…
Motivated by learning of correlated equilibria in non-cooperative games, we perform a large deviations analysis of a regret minimizing stochastic approximation algorithm. The regret minimization algorithm we consider comprises multiple…
The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on…
In this chapter we first briefly review the existing approaches to hedging in rough volatility models. Next, we present a simple but general result which shows that in a one-factor rough stochastic volatility model, any option may be…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…
Building upon factor decomposition to overcome the curse of dimensionality inherent in multivariate volatility processes, we develop a factor model-based multivariate stochastic volatility (fMSV) framework. We propose a two-stage estimation…
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest…
Models with a large number of latent variables are often used to fully utilize the information in big or complex data. However, they can be difficult to estimate using standard approaches, and variational inference methods are a popular…
Multi-fidelity Monte Carlo (MFMC) is a variance reduction method that leverages a multi-fidelity ensemble of models of varying cost and accuracy levels. Constructing an MFMC estimator with optimal variance requires knowledge of the…
We formulate a forward inflation index model with multi-factor volatility structure featuring a parametric form that allows calibration to correlations between indices of different tenors observed in the market. Assuming the nominal…
Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum…
Flexible variational distributions improve variational inference but are harder to optimize. In this work we present a control variate that is applicable for any reparameterizable distribution with known mean and covariance matrix, e.g.…
This paper develops a flexible and computationally efficient multivariate volatility model, which allows for dynamic conditional correlations and volatility spillover effects among financial assets. The new model has desirable properties…
We consider the computation of free energy-like quantities for diffusions in high dimension, when resorting to Monte Carlo simulation is necessary. Such stochastic computations typically suffer from high variance, in particular in a low…
Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is…
We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on \Ito stochastic differential equations in infinite dimensional spaces, and prove strong and weak…
We show how to achieve the notion of "multicalibration" from H\'ebert-Johnson et al. [2018] not just for means, but also for variances and other higher moments. Informally, it means that we can find regression functions which, given a data…
We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (HMM), that have been developed to solve partial differential…
In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian…