arXiv research

New model predicts dynamic volatility in uncertain financial markets.

Quantum methods model uncertain volatility in financial markets.

A method for accurate pricing of multidimensional derivatives under uncertain volatility.

In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead of using two deterministic bounds, the uncertain volatility fluctuates between …

Model quantifies uncertainty's impact on European option prices.

Novel pricing method for equity-indexed annuities under uncertain volatility and stochastic interest rate.

A machine learning approach to compute Black-Scholes prices with uncertain volatility.

Proposes a new uncertain volatility model with worst-case scenario analysis.

In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and cutting the obtained Black-S…

Paper uses ML for high-dimensional option pricing under uncertain volatility model.

In the present paper, given an evolving mixture of probability densities, we define a candidate diffusion process whose marginal law follows the same evolution. We derive as a particular case a stochastic differential equation (SDE) admitting a unique strong solution and whose density evolves as a mixture of Gaussian d…

The paper analyzes investment and consumption strategies under uncertain market conditions.

Optimizes trading large volumes of volatile assets with fast mean-reverting volatility.

This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both investment and consumption strategies, and model uncertainty on both drift and volatil…

We study a Markov-Functional (MF) interest-rate model with Uncertain Volatility Displaced Diffusion (UVDD) digital mapping, which is consistent with the volatility-smile phenomenon observed in the option market. We first check the impact of pricing Bermudan swaptions by the model. Next, we also investigate the future s…

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 holds for the multivariate process of all assets, whose density is a mixture of mult…

The target of this paper is to consider model the risky asset price on the financial market under the Knightian uncertainty, and pricing the ask and bid prices of the uncertain risk. We use the nonlinear analysis tool, i.e., G-frame work [26], to construct the model of the risky asset price and bid-ask pricing for the …

We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brownian motion recently introduced by Peng (20…

We study the point of transition between complete and incomplete financial models thanks to Dirichlet Forms methods. We apply recent techniques, developped by Bouleau, to hedging procedures in order to perturbate parameters and stochastic processes, in the case of a volatility parameter fixed but uncertain for traders;…

Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when th…

Study analyzes optimal execution under uncertain volatility and liquidity.

The study challenges the reliability of VaR due to market randomness.

The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is non-dominated. We propose studying this p…

A new method solves complex financial equations efficiently.

Study introduces AMVP and AMRR for dynamic portfolio optimization in volatile markets.

This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.

We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows us to numerically solve stochastic control problems with controlled volatility,…

Study validates SV models with jump component and long memory parameter, using robustness and sensitivity analysis.

Proposes a new way to represent uncertainty using implied volatility.

The Runge-Kutta-Legendre scheme improves pricing American options and other derivatives.

Investor optimizes worst-case portfolio in uncertain markets.

Paper develops a robust hedging framework to reduce market risk and uncertainty.

Policy shifts between Trump and Biden impact ESG investments, creating volatility.

This paper studies robust forward investment and consumption preferences within a zero-volatility context. Different from previous works, we consider an incomplete financial market model due to general investment portfolio constraints. We provide a new PDE characterization and a novel semi-explicit saddle-point constru…

The paper explores how to handle uncertain evidence in probabilistic models.

New method calculates Shapley values for uncertain functions.

We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that the derivative cannot be shorted, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of p…

In this paper, within the framework of uncertainty theory, the valuation of equity warrants is investigated. Different from the methods of probability theory, the equity warrants pricing problem is solved by using the method of uncertain calculus. Based on the assumption that the firm price follows an uncertain differe…

We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied probability distributions. We argue that volatility is not risk, but uncertaint…

Price and return predictions are limited by economic complexity, not just volatility.

Study calculates Bayes risk for semi-supervised learning with uncertain labels.

New algorithm for uncertain time series classification.

New algorithm for reinforcement learning in uncertain environments with unknown thresholds.

An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $α$-maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect…

This research predicts cryptocurrency price volatility using deep learning models.

Study shows SEC crypto classification led to significant market reactions.

The paper addresses portfolio allocation with uncertain covariance matrices, finding a logarithmic risk dependence.

Bayesian Gaussian process models handle uncertain data locations in PDE approximations.