Stochastic differential equations
Robust financial calibration: a Bayesian approach for neural stochastic differential equations
This paper offers a Bayesian framework for the calibration of financial models using neural stochastic differential equations.
Neural variance reduction for stochastic differential equations
This paper proposes the use of neural stochastic differential equations as a means to learn approximately optimal control variates, reducing variance as trajectories of the SDEs are simulated.
Neural joint S&P 500/VIX smile calibration
A one-factor stochastic local volatility model can solve the joint calibration problem
Neural stochastic differential equations for conditional time series generation using the Signature-Wasserstein-1 metric
Using conditional neural stochastic differential equations, the authors propose a means to improve the efficiency of generative adversarial networks and test their model against other classical approaches.
Sharp L¹-approximation of the log-Heston stochastic differential equation by Euler-type methods
The authors employ Euler-type methods to study the L¹ approximation of the log-Heston stochastic differential equation at equidistant time points.
Estimating risks of European option books using neural stochastic differential equation market models
The authors investigate how arbitrage-free neural stochastic differential equation market models can produce realistic scenarios for the joint dynamics of multiple European options on a single underlying and demonstrate how they can be used as a risk…
Robust pricing and hedging via neural stochastic differential equations
The authors propose a model called neural SDE and demonstrate how this model can make it possible to find robust bounds for the prices of derivatives and the corresponding hedging strategies.
Pricing barrier options with deep backward stochastic differential equation methods
This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic differential equations.
A review of tree-based approaches to solving forward–backward stochastic differential equations
This paper looks at ways of solving (decoupled) forward–backward stochastic differential equations numerically using regression trees.
Solving final value problems with deep learning
Pricing vanilla and exotic options with a deep learning approach for PDEs
Optimal extraction and taxation of strategic natural resources: a differential game approach
This paper studies the optimal extraction and taxation of nonrenewable natural resources.
The SABR forward smile
Thomas Roos presents the expressions for the implied volatilities of European and forward starting options
CVA and IM: welcome to the machine
Henry-Labordere proposes a neural networks-based technique to price counterparty risk and initial margin
The Garch linear SDE: explicit formulas and the pricing of a quanto CDS
A new closed-form approximation is applied to quanto CDS pricing
Volatility risk structure for options depending on extrema
In this paper, the authors give a decomposition formula to calculate the vega index (sensitivity with respect to changes in volatility) for options with prices that depend on the extrema (maximum or minimum) and terminal value of the underlying stock…
Calibration of local correlation models to basket smiles
The authors build a whole family of local correlation models by combining the particle method with a new, simple idea.