Study compares methods for recovering latent risk-neutral densities from option prices, finding DeepONet effective.
problem Accurately recovering latent risk-neutral densities from option prices is challenging.
method Two benchmarks and various methods (lognormal mixture, DeepONet, quote transformer) are used to compare recovery accuracy.
result DeepONet outperforms other methods in reducing error on latent density recovery.
Generative model prices options and extracts risk-neutral densities.
problem Price options and extract risk-neutral densities from market data.
method Model log-returns as a generative model, using neural nets for location, scale, and higher-order moments, with stringent conditions to avoid arbitrage.
result The model efficiently generates samples to price options and accommodates diverse risk-neutral densities.
We build on the work in Fackler and King 1990, and propose a more general calibration model for implied risk neutral densities. Our model allows for the joint calibration of a set of densities at different maturities and dates through a Bayesian dynamic Beta Markov Random Field. Our approach allows for possible time de…
A model-free framework extracts risk-neutral densities from short-dated options.
problem Arbitrage and bid-ask spread issues in short-dated options.
method Develops ARIES for filtering static arbitrage and SEDEx for density extraction.
result Robust density extraction across various market conditions and volatility smiles construction.
Framework improves risk neutral density estimation in illiquid markets.
problem Challenges in estimating Risk Neutral Density in illiquid markets.
method Introduces Deep Log-Sum-Exp Neural Network leveraging Deep and Transfer learning.
result Framework recovers Risk Neutral Density with few option quotes in severe illiquidity.
We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S\&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approac…
iCOS method estimates risk-neutral densities and option prices without model assumptions.
problem Estimating risk-neutral densities and option prices without model assumptions.
method Leverages Fourier-cosine technique using option-implied cosine series coefficients, without model assumptions.
result Effective in extracting information from option prices under various market conditions.
We investigate the forecasting ability of the most commonly used benchmarks in financial economics. We approach the usual caveats of probabilistic forecasts studies -small samples, limited models and non-holistic validations- by performing a comprehensive comparison of 15 predictive schemes during a time period of over…
Proposes a method to construct risk-neutral marginals from arbitrage-free option prices.
problem Lack of risk-neutral marginals that are free of arbitrage and easy to use.
method Explicit construction of risk-neutral marginals from discrete arbitrage-free option prices.
result Explicit construction guarantees risk-neutral marginals free of butterfly and calendar arbitrage.
The equity risk premium is derived from SPX option chains using a model-light approach.
problem Estimating the equity risk premium from option data.
method Model-light approach using Gaussian mixture models and exponential tilting.
result The equity risk premium is calculated from the real-world probability densities inferred from option quotes.
Generative model uses DDPMs for risk-neutral derivative pricing.
problem Derivative pricing using arbitrage-free models.
method Developed a framework using DDPMs to generate risk-neutral asset price dynamics.
result Empirically validated the method for both European and path-dependent derivatives.
Deep Hedging learns risk-neutral vol dynamics for option pricing.
problem Statistical arbitrage in market dynamics without transaction costs.
method Numerical approach to train market simulator and find risk-neutral density.
result Risk-neutral model for stochastic implied volatility can be used for pricing or Deep Hedging.
The study finds that specific distributions can be used for risk-neutral valuation in Heston's SV model.
problem Valuation of European options under Heston's stochastic volatility model.
method Analyzing scale-parameter distributions and proving their equivalence to Heston's solution.
result Any RND with mean as the forward spot price that satisfies Heston's option valuation solution must be a member of a scale-family of distributions.
This paper provides a neural approach to represent option implied information.
problem Link between implied density and volatility for arbitrage-free modeling.
method Minimalist perspective on implied volatility, neural representation with arbitrage constraints.
result Shallow feedforward network with a single hidden layer effectively approximates implied density and volatility.
In this note, we consider European options of type h(XT1,XT2,…,XTn) depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger \cite{Breeden} on the relation between derivatives of the call price and the risk-neutral density of the underlying asse…
This paper is concerned with the asymptotics for Greeks of European-style options and the risk-neutral density function calculated under the constant elasticity of variance model. Formulae obtained help financial engineers to construct a perfect hedge with known behaviour and to price any options on financial assets.
Adaptive multi-stage density ratio estimation improves learning of latent space EBM.
problem Learning energy-based models in latent space is computationally expensive and challenging.
method Adaptive multi-stage density ratio estimation using NCE to bridge the gap between prior and posterior densities.
result The method enables more expressive prior models and sharpens the latent space EBM.
GCAE uses density estimation to achieve reliable disentanglement in latent space.
problem Disentangled learning representations suffer from reliability issues.
method GCAE uses Gaussian Channel Autoencoder with Dual Total Correlation (DTC) to avoid the curse of dimensionality.
result GCAE achieves highly competitive and reliable disentanglement scores.
Paper proposes a novel auto-encoder for latent density estimation.
problem Challenges of learning generative probabilistic models due to curse of dimensionality.
method Joint dimensionality reduction and non-parametric density estimation framework using a novel estimator.
result Proposed model achieves promising results on various datasets.
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique o…
The paper reviews historical and modern approaches to asset pricing probability measures.
problem Constructing or selecting probability measures for asset pricing.
method Historical review of various approaches including state price theory, martingale measures, and modern data-driven methods.
result Modern asset pricing involves constructing, transforming, or selecting probability measures to represent market prices.
Entropy based ideas find wide-ranging applications in finance for calibrating models of portfolio risk as well as options pricing. The abstracted problem, extensively studied in the literature, corresponds to finding a probability measure that minimizes relative entropy with respect to a specified measure while satisfy…
Entropic framework models stock and option dynamics.
problem Modeling stock and option dynamics with incomplete information.
method Entropic inference framework, scale invariance, Fokker-Planck equation, risk-neutral measure.
result Derives dynamics of stock and option prices using entropic inference.
Optimizes risk-neutral probabilities for derivative pricing.
problem Deriving bounds on derivative values under multiple risk-neutral scenarios.
method Convex optimization over the set of risk-neutral probability distributions.
result Tractable finite-dimensional optimization problems for pricing.
Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent Variable Model (GPLVM) has successfully been used to find low dimensional manifolds in…
The paper shows how to calculate risk-neutral default probabilities from bid and ask CDS quotes.
problem Calculating risk-neutral default probabilities from market quotes.
method Using conic finance framework and Poisson process to formulate and solve the calibration problem.
result A unique solution for risk-neutral default probabilities and implied liquidity.
Simulates risk-neutral markets using neural spline flows.
problem Creating realistic risk-neutral market simulations.
method Developed a low-dimensional martingale representation and used neural spline flows for sampling.
result The calibrated simulator is closest to historical data with respect to Kullback-Leibler divergence.
Improved disentangled representation learning using a non-parametric latent density model.
problem Limited disentanglement in VAE due to constraints on latent density independence and complexity.
method Utilized the Indian Buffet Process (IBP) as a non-parametric latent density model to allow richer modeling capacity.
result IBP-VAE outperformed state-of-the-art VAEs in disentangling latent factors across various datasets.
Refines deep generative models to improve data density precision.
problem Achieving precise representation of data probability density in deep models.
method Iterated generative modeling to refine latent space, addressing topological obstructions.
result Latent Space Refinement (LaSeR) protocol improves generative model precision.
New models capture heterogeneous network density, improving community detection.
problem Empirical networks are often globally sparse but locally dense.
method Latent Poisson models generating hidden multigraphs.
result These models improve community detection in sparse networks.
We model messaging activities as a hierarchical doubly stochastic point process with three main levels, and develop an iterative algorithm for inferring actors' relative latent positions from a stream of messaging activity data. Each of the message-exchanging actors is modeled as a process in a latent space. The actors…
Project estimates risk-neutral dependence from option prices.
problem Extracting risk-neutral dependence from option prices.
method Projection estimator using portfolios of observed options.
result Estimates risk-neutral dependence in incomplete markets.
CEBMs learn flexible latent mappings from data.
problem Learning flexible latent mappings from data.
method CEBMs decompose joint density into tractable posterior over latent variables.
result CEBMs achieve competitive results in image modeling and latent space predictive power.
In this paper, we propose a new method for estimating the conditional risk-neutral density (RND) directly from a cross-section of put option bid-ask quotes. More precisely, we propose to view the RND recovery problem as an inverse problem. We first show that it is possible to define restricted put and call operators th…
DO-EM framework for quantum models improves generative tasks.
problem Lack of Expectation-Maximization framework for density operators.
method Demonstrated inequality for density operators, derived DO-EM framework.
result DO-EM framework outperforms probabilistic models in generative tasks.
Estimates the ratio of posterior distributions of latent variables.
problem Comparing posterior distributions of latent variables inferred from observations.
method Parametric model approximation and estimation using observed and prior samples.
result Consistent and asymptotically normal estimation of posterior ratio parameters.
Improves GANs by sampling from an energy-based model induced by discriminator scores.
problem Improving the quality of images generated by GANs.
method DDLS (Discriminator Driven Latent Sampling) using the sum of latent prior log-density and discriminator output score.
result Significantly improves Inception Score on CIFAR-10 dataset.
The variational autoencoder (VAE) is a powerful generative model that can estimate the probability of a data point by using latent variables. In the VAE, the posterior of the latent variable given the data point is regularized by the prior of the latent variable using Kullback Leibler (KL) divergence. Although the stan…
Examines GARCH intensity model for risk-neutral option pricing.
problem Volatility clustering, leverage effect, and conditional asymmetry in financial returns.
method Risk-neutral option pricing method under GARCH intensity model.
result Flexibility in volatility changes according to probability measure.
L-HNNs improve Bayesian inference by reducing gradient requirements and improving ESS.
problem Efficient Bayesian inference with complex target densities.
method Latent Hamiltonian Neural Networks (L-HNNs) with NUTS, incorporating online error monitoring.
result L-HNNs in NUTS with online error monitoring required 1--2 orders of magnitude fewer numerical gradients and improved ESS by an order of magnitude.
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent Pólya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's Gaussian process prior. The augmented posterior allows for efficient inference by Gi…
It can be difficult to tell whether a trained generative model has learned to generate novel examples or has simply memorized a specific set of outputs. In published work, it is common to attempt to address this visually, for example by displaying a generated example and its nearest neighbor(s) in the training set (in,…
Neural network models transform physical systems into latent Gaussian distributions.
problem Simplifying and solving classical Hamiltonian systems.
method Symplectic neural networks for canonical transformations.
result Captures nonlinear collective modes in latent space.
Paper presents a unified approach to interpolation and geodesics in latent spaces of generative models.
problem Finding geodesics and interpolating in latent spaces of non-Gaussian densities.
method General approach to interpolation and geodesics in latent space for arbitrary density.
result Maximizing quality measure of an interpolating curve is equivalent to finding geodesic.
This paper compares log-likelihood and BLEU scores for sequence generation tasks.
problem The discrepancy between density estimation and sequence generation performance.
method Comparing several density estimators on five machine translation tasks.
result The correlation between log-likelihood and BLEU varies depending on model families.
Nonparametric density deconvolution and denoising using simulation-based inference
problem Learning latent signals and their distributions in the presence of measurement noise
method Convolutional maximum mean discrepancy (convMMD) loss and likelihood-free framework
result Learn a latent generative model matching observed data distribution
Enhances GPLVM for multi-view data with scalable latent representation learning.
problem Limited kernel expressiveness and computational inefficiency in multi-view GPLVM.
method Introduces a new duality between spectral density and kernel function, uses NG-SM kernel, and applies random Fourier feature approximation for scalability.
result Consistently outperforms state-of-the-art models in learning meaningful latent representations across diverse datasets.
Meta-learning improves OoD detection with minimal in-distribution data.
problem Efficient OoD detection with limited in-distribution data.
method Meta-learning in latent space with Gaussian mixture models.
result Meta-learning enhances OoD detection performance.