If pricing kernels are assumed non-negative then the inverse problem of finding the pricing kernel is well-posed. The constrained least squares method provides a consistent estimate of the pricing kernel. When the data are limited, a new method is suggested: relaxed maximization of the relative entropy. This estimator …
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48 results for “Pricing Kernel”
Investigates cross-impact kernels for financial asset prices.
problem Understanding and parameterizing cross-impact kernels for financial asset prices.
method Examined martingale-admissible and no-statistical-arbitrage-admissible kernels, determined their overlap, and provided calibration formulas.
result Identified the overlap between martingale-admissible and no-statistical-arbitrage-admissible kernels and provided formulas for their calibration.
When investors have heterogeneous attitudes towards risk, it is reasonable to assume that each investor has a pricing kernel, and that these individual pricing kernels are aggregated to form a market pricing kernel. The various investors are then buyers or sellers depending on how their individual pricing kernels compa…
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over…
Study uses multi-kernel Hawkes models to analyze high-frequency price dynamics.
problem Understanding responsive speeds of market participants in high-frequency trading.
method Multi-kernel Hawkes models with conditional Hessian analysis for optimization.
result Existence of multi-kernels (UHF, VHF, HF) in high-frequency price dynamics.
Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.
problem Long-term decomposition of robust pricing kernels under G-expectation.
method Proposes and analyzes three types of quadratic G-BSDEs to decompose pricing kernels.
result Pricing kernels decomposed into four components: discounting, transitory, symmetric martingale, and volatility uncertainty.
We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that …
New methods price American options in rough volatility models.
problem Pricing American options under rough volatility.
method Integrating deep-signature and signature-kernel learning into optimal stopping problem solutions.
result Performance comparison in rough Heston and rough Bergomi models.
A heat kernel approach is proposed for the development of a general, flexible, and mathematically tractable asset pricing framework in finite time. The pricing kernel, giving rise to the price system in an incomplete market, is modelled by weighted heat kernels which are driven by multivariate Markov processes and whic…
Optimal hedging strategy found in markets with incomplete pricing kernels.
problem Finding optimal hedging in markets with incomplete pricing kernels.
method Demonstrated existence of an optimal hedge portfolio using an expected least squared-error criterion.
result Existence of an optimal hedge portfolio in Lévy-Ito markets.
Numerous kinds of uncertainties may affect an economy, e.g. economic, political, and environmental ones. We model the aggregate impact by the uncertainties on an economy and its associated financial market by randomised mixtures of Lévy processes. We assume that market participants observe the randomised mixtures only …
We discuss the finding that cross-sectional characteristic based models have yielded portfolios with higher excess monthly returns but lower risk than their arbitrage pricing theory counterparts in an analysis of equity returns of stocks listed on the JSE. Under the assumption of general no-arbitrage conditions, we arg…
The paper explores arbitrage opportunities in derivative markets under specific conditions.
problem Arbitrage opportunities in derivative markets under different conditions.
method Analyzes the relationship between pricing kernel monotonicity and stochastic arbitrage opportunities.
result Pricing kernel nonmonotonicity is equivalent to stochastic arbitrage opportunities under adequacy.
This paper constructs and studies the long-term factorization of affine pricing kernels into discounting at the rate of return on the long bond and the martingale component that accomplishes the change of probability measure to the long forward measure. The principal eigenfunction of the affine pricing kernel germane t…
Multiple Kernel Learning (MKL) is used to replicate the signal combination process that trading rules embody when they aggregate multiple sources of financial information when predicting an asset's price movements. A set of financially motivated kernels is constructed for the EURUSD currency pair and is used to predict…
New model explains option pricing with time-varying volatility risk aversion.
problem Time variations in the shape of the pricing kernel.
method Introduced a pricing kernel with time-varying volatility risk aversion combined with Heston-Nandi GARCH model.
result Variance risk ratio (VRR) emerges as a key variable in option pricing.
New volatility model for option pricing with time-varying risk premium.
problem Volatility risk premium is time-varying and not well captured by existing models.
method Combines Markov switching with Realized GARCH framework to derive a state-dependent pricing kernel.
result The model reduces option pricing errors by 15% or more compared to competing models.
Data-driven Option Pricingq-fin.PR
Data-driven method for option pricing using historical asset prices.
problem Tackling the gap between historical asset prices and risk-neutral option pricing.
method Identifying a pricing kernel process, solving utility maximization and functional optimization problems using deep learning.
result Demonstrated the efficiency of the data-driven option pricing methodology.
Algorithm maximizes revenue-risk by estimating price impact kernel and optimizing control problems.
problem Maximizing revenue-risk in a risky asset liquidation with unknown price impact.
method Alternates exploration and exploitation phases, uses novel kernel estimation and stability results.
result Sublinear regret achieved with high probability.
The paper introduces new methods for Asian option pricing using Laguerre quadrature.
problem Developing accurate pricing models for Asian options.
method Utilizes Laguerre quadrature and diffusion kernel approach.
result Demonstrates new techniques to solve complex Asian option pricing equations.
Researchers develop a generalised geometric Brownian motion for better asset pricing.
problem Irregularities in simple geometric Brownian motion for asset dynamics.
method Introduce a memory kernel to generalise GBM, derive moments and probability density functions.
result The performance of kernels in pricing options depends on option maturity and moneyness.
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of f…
A new method uses Gaussian processes and deep kernel learning to price high-dimensional American options efficiently.
problem Challenges in pricing high-dimensional American options, especially with excessive computational costs.
method Modified Gaussian process regression with deep kernel learning and sparse variational Gaussian processes.
result The method outperforms least squares Monte Carlo in high-dimensional scenarios, especially with Merton's jump diffusion model.
The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the Lévy-Vasicek case, avoiding issues of market incompleteness. In the Lévy-Vasicek mo…
The Volterra Heston model is used to price American options.
problem Pricing American options in the Volterra Heston model.
method Kernel-based approximations and simulation techniques.
result Convergence of American option prices in approximating models to the Volterra Heston model.
Study small-time CLTs for stochastic Volterra equations with various kernels.
problem Understanding the behavior of stochastic Volterra equations with different kernels.
method Proved convergence of finite-dimensional distributions, functional CLT, and limit theorems for smooth transformations.
result Derived asymptotic pricing formulae for digital calls in rough volatility models.
Optimizes insurance pricing by accounting for policyholders' price sensitivity.
problem Traditional insurance pricing does not consider policyholders' price sensitivity.
method Formulates insurance pricing as a decision-making problem and uses off-policy evaluation and stochastic control.
result Neural networks outperform existing techniques for policy optimization.
The general problem of asset pricing when the discount rate differs from the rate at which an asset's cash flows accrue is considered. A pricing kernel framework is used to model an economy that is segmented into distinct markets, each identified by a yield curve having its own market, credit and liquidity risk charact…
The paper optimizes investment strategies with constraints for life-cycle models.
problem Maximizing consumption, death benefit, and wealth under trading constraints.
method Deep pricing kernel approach to solve constrained portfolio optimization.
result Individuals reduce consumption, insurance demand, and wealth due to constraints.
We construct default-free interest rate models in the spirit of the well-known Markov funcional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and construct models by means of the so called propagation property. The propagation pr…
In the current literature, the analytical tractability of discrete time option pricing models is guaranteed only for rather specific types of models and pricing kernels. We propose a very general and fully analytical option pricing framework, encompassing a wide class of discrete time models featuring multiple-componen…
We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self-excitation, the price changes mean reversion…
We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for short-time asymptotic expansions of heat kernels, and obtain a family of general…
The Wiener chaos approach to interest rate modelling arises from the observation that the pricing kernel admits a representation in terms of the conditional variance of a square-integrable random variable, which in turn admits a chaos expansion. When the expansion coefficients factorise into multiple copies of a single…
We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation f…
Study models weather index insurance pricing by insurers and farmers, finding flexible pricing kernels boost profits.
problem Monopoly pricing of weather index insurance with risk and flexibility considerations.
method Bowley-type sequential game with insurer and farmer, using neural networks for farmer's payoff.
result Flexible pricing kernels increase insurer profits closer to indemnity insurance levels.
Proposes C2RM to mine cross-cryptocurrency relationships for better Bitcoin price prediction.
problem Limited consideration of historical relationships and interactions between cryptocurrencies for Bitcoin price prediction.
method C2RM module using Dynamic Time Warping for lead-lag relationship extraction and aggregation.
result Improves existing price prediction methods by significant performance improvement.
Optimal liquidation strategy with price impact and signal exploitation.
problem Maximizing revenue-risk in a market with transient and temporary price impact.
method Infinite dimensional stochastic control approach, backward stochastic differential equation, operator-valued Riccati equation.
result Explicit expression for the optimal trading strategy.
In this paper incomplete-information models are developed for the pricing of securities in a stochastic interest rate setting. In particular we consider credit-risky assets that may include random recovery upon default. The market filtration is generated by a collection of information processes associated with economic…
Develops multifactor approximations for SVEs with completely monotone kernels.
problem Approximating SVEs with kernels of completely monotone type.
method Multifactor approximation, Euler discretization, -estimation, convergence analysis.
result New multifactor Euler scheme reduces computational cost and outperforms SVEs for option pricing.
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.
The purpose of this article is to describe all possible beliefs of market participants on objective measures under Markovian environments when a risk-neutral measure is given. To achieve this, we employ the Martin integral representation of Markovian pricing kernels. Then, we offer economic and financial implications o…
Method interpolates option prices and volatilities without arbitrage.
problem Interpolating option prices and volatilities without arbitrage.
method Sparse modeling approach based on integral equations and SVD.
result Flexible and efficient framework for arbitrage-free interpolation.
We consider a model for linear transient price impact for multiple assets that takes cross-asset impact into account. Our main goal is to single out properties that need to be imposed on the decay kernel so that the model admits well-behaved optimal trade execution strategies. We first show that the existence of such s…
Paper proposes a new estimator for nested expectations with faster convergence.
problem Estimating nested expectations is computationally challenging.
method Nested kernel quadrature estimators with proof of faster convergence rate.
result The proposed method requires fewer samples for accurate estimation.
We propose a class of discrete-time stochastic models for the pricing of inflation-linked assets. The paper begins with an axiomatic scheme for asset pricing and interest rate theory in a discrete-time setting. The first axiom introduces a "risk-free" asset, and the second axiom determines the intertemporal pricing rel…
Tensor network surrogate for efficient option pricing in large portfolios.
problem Large-scale portfolio revaluation problems in market risk management.
method Tensor-train (TT) approximation for high-dimensional price surfaces, direct inference using Laplacian kernel and TT representations.
result Tensor surrogate achieves lower test error and faster evaluation times compared to standard GPR.
Transient market impact explained via Nash equilibrium in a game.
problem Understanding the transient nature of market impact.
method Analyzing a game between a trader and an arbitrageur, deriving decay kernels.
result Implied transient impact can be derived from trader behavior at Nash equilibrium.