This paper introduces the class of volatility modulated Lévy-driven Volterra (VMLV) processes and their important subclass of Lévy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First, deseasonalised spot prices can be modelled di…
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48 results for “Levy-driven pricing”
Fast and General Simulation of Lévy-driven Ornstein Uhlenbeck processes for Energy Derivativesq-fin.CP
New simulation technique speeds up Lévy-driven OU process pricing.
problem Inefficient Monte Carlo simulations of Lévy-driven OU processes.
method Numerical inversion of characteristic function combined with FFT for fast and accurate simulations.
result The proposed technique is at least one order of magnitude faster than existing methods.
A new model uses a Levy-driven process to value credit index swaptions.
problem Valuation of credit index swaptions in financial markets.
method Proposes a Levy-driven Ornstein-Uhlenbeck process to model risk-free rate and default intensities.
result Derives formulas for characteristic function, moments, and stationary distribution.
Extends option pricing framework without risk-free asset using Levy jumps.
problem Valuing derivatives in markets without a traded risk-free bond.
method Introduces common Levy jump dynamics, uses Ito-Levy calculus, FFT, and COS algorithms.
result Calibrations show jump models reduce pricing errors and fit volatility smiles better than Black-Scholes.
Develops a new model for day-ahead electricity prices using ambit fields.
problem The high-dimensional panel structure of electricity spot prices in European zones.
method Formulates a continuous time framework as an ambit field indexed by a cylinder surface, embedding intrinsic dependence structures.
result The model allows for pricing of derivatives on individual delivery periods, making products like spreads analytically tractable.
The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIB…
Novel weak MLMC scheme for Lévy-driven SDEs, applied to financial derivatives pricing.
problem Approximating solutions to Lévy-driven SDEs for financial derivatives pricing.
method Weak multilevel Monte-Carlo scheme with state space discretization of Lévy processes.
result Efficient approximation of financial derivatives pricing models.
Method verifies if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
problem Verifying if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
method Estimating parameters and approximating the driving process to test CAR(1) Lévy-driven hypothesis.
result Demonstrates method's effectiveness through simulations and real data examples.
A Monte Carlo method for pairs trading on mean-reverting spreads with Lévy processes.
problem Trading on mean-reverting spreads with flexible models.
method Monte Carlo simulation with variance gamma and alpha-gamma driving processes.
result Optimal trading strategies are affected by model parameters and correlation.
Approximation of the distribution of a stationary Markov process with application to option pricingmath.PR
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued càdlàg functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to …
Lévy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the Lévy driven Heath-Jarrow-Morton type term structure equation. This includes a full proof of existence and uniqueness in particular, which seems to have been lack…
Efficient CNN-LSTM based Parameter Estimation of Levy Driven Stochastic Differential Equationsstat.ML
Study improves parameter estimation for SDEs driven by Levy noise.
problem Challenges in estimating parameters of SDEs with non-Gaussian noises.
method Introduces PEnet, a CNN-LSTM model for efficient parameter estimation.
result PEnet offers superior accuracy and adaptability for various SDE scenarios.
Pricing of basket options Iq-fin.CP
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of Lévy driven models of stock markets. In our opinion, any market model should be based on a transparent and intuitively easily acceptable concept. In our case this is a linear system …
Paper models non-maturing deposits using a Lévy-driven Ornstein-Uhlenbeck process.
problem Managing non-maturing deposits as a major funding source for banks.
method Develops a multivariate Lévy-driven Ornstein-Uhlenbeck process with three sources of randomness.
result Models rare but severe events in deposit volumes with positive probability.
Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic vol…
We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral appro…
In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) Lévy processes to model the underlying asset of contingent claims. A DTC Lévy process is a generalized time-changed Lévy process whose continuous and pure jump parts are allowed to follow separate random time scal…
Proposes second-order Esscher transform for Lévy models in financial markets.
problem Risk management and quantification in markets with jumps and Lévy dynamics.
method Derives densities, equivalent measures, and pricing formulas for European call options.
result Option prices are bounded and monotonic with the second-order Esscher parameter.
New method for Bayesian inference of Lévy-driven SDEs with jumps.
problem Bayesian inference for Lévy-driven SDEs is challenging due to discontinuities and heavy tails.
method Neural exponential tilting framework for variational inference.
result Accurately captures jump dynamics and reliable posterior inference in heavy-tailed regimes.
Develops a PD estimation model using Lévy-driven processes for credit risk.
problem Estimating Probability of Default under new IFRS 9 regulations.
method Lévy-driven Ornstein-Uhlenbeck process with multiple latent variables, Integral Equation and PIDE formulation.
result Existence of weak and strong solutions for PD function, numerical schemes developed.
Develops a new bivariate process for energy markets with improved simulation methods.
problem Modelling energy markets with stochastic delays and efficient simulations.
method Introduces a novel bivariate Normal Inverse Gaussian process and a path simulation scheme.
result Improves simulation efficiency for energy market models.
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
problem Understanding Lévy-driven Ornstein-Uhlenbeck processes and their properties.
method Characterizes the Lévy triplet and deduces transition laws for finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions.
result Provides algorithms for generating skeleton of Ornstein-Uhlenbeck processes related to exponentially-modulated tempered stable laws.
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades the Black-Scholes this model, which essentially is based on the log-normal assum…
We consider the problem of utility maximization with exponential preferences in a market where the traded stock/risky asset price is modelled as a Lévy-driven pure jump process (i.e. the driving Lévy process has no Brownian component). In this setting, we study the terminal utility optimization problem in the presence …
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi…
In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility funct…
We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run fo…
On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficientsmath.PR
Study on non-negative solutions for stochastic Volterra equations with jumps.
problem Existence and uniqueness of non-negative solutions for stochastic Volterra equations with jumps and non-Lipschitz coefficients.
method Developed a nonnegative approximation approach and used Yamada--Watanabe approximation technique for convergence proof.
result Established conditions for strong existence and pathwise uniqueness of non-negative solutions.
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Lévy process with a high order scheme for the Brownian driven component, applied bet…
We derive asymptotic expansions for option data to detect infinite variation volatility.
problem Detecting infinite variation volatility in high-frequency option data.
method Nonparametric higher-order asymptotic expansions for small-time changes of characteristic functions of Itô semimartingales.
result Evidence of infinite variation volatility in high-frequency option data.
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes. The focus of our study is to give new characterizations of quasi self-duality for exponential Lévy processes such that the resulting market does not admit arbitrage opportunities. We derive …
MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.
problem Sampling from heavy-tailed and multimodal distributions when neither target nor proposal densities can be evaluated.
method Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA) with Score Balance Matching.
result MAFLA significantly improves finite-time sampling accuracy over unadjusted fractional Langevin dynamics.
Along with the recent advances in scalable Markov Chain Monte Carlo methods, sampling techniques that are based on Langevin diffusions have started receiving increasing attention. These so called Langevin Monte Carlo (LMC) methods are based on diffusions driven by a Brownian motion, which gives rise to Gaussian proposa…
Estimates graph process with high-frequency data, proving asymptotic properties.
problem Estimating graph process with high-frequency data.
method Discretized maximum likelihood estimators for GrOU process under high-frequency sampling.
result Asymptotic central limit theorems for estimators under finite and infinite jump activity.
Work on SGDm under heavy-tailed noise, revealing its generalization properties.
problem Understanding generalization of SGDm under heavy-tailed noise.
method Analysis of continuous-time limit (SDE) and discrete-time SGDm, establishing generalization bounds.
result SGDm can have worse generalization in the presence of heavy-tailed noise for quadratic loss functions.
This research explains why SGD generalizes better than ADAM in deep learning.
problem Understanding the generalization gap between SGD and ADAM in deep learning.
method Analyzing local convergence behaviors through Levy-driven stochastic differential equations (SDEs).
result SGD is more locally unstable and better escapes from sharp minima to flatter ones, leading to better generalization.
The paper uncovers the impact of price and payoff autocorrelations in multi-period asset pricing models.
problem Hidden dependence of asset pricing models on price and payoff autocorrelations.
method Obtained approximations of the basic pricing equation describing various parameters.
result Valid results for other pricing models like ICAPM and APM.
Benchmark-Neutral Pricingq-fin.MF
Paper introduces benchmark-neutral pricing for long-term contracts.
problem High prices of long-term contracts under risk-neutral pricing.
method Uses growth optimal portfolio as numeraire and new pricing measure.
result Identifies minimal possible prices for contingent claims.
We explore nature of price formation in financial markets and develop a theory of bid and ask price dynamics in which the two prices form due to quantum-chaotic interaction between buy and sell orders. In this model bid and ask prices are represented by eigenvalues of a 2x2 price operator corresponding to 'bid' and 'as…
New pricing algorithm learns demand curves and optimizes prices in dynamic markets.
problem Dynamic pricing in markets with incomplete demand information and shifting conditions.
method Actor-Critic Information-Directed Pricing (ACIDP) using IDS algorithms and auditing procedures.
result ACIDP outperforms UCB and TS in market environment shifts.
In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricin…
At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price,...). Thus, in practice, market participants face the problem of choosing a price when implementing their strategies. In this work, we propose …
Study utility indifference pricing in a Bachelier model with small linear price impact.
problem Utility indifference pricing in a model with linear price impact.
method Analyzes the Bachelier model with exponential utility indifference prices for vanilla European options.
result Computes the scaling limit of utility indifference prices for a vanishing price impact inversely proportional to risk aversion.
A pricing principle is introduced for non-attainable claims in incomplete markets.
problem Pricing non-attainable contingent claims in incomplete markets.
method Distorted Radon-Nikodym derivative and Tsallis relative entropy over a family of equivalent martingale measures.
result The pricing principle is closely related to backward stochastic differential equations and is arbitrage-free and time-consistent.
Price without transaction makes no sense. Trading volume authenticates its corresponding price, so there exist mutual information and correlation between price and trading volume. We are curious about fractal features of this correlation and need to know how structures in different scales translate information. To expl…
Revisits behavioral finance option pricing model to align with rational asset pricing theory.
problem Inconsistency between behavioral finance and rational asset pricing models in option pricing.
method Introduces arbitrage transaction costs to modify the behavioral finance option pricing formula.
result Modifies behavioral finance option pricing formula to be consistent with rational asset pricing theory.
The paper extends option pricing theory for markets with informed traders.
problem Discontinuity in option pricing for markets with informed traders.
method New models for option pricing in complete markets considering informed traders' information on stock price direction and return mean.
result The discontinuity puzzle in option pricing is resolved using continuous diffusion price processes.
How does dynamic price information flow among Northern European electricity spot prices and prices of major electricity generation fuel sources? We use time series models combined with new advances in causal inference to answer these questions. Applying our methods to weekly Nordic and German electricity prices, and oi…