Levy processes
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.
Stability and convergence of Galerkin schemes for parabolic equations with application to Kolmogorov pricing equations in time-inhomogeneous Lévy models
In this paper the authors derive stability and convergence of fully discrete approximation schemes of solutions to linear parabolic evolution equations governed by time-dependent coercive operators.
Nonhomogeneous bivariate compound Poisson process with short-term periodicity
This paper presents new results on the nonhomogeneous bivariate compound Poisson process with a short-term periodic intensity function.
Podcast: Hagan on convexity, volatility and the London Whale
Ex-JP Morgan quant discusses his latest work and the risk failures that cost the bank $6bn in 2012
Optimal extraction and taxation of strategic natural resources: a differential game approach
This paper studies the optimal extraction and taxation of nonrenewable natural resources.
Risk-neutral densities: advanced methods of estimating nonnormal options underlying asset prices and returns
This work expands the analysis in Cooper (1999) and Santos and Guerra (2014), and the performance of the nonstructural models in estimating the "true" RNDs was measured through a process that generates "true" RNDs that are closer to reality, due to the…
Option pricing in exponential Lévy models with transaction costs
We present an approach for pricing European call options in the presence of proportional transaction costs, when the stock price follows a general exponential Lévy process.
Pricing multivariate barrier reverse convertibles with factor-based subordinators
In this paper, the authors study factor-based subordinated Lévy processes in their variance gamma (VG) and normal inverse Gaussian (NIG) specifications, and focus on their ability to price multivariate exotic derivatives.
European option pricing under geometric Lévy processes with proportional transaction costs
This paper considers the problem of European option pricing in the presence of a proportional transaction cost when the price of the underlying follows a jump–diffusion process.
Robust option pricing with characteristic functions and the B-spline order of density projection
This paper extends and refines the method of option pricing by frame projection of risk-neutral densities to incorporate B-splines.
Error analysis in Fourier methods for option pricing
The authors provide a bound for the error committed when using a Fourier method to price European options, when the underlying follows an exponential Lévy dynamic.
Operational risk modelled analytically II: classification invariance
In a simple model, Vivien Brunel establishes the properties of an operational risk model under the requirement of classification invariance
Transform-based evaluation of prices and Greeks of lookback options driven by Lévy processes
The authors develop a technique, based on numerical inversion, to compute the prices and Greeks of lookback options driven by Lévy processes.
Operational loss with correlated frequency and severity: an analytical approach
To enable autocorrelation in the frequency distribution, this paper proposes a significant generalization of the LDA model that involves treating operational risk as a Lévy jump-diffusion.
Pricing crude oil options using Lévy processes
This paper employs the fractional fast Fourier transform to calibrate parameters in an optimization setup.
Hedging error measurement for imperfect strategies
Jack Baczynski, Jonathan da Silva and Rosalino Junior present an index for measuring hedging errors