Partial integro-differential equation
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.
Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model
Stability and convergence of Galerkin schemes for parabolic equations with application to Kolmogorov pricing equations in time-inhomogeneous Lévy models
Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options
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.
Efficient solution of backward jump-diffusion partial integro-differential equations with splitting and matrix exponentials
A unified approach for solving jump-diffusion partial integro differential equations is proposed.
Numerical methods for the quadratic hedging problem in Markov models with jumps
In this paper algorithms are developed using the Hamilton–Jacobi–Bellman approach for parabolic partial integrodifferential equations related to the quadratic hedging strategy in incomplete markets.
A novel partial integrodifferential equation-based framework for pricing interest rate derivatives under jump-extended short-rate models
Interest rate derivatives under jump-extended short-rate models have commonly been valued using lattice methods. This paper proposes a much faster and more accurate valuation method based on partial integrodifferential equations.
Universal Barriers
As our survey in this issue shows, there is an increasing volume of barrier products traded in the forex options market. Here, Alexander Lipton and William McGhee discuss the pricing of barriers under various model frameworks, with particular focus on…