Meshfree methods based on radial basis function (RBF) approximation are of interest for
numerical solution of partial differential equations (PDEs) because they are flexible with …

We develop an algorithm for computing the solution of a large system of linear ordinary
differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to …

This book covers foreign exchange options from the point of view of the finance practitioner.
It contains everything a quant or trader working in a bank or hedge fund would need to know …

In this paper, we design an efficient and accurate numerical method for solving the time-
fractional Black–Scholes equation governing European options. The time-fractional Black …

We derive a new high-order compact finite difference scheme for option pricing in stochastic
volatility models. The scheme is fourth order accurate in space and second order accurate in …

In this article, a simple, effective adaptation of Alternating Direction Implicit time
discretization schemes is proposed for the numerical pricing of American-style options under …

In this paper we present a numerical method to price options based on Radial Basis
Function generated Finite Differences (RBF-FD) in space and the Backward Differentiation …

This paper addresses the joint calibration problem of SPX options and VIX options or
futures. We show that the problem can be formulated as a semimartingale optimal transport …

In this paper, we prove an approximate formula expressed in terms of elementary functions
for the implied volatility in the Heston model. The formula consists of the constant and first …

We calibrate neural stochastic differential equations jointly to S&P 500 smiles, VIX futures,
and VIX smiles. Drifts and volatilities are modeled as neural networks. Minimizing a suitable …