The FD= and FDHESSIAN= options specify the use of finite difference approximations of the derivatives. The FD= option specifies that all derivatives are approximated using function evaluations, and ...

In the current low rates environment, the classic stochastic alpha beta rho (SABR) formula used to compute option-implied volatilities leads to arbitrages. In "Arbitrage free SABR", Hagan et al ...

A number of insurance industry practices have recently been reviewed and criticized by New York state Attorney General Eliot Spitzer, as well as various U.S. state insurance regulators. After initial ...

A family of uniformly accurate finite-difference schemes for the model problem $-\varepsilon u'' + a(x)u' + b(x)u = f(x)$ is constructed using a general finite-difference framework of Lynch and Rice ...

Peter Austing shows how to set up finite difference solvers to exactly recover the prices of all vanilla options on the grid. The approach leads to a specific discretisation of Dupire’s formula. It ...

First-order derivatives: n additional function calls are needed. Second-order derivatives based on gradient calls, when the "grd" module is specified (Dennis and Schnabel 1983): n additional gradient ...

Vol. 24, No. 3, SPECIAL ISSUE DEDICATED TO THE 70TH BIRTHDAY OF PROFESSOR LIN QUN (MAY 2006), pp. 252-264 (13 pages) In this work, we propose an efficient numerical method for computing the ...

Finite-Difference Time-Domain (FDTD) methods have become a cornerstone in the numerical solution of Maxwell’s equations, enabling detailed electromagnetic analysis across a wide range of applications.