Constraints in the Levenberg-Marquardt least-squares optimization
The standard Levenberg-Marquardt (LM) optimizer does not support box constraints. We explore here two different approaches to add box constraints for a given unconstrained LM algorithm.
The state of open-source quadratic programming convex optimizers
I explore here a few open-source optimizers on a relatively simple problem of finding a good convex subset, but with many constraints: 30104 constraints for essentially 174 variables. My particular problem can be easily expressed in the form of a quadratic programming problem.
Staying arbitrage-free with Andreasen-Huge one-step interpolation
Not long ago, I wrote about Andreasen-Huge arbitrage-free volatility interpolation method. What we get out of Andreasen-Huge method, is a list of discrete option prices. What about option prices for strikes not on the grid?
On the Quality of Research Publications
I spent the last week-end to review a paper for the journal Expert Systems with Applications. It was a paper on a variant of Spider Monkey Optimization, which is in the same spirit as differential evolution or particle swarm optimization. While the manuscript was relatively interesting in itself, and there was definitely some non-trivial amount of work behind it, it was riddled with errors.
Webassembly still fragile
As I am preparing the website for my upcoming book on equity derivatives models, I played around with webassembly to run some C++ code from your web browser...
Particle Swarm Optimization on Heston Small-Time Expansion
Here, I look at the problem of calibrating a Heston small-time expansion, the one from Forde & Jacquier. This can be useful to find a good initial guess for the exact Heston calibration, computed with much costlier characteristic function Fourier numerical integration. I conclude with the madness of the life science inspired optimizers...
Particle Swarm Optimization
Some of my findings: a lot of publications. 45000 citations for the most popular one! Which are the ones that matter? Many different standards, but not a single one clearly expressed. Some surprisingly ugly source code.
Differential evolution vs. Simulated annealing
The differential evolution (DE) algorithm is somewhat popular in quantitative finance, for example to calibrate stochastic volatility models such as Heston. An older technique, much more popular in physics is simulated annealing (SA). There are few papers on its use for stochastic volatility calibration, most don't find the technique competitive or even usable.
A spline to fill the gaps with Andreasen-Huge one-step method
I recently stumbled upon a blog which suggested to not stay flat with Andreasen-Huge arbitrage free volatility interpolation method. What about using a spline?