-
Efficient Finite Difference Grid Stretching for Finance
Discontinuities in the payoff or its derivatives are common in financial PDEs. If not handled properly, those discontinuities may decrease the accuracy of the finite difference scheme significantly. Are insertions at relevant locations good enough? What about streched grids? A new efficient stretching is proposed.
-
Klein summation and Monte-Carlo simulations
In parallelized Monte-Carlo simulations, the order of summation is not always the same. When the mean is calculated in running fashion, this may create an artificial randomness in results which ought to be reproducible. Does the Klein summation help addressing this issue? Are there better alternatives?
-
Exponential B-Spline Collocation and Julia Automatic Differentiation
New algorithms for polynomial stochastic collocation and exponential B-spline collocation are available now in my github repo. I had a few surprises while recreating those in Julia and using the forward automatic differentiation.
-
The Cos Method, Go and Julia
As I am preparing the third edition of my book (which I plan to complete this month), I am also moving some of the algorithms I coded in the Go language to Julia and at the same time make those public. Among those is the Cos method.
-
The Fastest Implied Volatility Algorithms, Go vs. Julia
In the second edition of my book, I presented how to combine the good Black-Scholes implied volatility initial guess of Dan Stefanica and Rados Radoicic with a relatively simple solver. Here, I present how to further enhance the performance, and compare as well implementations in the Go language vs. the Julia language.
-
Why did I choose the Go language?
Recently, a reader of my book asked me why did you choose the Go language?. Here is a more elaborate answer. And, would I still choose it now?
-
Julia and Python for the RBF collocation of a 2D PDE with multiple precision arithmetic
This is not going to be a comparison between Julia and Python in general. I am sure there exists already many great articles on Julia vs. XYZ language available on the internet. The below is more a hands on Julia from a numerical scientist point of view, when applied to the RBF collocation of a 2D PDE.
-
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?
