Chase the Devil

I stumbled upon a new short book Financial Models in Production from O.

I was wondering what were exactly the eigenvalues of the Mersenne-Twister random number generator transition matrix.

Several years ago, I read the book No Logo from Naomi Klein.

My previous post described the recent view on random number generators, with a focus on the Mersenne-Twister war.

These days, there seems to be some sort of small war to define what is a modern good random number generators to advise for simulations.

A while ago, I wondered how to make some implementation of Sobol support 64-bits integers (long) and double floating points.

What has been happening to the INTC stock today may be revealing of the future.

The stock market crashed by more than 7% on March 9, 2020.

Today my 6-years old son came with a math homework.

Many benchmarks show impressive performance gains with the use of Numba or Pypy.

I just moved my blog to a static website, created with Hugo, I explain the reasons why here.

Out of curiosity, I tried quadprog as open-source quadratic programming convex optimizer, as it is looks fast, and the code stays relatively simple.

This is a follow up to my previous post where I explore the probability of a TSLA stock crash, reproducing the results of Timothy Klassen.

Timothy Klassen had an interesting post on linkedin recently, with the title “the options market thinks there is a 16% chance that Tesla will not exist in January 2020”.

I was wondering if I could use the SABR moments to calibrate a model to SABR parameters directly.

This is a follow-up to my posts on the implied risk-neutral density (RND) of the SPW options before and after the big volatility change that happened in early February with two different techniques: a smoothing spline on the implied volatilities and a Gau…

It has been a while since the good old object-oriented (OO) programming is not trendy anymore.

In the previous post, I showed a plot of the probability implied from SPW options before and after the big volatility change of last week.

Yesterday the American stocks went a bit crazy along with the VIX that jumped from 17.50 to 38.

Several months ago, I had a quick look at a recent paper describing how to use Wavelets to price options under stochastic volatility models with a known characteristic function.

I would have never really expected that when I started writing papers, but little by little there is a growing list of books citing my papers: Applied Quantitative Finance for Equity Derivatives by Jherek Healy: the most recent book on equity derivatives…

It is a relatively common belief that the vanilla Android experience is better, as it runs smoother.

A few years ago, when Git was rising fast and SVN was already not hype anymore, a friend thought that SVN was for many organizations better suited than Git, with the following classical arguments, which were sound at the time: Who needs decentralization f…

Machine learning and artificial intelligence are the current hype (again).

Around 15 years ago, I wrote a small Java applet to try and show the Benham disk effect.

There are not many blogs on quantitative finance that I read.

In their paper “Nonnegativity-, Monotonicity-, or Convexity-Preserving Cubic and Quintic Hermite Interpolation”, Dougherty, Edelman and Hyman present a simple filter on the first derivatives to maintain positivity of a cubic spline interpolant.

Dan Stefanica and Rados Radoicic propose a quite good initial guess in their very recent paper An Explicit Implied Volatility Formula.

The VIX implied volatilities used to look like a logarithmic function of the strikes.

In order to fit the implied volatility smile of equity options, one of the most popular parameterization is Jim Gatheral’s SVI, which I have written about before here.

The new Heston discretisation scheme I wrote about a few weeks ago makes use a discrete random variable matching the first five moments of the normal distribution instead of the usual normally distributed random variable, computed via the inverse cumulati…

This is a note for those who want to setup a Samsung wireless printer under Linux.

A couple weeks ago, I wrote about a new Heston discretisation scheme which was at least as accurate as Andersen QE scheme and faster, called DVSS2.

The gnome shell has been crashing on me more regularly lately.

Many papers present formulae to price Asian options in the Black-Scholes world only for the fixed strike Asian case, that is a contract that pays \( \max(A-K,0)\) at maturity \(T\) where \(A = \sum_{i=0}^{n-1} w_i S(t_i) \) is the Asian average.

It is relatively well known that the Black-Scholes volatility can not grow faster than \(\sqrt{\ln(K)}\).

I stumbled recently upon a new Heston discretisation scheme, in the spirit of Alfonsi, not more complex and more accurate.

Jesper Andreasen and Brian Huge propose an arbitrage-free interpolation method based on a single-step forward Dupire PDE solution in their paper Volatility interpolation.

We will assume zero interest rates and no dividends on the asset \(S\) for clarity.

We have seen earlier that a simple parabola allows to capture the smile of AAPL 1m options surprisingly well.

In finance, and also in science, the Mersenne-Twister is the de-factor pseudo-random number generator (PRNG) for Monte-Carlo simulations.

I found back some old notes I had written about the book “Le capital au XXI siecle” from Thomas Piketty.

Last year, I was kindly invited at the workshop on Models and Numerics in Financial Mathematics at the Lorentz center.

In my previous post, I looked at de-arbitraging volatilities of options of a specific maturity with the shooting method.

In my previous post, I looked at de-arbitraging volatilities of options of a specific maturity with SVI (re-)calibration.

Yesterday, I wrote about some calendar spread arbitrages with SVI.

Zeliade wrote an excellent paper about the calibration of the SVI parameterization for the volatility surface in 2008.

I had a look at how to price under Local Volatility with Cash dividends in my previous post.

The Dupire equation for local volatility has been derived under the assumption of Martingality, that means no dividends or interest rates.

In a previous post, I took a look at least squares spline and parabola fits on AAPL 1m options market volatilities.