Chase the Devil

A while ago, I have applied a relatively simple adaptive Filon quadrature to the problem of volatility swap pricing.

In my paper “Fast and Accurate Analytic Basis Point Volatility”, I use a table of Chebyshev polynomials to provide an accurate representation of some function.

I am experimenting a bit with least squares splines.

I recently had some fun trying to work directly with the option chain from the Nasdaq website.

The option chain on Yahoo finance shows an implied volatility number for each call or put option in the last column.

Tufte proposes interesting guidelines to present data, or even to design written semi-scientific papers or books.

When the dividend curve is built from discrete cash dividends, the dividend yield is discontinuous at the dividend time as the asset price jumps from the dividend amount.

I moved my blog from blogger to Hugo.

On the Wilmott forum, Pat Hagan has recently suggested to cap the equivalent local volatility in order to control the wings and better match CMS prices.

There is something funny going on with upcoming generic top level domains (gTLDs), they seem to be looked up in a strange manner (at least on latest Linux).

I am ambivalent towards David Foster Wallace.

I just stumbled upon this particularly illustrative case where the Crank-Nicolson finite difference scheme behaves badly, and the Rannacher smoothing (2-steps backward Euler) is less than ideal: double one touch and double no touch options.

I was wondering how to generate some nice cloudy like texture with a simple program.

I have looked a few months ago already at Julia, Dart, Rust and Scala programming languages to see how practical they could be for a simple Monte-Carlo option pricing.

In his book "Monte Carlo Methods in Finance", P.

There are not many arbitrage free extrapolation schemes.

I am looking at various extrapolation schemes of the implied volatilities.

I seem to never be entirely happy with any of the linux desktops these days.

C.

Here are the main steps of Hagan derivation.

I looked nearly two years ago already at the arbitrage free SABR of Andreasen-Huge in comparison to the arbitrage free PDE of Hagan and showed how close the ideas were: Andreasen-Huge relies on the normal Dupire forward PDE using a slightly simpler local…

A few recent programming languages sparked my interest: Julia because of the wide coverage of mathematical functions, and great attention to quality of the implementations.

I have looked at jump effects on volatility vs. variance swaps.

Antonov et al. present an interesting view on SABR with negative rates: instead of relying on a shifted SABR to allow negative rates up to a somewhat arbitrary shift, they modify slightly the SABR model to allow negative rates directly: $$ dF_t = |F_t|^\b…

There is very little information on variance swaps on a foreign asset.

Beside the problem with the discreteness of the replication, variance swaps are sensitive to jumps.

People regularly believe that Variance swaps need to be priced by discrete replication, because the market trades only a discrete set of options.

It’s quite incredible that Gnome 3.0 was almost an identical mess as KDE 4.0 had been a year or two earlier.

In most financial Monte-Carlo simulations, there is the need of generating normally distributed random numbers.

In an earlier post, I mentioned the similarities between the Guyon-Labordere particle method and the Vanderstoep-Grzelak-Oosterlee “bin” method to calibrate and price under Local Stochastic volatility.

In papers around volatility and cash (discrete) dividends, we often encounter the example of the flat volatility surface.

There is an interesting course on Machine Learning on Coursera, it does not require much knowledge and yet manages to teach quite a lot.

Quasi-Random numbers (like Sobol) are a relatively popular way in finance to improve the Monte-Carlo convergence compared to more classic Pseudo-Random numbers (like Mersenne-Twister).

Recently, some instabilities were noticed in the Carr-Lee seasoned volatility swap price in some situations.

Without knowing that it was a well known general concept, I first noticed the use of the Lamperti transform in the Andersen-Piterbarg “Interest rate modeling” book p.292 “finite difference solutions for general phi”.

I stumbled upon an unexpected problem: the one touch barrier formula can break down under negative rates.

I have been looking at various ways of finding initial guesses for SVI calibration (Another SVI Initial Guess, More SVI Initial Guesses, SVI and long maturities issues).

The variance under SVI becomes linear when the log-moneyness is very large in absolute terms.

On long maturities equity options, the smile is usually very much like a skew: very little curvature.

In the previous post, I showed one could extract the SVI parameters from a best fit parabola at-the-money.

The SVI formula is: $$w(k) = a + b ( \rho (k-m) + \sqrt{(k-m)^2+ \sigma^2}$$ where k is the log-moneyness, w(k) the implied variance at a given moneyness and a,b,rho,m,sigma the 5 SVI parameters.

In a talk at the Global Derivatives conference of Amsterdam (2014), Pat Hagan presented some new SABR formulas, supposedly close to the arbitrage free PDE behavior.

It's relatively well known that Heston does not fit the market for short expiries.

Most developers have strong opinions on dynamic types programming languages vs static types programming languages.

I have found a particularly nice initial guess to calibrate SABR.

I presented in an earlier post that I was mostly disillusioned with interview questions, it’s better to find out if you can learn something out of a candidate.Well there is maybe one very simple question that could be revealing, for people who pretend to…

While I was playing around calibrating the arbitrage free SABR model from Hagan (using the PDE on probability density approach), I noticed a misbehavior for some short maturity smiles.

There was a big debate at work around Exception declaration in a Java API.

Many people (and notoriously, Linus Torvald) complained about Gnome-shell, especially the early iterations.

While playing around with differential evolution to calibrate SABR, I noticed that sometimes, several set of parameters can lead to a very similar smile, usually the good one is for relatively low vol of vol and the bad one is for relatively high vol of v…