Chase the Devil

There are relatively few studies quantifying the exact efficacy of scrambling over the more traditional random digital shift initialization of Sobol sequences.

You may or may not have heard that a piecewise-linear interpolation of caplet vols is not stable, it leads to oscillations in the caplet stripping procedure (implying caplet volatilities from cap vol market quotes).

I have been looking at various techniques for cliquet pricing with a focus on the Heston model.

Around 2014, I proposed a few Bachelier implied volatility “solvers”.

This note compares special-function choices at the level that matters to the implied volatility solvers: the normalized Black beta price, not standalone erfcx(x).

The use of erfcx instead of direct erfc or CDF in a Black-Scholes implied volatility solver leads to gain in accuracy and performance in general.

Choi, Huh and Su have a very good paper entitled Tighter uniform bounds for Black–Scholes implied volatility and the applications to root-finding.

Several years ago, I had explored accuracy and performance of different ways to imply the Black-Scholes volatility.

In my last post, I had a look at Quantlib implementation of a new scrambling method for Sobol due to Brent Burley of Walt Disney Studios Practical Hash-based Owen Scrambling.

I struggled a bit having Jack Audio Connection Kit working in Opensuse Tumbleweed.

The state of the art of Sobol scrambling has changed slightly recently, thanks to the paper from Brent Burley of Walt Disney Studios Practical Hash-based Owen Scrambling.

Recently, I have spent some time on simple neural networks.

Thomas Roos recently put a preprint on SSRN called Simple, Flexible, Analytic, Arbitrage Free Volatility Interpolation.

Leif Andersen and Mark Lake recently proposed the use of Non-Uniform Fast Fourier Transform for option pricing via the characteristic function.

The modern rough volatility models adopt a forward variance curve terminology (see for example this paper on a rational approximation for the rough Heston, or this presentation on affine forward variance models or this paper on affine forward variance mod…

I recently saw a news about a great new simulation scheme for the Heston model by Abi Jaber.

Fabrice Rouah wrote two books on the Heston model: one with C# and Matlab code, and one with VBA code.

Around 10 years ago, while reading the excellent paper of Etore and Gobet on stochastic Taylor expansions for the pricing of vanilla options with discrete (cash) dividends, I had the idea of a small improvement, by using a more precise proxy for the Taylor

My 12 years old child recently had a presentation to do with 3 other children for school, the subject was food and health.

An interesting idea to calibrate the Heston model in a more stable manner and reduce the calibration time is to make use of variance swap prices.

I recently upgraded a desktop computer, and to my surprise, the new motherboard was not fully supported by most Linux distributions.

I had the opportunity to receive a free book on climate change, through the company I am working for.

It is well known that vanilla option prices must increase when we increase the implied volatility.

When computing the derivative of a function by finite difference, which step size is optimal?

The COS method is a fast way to price vanilla European options under stochastic volatility models with a known characteristic function.

I never paid too much attention to it, but the term-structure of variance swaps is not always realistic under the Schobel-Zhu stochastic volatility model.

In the previous post, I presented a new stochastic expansion for the prices of Asian options.

Many years ago, I had applied the stochastic expansion technique of Etore and Gobet to a refined proxy, in order to produce more accurate prices for vanilla options with cash dividends under the Black-Scholes model with deterministic jumps at the dividend…

In the Black-Scholes model with a term-structure of volatilities, the Log-Euler Monte-Carlo scheme is not necessarily exact.

In my previous blog post, I looked at the roughness of the SVCJ stochastic volatility model with jumps (in the volatility).

I was wondering if adding jumps to stochastic volatility, as is done in the SVCJ model of Duffie, Singleton and Pan “Transform Analysis and Asset Pricing for Affine Jump-Diffusion” also in Broadie and Kaya “Exact simulation of stochastic volatility and ot…

I received a few e-mails asking me for the code I used to measure roughness in my preprint on the roughness of the implied volatility.

I was experimenting with the recent SABR basket approximation of Hagan.

The Clenshaw-Curtis quadrature is known to be competitive with Gauss quadratures.

During my vacation, I don’t know why, but I looked at some stability issue with ghost points and the explicit method.

The paper The Moment Formula for Implied Volatility at Extreme Strikes by Roger Lee redefined how practioners extrapolate the implied volatility, by showing that the total implied variance can be at most linear in the wings, with a slope below 2.

In a Wilmott article from 2018 (Wilmott magazine no. 97) titled “Arbitrage in the perfect volatility surface”, Uwe Wystup points out some interesting issues on seemingly innocuous FX volatility surfaces: a cubic spline tends to produce artificial peaks/mo…

I recently presented my latest published paper On the Bachelier implied volatility at extreme strikes at the Princeton Fintech and Quant conference.

I have been a long time user of Fedora at work and have been happy quite happy about it.

This is a follow up of my previous post on rough volatility.

It is well-known that the assumption of constant volatility in the Black-Scholes model for pricing financial contracts is wrong and may lead to serious mispricing, especially for any exotic derivative contracts.

When writing a Monte-Carlo simulation to price financial derivative contracts, the most straightforward is to code a loop over the number of paths, in which each path is fully calculated.

This blog post from Jherek Healy presents some not so obvious behavior of automatic differentiation, when a function is decomposed into the product of two parts where one part goes to infinity and the other to zero, and we know the overall result must go…

As described on wikipedia, a quadratic programming problem with n variables and m constraints is of the form $$ \min(-d^T x + 1/2 x^T D x) $$ with the constraints \( A^T x \geq b_0 \), were \(D\) is a \(n \times n\)-dimensional real symmetric matrix, \(A\)

In the context of my thesis, I explored the use of stochastic collocation to capture the marginal densities of a positive asset.

Steven Koonin, who was Secretary for Science, Department of Energy, in the Obama administration recently wrote a somewhat controversial book on climate science with the title Unsettled.

Github recently moved to support only ssh access via public/private keys.

One thing that motivated me for vaccination is the fake news propaganda against the Covid-19 vaccines.

This is a follow up on my parents phishing scam.

This is the story of their hack.