• A New Asian Basket Spread Option Approximation Apr 22, 2025
• Calibrating Heston to Variance Swaps - a bad idea? Feb 11, 2025
• Monotonicity of the Black-Scholes Option Prices in Practice Sep 29, 2024
• Copilot vs ChatGPT on the Optimal Finite Difference Step-Size Jul 25, 2024
• News on the COS Method Truncation May 13, 2024
• Variance Swap Term-Structure under Schobel-Zhu Mar 26, 2024
• New Basket Expansions and Cash Dividends Mar 23, 2024
• New Approximations for the Prices of Asian and basket Options Mar 17, 2024
• Easy Mistake With the Log-Euler Discretization On Black-Scholes Mar 11, 2024
• Roughness of Pure Jumps Dec 18, 2023
• Roughness of Stochastic Volatility with Jumps Dec 7, 2023
• Measuring Roughness with Julia Nov 7, 2023
• Black with Bachelier Oct 3, 2023
• Clenshaw-Curtis Quadrature Implementation by FFT in Practice Sep 27, 2023
• Ghost Vacations Aug 20, 2023
• Maximum Implied Variance Slope May 22, 2023
• The Return of the Arbitrage in the Perfect Volatility Surface Mar 29, 2023
• Princeton Fintech and Quant conference of December 2022 Dec 4, 2022
• Roughness of the Implied Volatility Jul 9, 2022
• Volatility: Rough or Not? A Short Review May 10, 2022
• Monte-Carlo Parallelization: to vectorize or not? Apr 9, 2022
• More Automatic Differentiation Awkwardness Jan 4, 2022
• Quadprog in Julia Nov 21, 2021
• Positive Stochastic Collocation Aug 31, 2021
• Remarkable Coincidences, Bad Book? Nov 21, 2020
• More on random number generators Oct 10, 2020
• The war of the random number generators Sep 17, 2020
• Sobol with 64-bits integers Sep 9, 2020
• March 9, 2020 crash - where will CAC40 go? Mar 9, 2020
• Numba, Pypy Overrated? Feb 12, 2019
• Fixing NaNs in Quadprog Oct 7, 2018
• On the Probability of a Netflix Stock Crash Jul 12, 2018
• On the Probability of a TSLA Stock Crash Jul 11, 2018
• The Fourth Moment of the Normal SABR Model Jun 11, 2018
• Implying the Probability Density from Market Option Prices (Part 2) May 27, 2018
• Implying the Probability Density from Market Option Prices Feb 13, 2018
• Where is the S&P 500 going to end? Feb 6, 2018
• Discrete Sine Transform via the FFT Feb 5, 2018
• Quantitative Finance Books Citing My Papers Dec 9, 2017
• Blogs on Quantitative Finance Jun 21, 2017
• Typo in Hyman non-negative constraint - 28 years later May 23, 2017
• Implied Volatility from Black-Scholes price Apr 2, 2017
• The VIX starts smiling Mar 21, 2017
• When SVI Breaks Down Mar 16, 2017
• Brownian Bridge and Discrete Random Variables Jan 26, 2017
• A new scheme for Heston - Part 2 Jan 23, 2017
• Equivalence between floating-strike and fixed-strike Asian options Jan 18, 2017
• Bachelier Normal Volatility Asymptotics Jan 17, 2017
• A new scheme for Heston Jan 6, 2017
• Andreasen-Huge interpolation - Don't stay flat Dec 13, 2016
• Put-Call parity and the log-transformed Black-Scholes PDE Dec 5, 2016
• Benaim et al. extrapolation does not work on equities Oct 4, 2016
• AES for Monte-Carlo Aug 17, 2016
• Number of regressors in a BSDE Jul 26, 2016
• Shooting arbitrage - part II Jul 5, 2016
• Shooting arbitrage - part I Jun 22, 2016
• Dearbitraging a weak smile on SVI with Damghani's method Jun 15, 2016
• Arbitrage in Zeliade's SVI example Jun 14, 2016
• Dupire Local Volatility with Cash Dividends Part 2 May 29, 2016
• Dupire Local Volatility with Cash Dividends May 19, 2016
• SVI, SABR, or parabola on AAPL? May 12, 2016
• Adaptive Filon quadrature for stochastic volatility models May 12, 2016
• Least Squares Rational Function Apr 21, 2016
• Least Squares Spline for Volatility Interpolation Feb 19, 2016
• The Mystic Parabola Feb 16, 2016
• Yahoo Finance Implied Volatility Feb 3, 2016
• Linear and Flat forward interpolation with cash dividends Jan 19, 2016
• Go for Monte-Carlo Aug 22, 2015
• Bumping Correlations Jul 25, 2015
• Andreasen Huge extrapolation Jul 13, 2015
• Unintuitive behavior of the Black-Scholes formula - negative volatilities in displaced diffusion extrapolation Jul 7, 2015
• Square Root Crank-Nicolson Jun 19, 2015
• Decoding Hagan's arbitrage free SABR PDE derivation May 8, 2015
• Matching Hagan PDE SABR with the one-step Andreasen-Huge SABR Apr 30, 2015
• Modern Programming Language for Monte-Carlo Apr 18, 2015
• Volatility Swap vs Variance Swap Replication - Truncation Mar 16, 2015
• Arbitrage free SABR with negative rates - alternative to shifted SABR Mar 11, 2015
• Variance swaps on a foreign asset Feb 24, 2015
• Jumps impact: Variance swap vs volatility swap Feb 20, 2015
• Variance Swap Replication : Discrete or Continuous? Feb 19, 2015
• Monte Carlo & Inverse Cumulative Normal Distribution Feb 3, 2015
• Local Stochastic Volatility - Particles and Bins Jan 30, 2015
• Flat Volatility Surfaces & Discrete Dividends Nov 25, 2014
• Machine Learning & Quantitative Finance Nov 18, 2014
• Pseudo-Random vs Quasi-Random Numbers Nov 12, 2014
• Integrating an oscillatory function Nov 5, 2014
• The elusive reference: the Lamperti transform Nov 3, 2014
• Barrier options under negative rates: complex numbers to the rescue Oct 2, 2014
• Initial Guesses for SVI - A Summary Sep 26, 2014
• Asymptotic Behavior of SVI vs SABR Sep 23, 2014
• SVI and long maturities issues Aug 1, 2014
• More SVI Initial Guesses Jul 31, 2014
• Another SVI Initial Guess Jul 29, 2014
• New SABR Formulae Jul 16, 2014
• Heston or Schobel-Zhu issues with short expiries Jul 3, 2014
• Moore-Penrose Inverse & Gauss-Newton SABR Minimization Jun 24, 2014
• On the importance of accuracy for bpvol solvers Jun 12, 2014
• Two SABR for the same smile May 20, 2014
• Heston vs SABR slice by slice fit May 15, 2014
• Quadratic Spline with Knots at Mid-Points May 14, 2014
• Non-linear Option Pricing Apr 18, 2014
• Building a more accurate basis point volatility formula Apr 5, 2014
• Fast and Accurate Implied Volatility Solver Mar 19, 2014
• Arbitrage Free Interpolation of Option Prices using Piecewise Constant Density Mar 17, 2014
• C2 Arbitrage Free Interpolation with Tension Splines Mar 11, 2014
• Bachelier and Black-Scholes Fits of the Volatility Surface, what about SABR? Mar 7, 2014
• Arbitrage Free Wiggles Mar 3, 2014
• Adjoint Delta for Monte-Carlo Feb 25, 2014
• SVI on top of SABR Feb 20, 2014
• Smart Initial Guess for Schobel-Zhu Feb 19, 2014
• A Look at Small Time Expansions for Heston Feb 12, 2014
• A Small-Time Schobel-Zhu Expansion Feb 10, 2014
• Brownian Bridge or Not with Heston Quadratic Exponential QMC Jan 24, 2014
• Adjoint Algorithmic Differentiation for Black-Scholes Jan 21, 2014
• Placing the Strike on the Grid and Payoff Smoothing in Finite Difference Methods for Vanilla Options Jan 12, 2014
• Coordinate Transform of the Andreasen Huge SABR PDE & Spline Interpolation Jan 8, 2014
• Levenberg Marquardt & Constraints by Domain Transformation Dec 17, 2013
• Arbitrage Free SABR - Another View on Hagan Approach Dec 14, 2013
• American Option on Forward/Futures Nov 21, 2013
• Spikes in Heston/Schobel-Zhu Local Volatility Nov 20, 2013
• Local Stochastic Volatility with Monte-Carlo Oct 16, 2013
• Heston, Schobel-Zhu, Bates, Double-Heston Fit Oct 7, 2013
• Second Cumulant of Heston Oct 3, 2013
• Maxima for Symbolic Calculus Oct 2, 2013
• Making Classic Heston Integration Faster than the Cos Method Sep 5, 2013
• Attari, Lord-Kahl & Cos Methods Comparison on Heston Aug 28, 2013
• Julia and the Cumulative Normal Distribution Aug 13, 2013
• The COS method for Heston Aug 2, 2013
• Octave vs Scilab for PDEs in Finance Jul 30, 2013
• The CUDA Performance Myth II Jul 12, 2013
• Bessel and Harmonic Kinks in the Forward Jul 2, 2013
• The Finite Difference Theta Scheme Optimal Theta Jun 18, 2013
• Akima for Yield Curve Interpolation ? Jun 3, 2013
• 2 Ways for an Accurate Barrier with Finite Difference Jun 2, 2013
• SABR with the new Hagan PDE Approach May 28, 2013
• SABR with Andreasen-Huge May 24, 2013
• Large Steps in Schobel-Zhu/Heston the Lazy Way May 17, 2013
• Exact Forward in Monte-Carlo May 13, 2013
• Quasi Monte Carlo in Finance May 13, 2013
• Upper Bounds in American Monte-Carlo Apr 30, 2013
• Quasi Monte-Carlo & Longstaff-Schwartz American Option price Apr 22, 2013
• A Fast Exponential Function in Java Apr 19, 2013
• Root finding in Lord Kahl Method to Compute Heston Call Price (Part III) Apr 12, 2013
• Root finding in Lord Kahl Method to Compute Heston Call Price (Part II) Apr 11, 2013
• Root finding in Lord Kahl Method to Compute Heston Call Price Apr 9, 2013
• From Double Precision Normal Density to Double Precision Cumulative Normal Distribution Apr 2, 2013
• Cracking the Double Precision Gaussian Puzzle Mar 22, 2013
• A Double Precision Puzzle with the Gaussian Mar 20, 2013
• A Seasoned Volatility Swap Mar 14, 2013
• A Volatility Swap and a Straddle Mar 12, 2013
• Local Volatility Delta & Dynamic Nov 29, 2012
• GPU computing in Finance Oct 15, 2012
• Binary Voting Sep 7, 2012
• Adaptive Quadrature for Pricing European Option with Heston Jun 25, 2012
• Gnome Shell more stable than Unity on Ubuntu 12.04 Jun 14, 2012
• Why primitive arrays matter in Java Feb 29, 2012
• Generating random numbers following a given discrete probability distribution Jan 9, 2012
• Quant Interview & Education Dec 21, 2011
• Gnome 3 not so crap after all Nov 30, 2011
• Good & Popular Algorithms are Simple Nov 17, 2011
• exp(y*log(x)) Much Faster than Math.pow(x,y) Apr 8, 2011
• SIMD and Mersenne-Twister Feb 5, 2011
• XORWOW L'ecuyer TestU01 Results Jan 12, 2011
• The CUDA Performance Myth Jan 3, 2011
• Another Look at Java Matrix Libraries Nov 29, 2010
• Street Fighting Mathematics Book Jul 28, 2010
• double[][] Is Fine Nov 26, 2009
• The Pain of Java Matrix Libraries Nov 26, 2009