BBQ April Replay

Please register to join us virtually for the April installment of the Bloomberg Quant (BBQ) Seminar Series – broadcast from New York City. In this seminar chaired by Bruno Dupire, Julien Guyon will present the keynote, followed by “lightning talks” of 5 minutes each in quick succession. 5:30 PM Keynote: Julien Guyon ENPC, Institut Polytechnique de Paris & NYU Tandon Hysteresis is the dependence of the state of a system on its history. A family of continuous-time hysteretic stochastic volatility (SV) models is presented as an extension of classical SV models. A simple linear additive variance feedback loop, motivated by empirical studies, accounts for three important stylized facts of equity markets that classical continuous-time SV models fail to capture: (a) the dependence of current variance on past variances, (b) the time-asymmetry of large volatility spikes---the most compelling evidence of hysteresis---, and (c) large positive VIX skews. Our models take the form of random Volterra ODEs, for which we prove wellposedness and positivity for general feedback convolution kernels and derive semi-explicit solutions using the theory of the resolvent for linear Volterra equations. A deterministic variance input curve can be used to exactly fit the observed variance swap term-structure. The models can be made Markovian by using kernels that are convex combinations of decreasing exponentials. In this case, explicit formulas for the VIX are derived, and an expansion at order two in small volatility-of-volatility, along the lines of the Bergomi-Guyon expansion, provides an approximation of the smile. The expansion shows that, contrary to a common belief, the power-law-like term-structure of at-the-money skew observed in equity markets can be produced by classical one-factor SV models, provided hysteresis is taken into account. Numerical experiments illustrate the properties of our hysteretic SV models, contrast them with classical SV models, and assess the accuracy of the smile expansion for market-calibrated parameters. This is ongoing joint work with Jules Delemotte and Stefano De Marco. 6:30 PM Lightning Talks • Nassim Taleb | NYU & Universa Investments & American University in Beirut Hidden Optionality in American Options • Stan Uryasev | Stony Brook University Thinking Canvases of Oxana Uryasev • Mykola Kishmar | Columbia University Quant’s Intuitive Guide to Quantum Advantage • Guixin Liu | Bloomberg Extracting Structure from Pairwise Comparisons • Othmane Zarhali | Université Paris Dauphine – CNRS From Rough to Multifractal Volatility: Topics Around the Log S-fBM Model