Main Conference Day Three - GMT (Greenwich Mean Time, GMTZ)
- Marcus Wunsch - Senior Lecturer, ZHAW School of Management and Law
Understanding the relationship between expectation and price is central to applications of mathematical finance, including algorithmic trading, derivative pricing and hedging, and the modelling of margin and capital. In this presentation, the link is established via dynamic entropic risk optimisation, which is promoted for its convenient integration into established pricing methodologies.
- Paul McCloud - Head of Global Fixed Income Quantitative Research, Nomura
Since the advent of SOFR as the default dollar interest rate benchmark, some of the most liquid options are mid-curve (SR3) SOFR options. These are American options on quarterly futures contracts whose expiry date is situated somewhere between the present date and the start of the futures contract fixing period. We base our calculation on a short-rate model we introduced at previous QuantMinds conferences to calculate SOFR caplet prices and conditional prices of futures contracts, incorporating smile and skew effects as an asymptotic adjustment. We extend this work to allow analytic pricing of mid-curve SOFR options. The formulae we present allow straightforward fitting of the model to mid-curve option prices using nothing more than simple quadratures.
- Colin Turfus - Researcher, Independent
- Aurelio Romero-Bermudez - Senior Quantitative Analyst, ING
We consider possibly non-Markovian local stochastic volatility (LSV) models and show that, by applying a filtering-type conditioning, one can recover an underlying Markovian structure. The resulting conditional dynamics naturally lead to rough partial differential equations (RPDEs) via a Feynman–Kac-type representation. These RPDEs provide a new proxy for the leverage function—typically accessible only through particle-based simulation methods—offering new insights and computational advantages for modelling and calibration.
- Peter Friz - Professor of Mathematics, TU Berlin, Weierstraß-Institut Berlin
The state of play in quantum computing
- Davide Venturelli - Associate Director - Quantum Computing & Research Scientist, USRA
- Luca Magri - Professor in Scientific Machine Learning, Imperial College London
Hear from various institutions followed by an interactive Q&A panel.
- Davide Venturelli - Associate Director - Quantum Computing & Research Scientist, USRA
- Nicholas Chancellor - Advanced Technology Team, Quantum Computing Inc
- Wesley Coelho - Quantum Optimisation Lead, PASQAL
- Marco Pistoia - Senior Vice President of Industry Relations, IonQ
- Vincent van Wingerden - Director of Strategic Partnerships, Classiq IO
- Maurizio Garro - Senior Lead, IBOR Transition Programme, Lloyds
Although recent advances have made it feasible to estimate dynamic covariance matrices in high dimensions, portfolio managers face significant model risk when selecting a single forecast approach. We propose several forecast combination methods to mitigate model uncertainty and the risk of relative underperformance. These include distance-based approaches that penalize models producing forecasts that diverge excessively from others, as well as two optimization-based methods, which balance variance reduction with portfolio stability relative to individual models. Using daily U.S. stock data from 1980 to 2022, we evaluate ten individual covariance forecasting models and several combination strategies, constructing long-only minimum variance portfolios for universes of up to 1000 stocks. Forecast combinations--particularly simple ones--reduce model risk and deliver realized volatility close to the best individual models. However, optimization-based combinations often introduce additional turnover, potentially offsetting their benefits after transaction costs. Our results highlight the trade-off between improved risk forecasts and higher turnover, suggesting turnover-aware forecast combination as a direction for future research.
- Alexandre Rubesam - Associate Professor of Finance, IÉSEG School of Management
We reveal a geometric structure underlying both hedging and investment products. The structure follows from a simple formula expressing investment risks in terms of returns. This informs optimal product designs. Optimal pure hedging (including cost-optimal products) and hybrid hedging (where a partial hedge is built into an optimal investment product) are considered. Duality between hedging and investment is demonstrated with applications to optimal risk recycling. A geometric interpretation of rationality is presented.
- Andrei Soklakov - APAC Head of Prime and Delta One Quantitative Analytics, Citi
Constructing an efficient hedge portfolio for derivatives within risk limits, which are typically based on Greeks, is crucial from both trading and risk management perspectives. Therefore, we propose simple algorithms to optimize the hedge portfolio with complex Greeks, inspired by the proximal point method with the Sinkhorn algorithm. One algorithm focuses on optimizing cost, while the other optimizes both cost and CVaR (conditional value at risk) with constraints to limit the residual Greeks. Our algorithms consist of iterations involving only simple vector and matrix calculations, similar to the Sinkhorn algorithm, which is now widely used in machine learning; thus, linear programming solvers are not needed. In numerical examples, we explore two ways to improve the hedge portfolio for Bermudan swaptions, moving away from conventional anti-diagonal vega hedging with coterminal swaptions. The results of the optimized cost, CVaR, and hedge positions produced by our algorithms are consistent with insights on hedging under various constraints.
- Shin Kobayashi - Senior Manager, Mitsubishi UFJ Morgan Stanley Securities
- Marco Bianchetti - Head of Market and Counterparty Risk IMA Methodologies, Intesa Sanpaolo
This is actually an increasingly acute issue since the COVID market crash, where the hedging of large quantities of short term Equity options, sold by banks to the retail market, has had a large and paradoxical impact on the equity market itself, with the consequence of reinforcing any market drawdowns. This phenomenon was before COVID limited to a few albeit recurrent market crashes and ONLY wholesale market, which was actually the focus of my Ph. D (2006) and academic and practitioners papers (2012,2016,2017,2019) and presentations of previous business and academic conferences (QuantMinds 2016, and award of the Best investment presentation at the US Society of Actuary Conference in 2018).
- Aymeric Kalife - Associate Professor, Paris Dauphine University
Most counterparties do not have traded CDS instruments. This poses a challenge for calculating CVA which relies on risk-neutral default probabilities. Here we present a new model for the estimation of credit spreads using equity market data. In contrast to traditional equity-credit models, we take an empirical approach in order to determine a simple functional relationship that can be used in practice for CVA risk management. We find that our approach out-performs models that rely solely on credit data as well as alternative equity-credit models in the literature.
- Matthias Arnsdorf - Global Head of Counterparty Credit & Market Risk Modelling, JP Morgan Chase
- Daniel Mayenberger - Head of Quants Markets Solutions – Digital Products, J.P. Morgan
We propose an arbitrage-free multi-marginal discrete-time model for an asset price, calibrated to option market data using a minimum-entropy criterion. We then extend this framework to continuous time via a purely forward Markov functional approach. Our methodology is computationally efficient, and we present extensive empirical results across multiple assets to demonstrate its robustness and practical applicability. This is joint work with Julien Guyon.
- Florian Bourgey - Quantitative Researcher, Bloomberg LP
- Julien Hok - Quantitative Analysis, Investec Bank
Hear from various institutions followed by an interactive Q&A panel.
Reflecting on the quantum computing landscape
- David Shaw - Chief Analyst, Global Quantum Intelligence
- Gbenga Ibikunle - Professor and Chair of Finance, University of Edinburgh
We propose a nonparametric data-driven methodology for hedging using generative models. In contrast with model-based hedging approaches relying on sensitivity analysis of model pricing functions, our approach uses a conditional generative model trained on market data to simulate realistic market scenarios given current market conditions and computes hedge ratios which minimize risk across these scenarios. The approach incorporates transaction costs, leads to an optimal selection of hedging instruments, and adapts to market conditions. We illustrate the effectiveness of this methodology for hedging option portfolios using VolGAN, a generative model for implied volatility surfaces. The out-of-sample performance of the method matches and improves over delta and delta-vega hedging, without retraining the model for more than 4 years after the training period.
This talk is based on Cont, R., Vuletić, M. Data-driven hedging with generative models. Ann Oper Res (2025). https://doi.org/10.1007/s10479-025-06867-3
- Milena Vuletić - Quantitative Researcher, Squarepoint
- Luitgard Veraart - Professor, London School of Economics and Political Science
- Tasche model
- Stochastic variance approach
- LGD driver model
- Calibration strategy
- Marco Bianchetti - Head of Market and Counterparty Risk IMA Methodologies, Intesa Sanpaolo
- Luca Lamorte - Expert Risk Manager, Market And Counterparty Risk IMA Methodologies, Market and Financial Risk Management, Intesa Sanpaolo
- Marcus Wunsch - Senior Lecturer, ZHAW School of Management and Law
- The Quintic Ornstein-Uhlenbeck (OU) model: a new, tractable, and production-friendly stochastic volatility model
- Explicit expressions for the VIX
- Characteristic functions of the log spot and the affine structure
- Fitting the joint SPX/VIX volatility surface across time
- Consistent modelling of spot/vol dynamics via SSR (skew stikiness ratio)
Based on joint work with Eduardo Abi Jaber (Ecole Polytechnique), Xuyang Lin (Ecole Polytechnique), and Camille Illand (AXA Investment Managers).
- Shaun Li - Quantitative Strategist, Morgan Stanley
A family of stochastic volatility models with memory in the volatility process is introduced, as an extension of Bergomi models.
- The volatility feedback accounts for the time-asymmetry of equity markets, notably the asymmetry of large positive VIX spikes.
- With the aim to keep the forward variance process as explicit as possible while including the volatility feedback, we mix Ornstein-Uhlenbeck factors with the path-dependent vol framework of Guyon and Lekeufack (2023), introducing weighted averages of past squared returns. Convex combinations of exponential feedback kernels yield handy Markov models.
- Expansion of the SPX smile in small volatility of volatility, along the lines of the Bergomi-Guyon expansion.
- Comparison with classical Bergomi models and the Quintic OU model.
Joint work with Jules Delemotte (Polytechnique) and Julien Guyon (Ecole des Ponts)
- Stefano De Marco - Professor, Ecole Polytechnique
- Marcus Wunsch - Senior Lecturer, ZHAW School of Management and Law
- “Next-Gen Risk Architecture” strategic leadership in evolving institutional risk frameworks.
- “Cross-Disciplinary AI” practical ML/AI applications
- “Dynamic Market Defense” real-world, high-frequency trading and systemic risk control aspects he oversees.
- “Model Integrity” model risk management, resilience, and continuous validation.
- Maurizio Garro - Senior Lead, IBOR Transition Programme, Lloyds
- Maurizio Garro - Senior Lead, IBOR Transition Programme, Lloyds
Forward MtM (FMtM) Pricers are crucial whenever we need to evaluate a future MtM inside a simulated market for the purpose of computing a final t0 price. For instance, XVA pricing has relied on either analytical pricers for simple payoffs or regression pricers for more complicated ones. Evaluating the performance of these pricers is of utmost importance whenever the final t0 price has a heavy dependence on the distribution of FMtMs. To that end, we propose a framework based on Monte Carlo Branching Simulation to compute the Squared Error between an FMtM that we would like to assess, and the true reference FMtM which we don’t necessarily know. The Squared Error has the advantage of accounting for differences across the entire distribution of FMtMs. It can be used both as a selection criteria from a pool of available FMtM pricers, and as a tool to measure the performance of a single FMtM pricer. While it is one of the best ways to achieve that, we recognize that in some applications such as XVA this could be too strict as only the average positive part of FMtMs is needed. We thus propose a moment based approach also using Branching Simulation to evaluate the ability of an FMtM pricer to accurately calculate the average of a function of FMtMs under certain conditions. This effectively loosens the constrains of testing the entire FMtM distribution via the Squared Error.
As a numerical application, we use Regression Pricers in the context of XVA.
- Anas Bakkali - Vice President, XVA Quantitative Analytics, NatWest
In this session we look at the history of derivative pricing adjustments, including XVA, showing that the majority of well-known adjustments can be seen as manifestations of a single fundamental representation that unifies these approaches. We look at historic examples, ranging from a classic option pricing adjustment for vol, to funding value adjustments. We then consider the important problem of trying to estimate the impact of unmodelled risk factors, and consider how the representation can suggest ways to attack this problem, which can be a headache for everybody from traders, risk managers and quants to senior management.
- Benedict Burnett - Director, XVA Quant Lead, Barclays
- Benjamin Piau - Director, XVA Quant, Barclays
- Alexander Nichols - Senior Quant, Independent
- Marco Bianchetti - Head of Market and Counterparty Risk IMA Methodologies, Intesa Sanpaolo
