Mathematical Finance

Elicitability and identifiability of tail risk measures
2024-10-18 13:00 - 14:00 (America/Chicago) | via Zoom
Speaker: Dr. Tobias Fissler, Department of Mathematics, ETH Zurich
Abstract: Tail risk measures are fully determined by the distribution of the underlying loss beyond its quantile at a certain level, with Value-at-Risk and Expected Shortfall being prime examples. They are induced by law-based risk measures, called their generators, evaluated on the tail distribution. This talk establishes joint identifiability and elicitability results of tail risk measures together with the corresponding quantile, provided that their generators are identifiable and elicitable, respectively. As an example, we establish the joint identifiability and elicitability of the tail expectile together with the quantile. The corresponding consistent scores constitute a novel class of weighted scores, nesting the known class of scores of Fissler and Ziegel for the Expected Shortfall together with the quantile. For statistical purposes, our results pave the way to easier model fitting for tail risk measures via regression and the generalized method of moments, but also model comparison and model validation in terms of established backtesting procedures.
The talk is based on joint work with Ruodu Wang, Fangda Liu and Linxiao Wei.

Estimation and backtesting of risk measures with emphasis on distortion risk measures
2024-10-25 10:00 - 11:00 | via Zoom
Speaker: Prof. Hideatsu Tsukahara, Dept.. of Economics, Seijo University, Tokyo
Abstract: Statistical methodology has an important role to play in risk measurement. In this paper, we will review and discuss some statistical issues on risk measures. Examples we consider are value-at-risk, expected shortfall, expectiles, and distortion risk measures. Several methods of estimating these risk measures based on time series data have been proposed, and we will try to explain in some detail. Another main issue we would like to address is a problem of backtesting: the evaluation of risk measurement procedures using historical data, by comparing ex ante estimates of loss distributions or risk measures with the ex post realized losses. There have been several suggestions concerning backtestability of risk measures, which will be discuss in detail. We also examine and suggest backtesting procedures for predictive distributions, expected shortfall and distortion risk measures.

Pricing options with a new hybrid neural network model
2024-11-04 12:00 - 13:00 | via Zoom
Speaker: Dr. Yossi Shvimer, Research Associate, School of Finance and Management, SOAS University of London
Abstract: A novel hybrid option pricing model using a deep learning neural network has been developed. The hybrid model keeps the traditional option pricing model with the same input parameters while simultaneously adjusting the model with neural network methods to improve accuracy when applied to real market data, especially in OTM options. The new hybrid model demonstrates superior accuracy compared to both traditional parametric and non-parametric option pricing models for both Call and Put options across all moneyness levels. The empirical results of the hybrid model provide an explanation for the deviation from the Put-Call parity observed in real market data.

Stochastic dominance, stochastic volatility, and jump risk: new theory interprets old results
2024-11-15 14:00 - 15:00 | via Zoom
Speaker: Prof Stylianos Perrakis, John Molson School of Business, Concordia Univ, Montreal
Abstract: The stochastic dominance (SD) approach is applied to the valuation of index options in frictionless markets for a wide class of stochastic volatility (SV) processes. SD allows for the derivation of a unique, exponential option pricing kernel based on the physical underlying return and volatility dynamics. A lower bound and an upper bound on option prices are obtained, for a wide class of stochastic volatility jump (SVJ) processes that feature jumps in addition to diffusion. Using parameter estimates for the physical process from high-profile studies, the bounds are shown to be remarkably tight, especially for the empirically important class of short-term near-the-money options. The bounds are in many cases inconsistent with separate parameter estimates for the risk-neutral process that are extracted from observed option prices: for many option series, the risk-neutral value exceeds the SD upper bound. This inconsistency points at the possibility that the distributional shape of the risk-neutral process is mis-specified or that the parameters are estimated without properly taking the option bid-ask spread into account.

Inverse Problem for Forecasting Stock Options Prices
2024-11-22 14:00 - 15:00 | via Zoom
Speaker: Dr. Kirill Golubnichiy, Dept of Math & Statistics, Texas Tech University
Abstract: We present a new heuristic mathematical model for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the Black-Scholes equation supplied by new intervals for the underlying stock and new initial and boundary conditions for option prices. The Black-Scholes equation was solved in the positive direction of the time variable, This ill-posed initial boundary value problem was solved by the so-called Quasi-Reversibility Method (QRM). This approach with an added trading strategy was tested on the market data for 368 stock options and good forecasting results were demonstrated. In the current paper, we use the geometric Brownian motion to provide an explanation of that effectivity using computationally simulated data for European call options. We also provide a convergence analysis for QRM. The key tool of that analysis is a Carleman estimate.

Deep learning-based portfolio optimization with transaction costs
2025-01-17 09:00 - 10:00 | via Zoom
Speaker: Prof. Aihua (Eva) Zhang, College of Science, Math & Tech., Wenzhou-Kean University, Wenzhou China
Abstract: In order to obtain the optimal portfolio strategy maximizing the accumulated terminal wealth with transaction costs, in this paper, we propose a new prediction-based portfolio method combining with a long short-term memory (in short, LSTM) network which is an extended type of recurrent neural networks in deep learning. Our proposed method, named as LSTM-Prediction-based Portfolio (LSTM-PbP) with transaction costs, consists of two technical steps: finding the optimal portfolio strategy and predicting the future relative prices. For the price prediction, we use multi-layer LSTM; while for the optimal portfolio strategy, we solve the constraint maximization problem via relative entropy. We then update the future portfolio weights using the predicted prices and past portfolio weights. We iterate the process until the final investment period. Numerical experiments are also provided to show the accumulated wealth by following the obtained optimal portfolio strategy in comparison with the accumulated wealth under buy-and-hold strategy. The numerical results show that our model consistently outperforms the buy-and-hold strategy.

Robust estimation of the range-based GARCH model: Forecasting volatility, value at risk and expected shortfall of cryptocurrencies
2025-01-24 13:00 - 14:00 | via Zoom
Speaker: Prof. Piotr Fiszeder, Dept. Econ. & Stat., Nicolaus Copernicus Univ., Torun, Poland
Abstract: Traditional volatility models do not work well when volatility changes rapidly and in the presence of outliers. Therefore, two lines of improvements have been developed separately in the existing literature. Range-based models benefit from efficient volatility estimates based on low and high prices, while robust methods deal with outliers. We propose a range-based GARCH model with a bounded M-estimator, which combines these two improvements with a third new improvement: a modified robust method, which adds elasticity in treating the outliers. We apply this model to Bitcoin, Ethereum Classic, Ethereum, and Litecoin and find that it forecasts variances, value at risk, and expected shortfall more accurately than the standard GARCH model, the standard range-based GARCH model, and the GARCH model with the robust estimation. Utilization of high and low prices joined with a novel treatment of outliers makes our model perform well during extreme periods when traditional volatility models fail.
This work is joint with
Prof. Marta Malecka, Faculty of Economics and Sociology, University of Łódź, Łódź, Poland
and
Peter Molnár, UiS Business School, University of Stavanger, Stavanger, Norway.

Hedonic Models Incorporating Environmental, Social, and Governance Factors for Time Series of Average Annual Home Prices
2025-01-31 14:00 - 15:00 | via Zoom
Speaker: Jason Bailey, Dept. of Mathematics & Statistics, Texas Tech University
Abstract:

Do online attention and sentiment affect cryptocurrencies’ correlations?
2025-02-07 12:00 - 13:00 | via Zoom
Speaker: Prof. Aurelio Bariviera, Dept. of Business, Universitat Rovira i Virgili, Reus, Spain
Abstract: This paper adopts a versatile conditional correlation approach to explore daily seasonality in the major cryptocurrencies. Given the lack of clear fundamental value in this market and the active online profile of investors, the study also relates cryptocurrency cross-correlations to online market attention and sentiment. Our results highlight that while investor attention has a positive effect, sentiment has a much stronger negative impact on the correlations. These findings can offer interesting insights for investors and regulators, as the influence of market attention and sentiment on the correlations has important implications for portfolio diversification and market stability.

Multi-asset return risk measures
2025-02-21 12:00 - 13:00 | via Zoom
Speaker:

Water as a commodity in hydropower generation
2025-02-28 14:00 - 15:00 | via Zoom
Speaker: Prof. Eduardo Schwartz, Beedie School of Business, Simon Fraser Univ.
Abstract: The increased impact of extreme weather events and draughts has prompted the rapid growth of the water market. This paper analyzes the optimal operation of a reservoir that generates electricity and manages the water by trading water rights. We extend the framework introduced in a recent paper by Figuerola-Ferretti, Schwartz, and Segarra (2024) to include the water price process in a model that accounts for water inventory and the electricity price as two independent price processes. The model is implemented under the stochastic optimal control approach and calibrated using monthly data for a reservoir in the estate of California. The water price process and the dynamics of inflow into the reservoir include their dependence on the California Drought Severity Index. Results show that the underlying water and electricity price dynamics exhibit a high degree of uncertainty and seasonality. They also demonstrate that, under the calibrated model parameters on average for the parameters used, around 25% of the revenue generated by the reservoir arises from the revenue obtained from selling water rights. The water contribution to revenue generation would increase under enhanced severity of climate change.

Dynamic tail risk forecasting: What do realized skewness and kurtosis add?
2025-03-14 12:00 - 13:00 | via Zoom
Speaker: Prof. Giuseppe Storti, Dept. Econ & Stat., University of Salerno, Fisciano, IT
Abstract: This paper compares the accuracy of tail risk forecasts with a focus on including realized skewness and kurtosis in ”additive” and ”multiplicative” models. Utilizing a panel of 960 US stocks, we conduct diagnostic tests, employ scoring functions, and implement rolling window forecasting to evaluate the performance of Value at Risk (VaR) and Expected Shortfall (ES) forecasts. Additionally, we examine the impact of the window length on forecast accuracy. We propose model specifications that incorporate realized skewness and kurtosis for enhanced precision. Our findings provide insights into the importance of considering skewness and kurtosis in tail risk modeling, contributing to the existing literature and offering practical implications for risk practitioners and researchers.

No Seminar: Spring Vacation
2025-03-21

Portfolio optimization in deformed time
2025-03-28 12:00 - 13:00 | via Zoom
Speaker: Assoc. Prof. Malick Fall, Center for Research in Economics and Management, Univ. of Rennes, Fr.
Abstract: The expected return and covariance matrix are commonly calculated on a calendar time scale (e.g. daily or monthly data). In this article, we assess the relevance of calculating them on a new time scale derived from traded volume. In particular, we evaluate portfolio optimizations where returns evolve on a data-based rather than calendar time scale. We empirically test the impact of this change of scale by comparing the performance of two well-known portfolio optimizations in an out-of-sample framework. We find that this change leads to gains in both risk-adjusted return and risk. We also find that the degree of deviation from the normal distribution (and independence) of returns is greater with returns calculated in calendar time than in data-based time, which explains the outperformance of this new approach.

Measures of stochastic non-dominance in portfolio optimization
2025-04-04 12:00 - 13:00 | via Zoom
Speaker: Prof. Miloš Kopa, Dept. Probability & Mathematics, Charles University, Prague
Abstract: Stochastic dominance rules are well-characterized and widely used. This work aims to describe and better understand the situations when they do not hold by developing measures of stochastic non-dominance. They quantify the error caused by assuming that one random variable dominates another one when it does not. To calculate them, we search for a hypothetical random variable that satisfies the stochastic dominance relationship and is as close to the original one as possible. The Wasserstein distance between the optimal hypothetical random variable and the original one is considered as the measure of stochastic non-dominance. Depending on the conditions imposed on the probability distribution of the hypothetical random variable, we distinguish between general and specific measures of stochastic non-dominance. We derive their exact values for random variables with uniform, normal, and exponential distributions. We present relations to almost first-order stochastic dominance and to tractable almost stochastic dominance. Using monthly returns of twelve assets captured by the German stock index DAX, we solve portfolio optimization problems with the first-order and second-order stochastic dominance constraints. The measures of stochastic non-dominance allow us to compare the optimal portfolios with respect to different orders of stochastic dominance from a new angle. We also defined the closest dominating and closest approximately dominating portfolios. They brought a better understanding of the relationship between the two types of optimal portfolios. Using moving window analysis, the relationship of the in-sample measure of stochastic non-dominance to out-of-sample performance was studied, too.

Custom ESG Indexing: How Direct ESG Indexing Can Solve Many Responsible Investing Problems
2025-04-11 14:00 - 15:00 | via Zoom
Speaker: Prof. Dr. Dirk Soehnholz, CEO: Soehnholz ESG GmbH and Soehnholz Asset Management GmbH; Prof. of Asset Management, Leipzig University
Abstract: Responsible investments are booming, but criticism has been growing, too. I start by outlining the different dimensions and characteristics of responsible investments. I also describe a free tool to develop bespoke, responsible investment policies that could serve as the basis to select appropriate funds.
There are now many standard active and passive, so called responsible mutual funds available. I use three ambitious sustainable funds to show sustainability limits. In summary, since responsible investments can vary pretty much by investor, most standard funds may not be ideal for investors.
Much of the legitimate criticism of responsible investing can be avoided with bespoke portfolios. I outline simple ways to customize responsible portfolios with direct investments, not limited to equity investments. There are many arguments for rather concentrated direct rule-based ESG investments. These (self-indexed) solutions could be efficiently delivered by wealth managers or used by self-directed investors. An (over-)diversification focus of mutual fund providers and investment advisors may be the biggest limitation for the growth of direct or custom ESG indexing. Most of the arguments apply to private and institutional investors alike, although institutional investors will probably diversify more than private investors.

Option pricing in a stochastic delay volatility model
2025-04-18 12:00 - 13:00 | via Zoom
Speaker: Prof. Álvaro Guinea Julia, Dept. Industrial Org., Comillas Pontifical University ICADE-ICAI, Madrid
Abstract: This work introduces a new stochastic volatility model with delay parameters in the volatility process, extending the Barndorff–Nielsen and Shephard model. It establishes an analytical expression for the log price characteristic function, which can be applied to price European options. Empirical analysis on S&P500 European call options shows that adding delay parameters reduces mean squared error. This is the first instance of providing an analytical formula for the log price characteristic function in a stochastic volatility model with multiple delay parameters. We also provide a Monte Carlo scheme that can be used to simulate the model.

Drought parametric insurances by a Two-Step machine learning approach under climate change scenarios
2025-04-25 12:00 - 13:00 | via Zoom
Speaker: Dr. Hirbod Assa, Founding team | Quantitative researcher, Edge Technologies; Director and founder, Model Library Ltd.
Abstract: In this paper, we utilize data from the IPCC to develop a predictive model for the Palmer Drought Severity Index (PDSI). Our approach involves a two-step modeling process: initially applying a random forest regression, followed by a linear regression correction, achieving a forecasting accuracy exceeding 94%. This method aims to predict the drought index using a minimal set of climate indices, with projections extending to the year 2100 based on CORDEX CMIP5 models. The analysis focuses on selected U.S. states, assessing the impacts of different climate scenarios and climate change under various RCP pathways. On that basis we design a parametric insurance on drought index. If time permits, we will also explore the implications of these drought projections on supply chain risks in the beef commodity market.

ESG Mania and Institutional Trading
2025-05-02 14:00 - 15:00 | via Zoom
Speaker: Prof. Riza Demirer, Dept. Economics & Finance, School of Business, Southern Illinois University, Edwardsville, IL
Abstract: Recent years have seen that institutional investors simultaneously crowd in (buy) the ESG stock market. The aim of this study is to investigate the underlying motivations and their economic consequences. The empirical results are consistent with the hypothesis of ESG washing rather than that of impact investing, that is ESG-washing investors dominate the market. Specifically, institutional herding exists widely in the ESG market; small, dedicated, and ill-performed institutions exhibit strong intensity to herd into the ESG stock market; herding institutions experienced outflows recently and attract more flows when they herd. Herding institutions neither outperform nor that their trading significantly impacts stock prices (except in bad times). Our study highlights the mixed and complicated motivations of ESG investors from an institutional perspective, which helps reconcile the opposite findings of sincere ESG investing and washing behavior documented in the growing literature on sustainable investments.

Discrete-time hedging, basis risk, and covariance-dependent pricing kernels
2025-08-29 14:00 - 15:00 | via Zoom
Speaker: Prof. Maciej Augustyniak, Dept. of Mathematics & Statistics, University of Montreal
Abstract: Basis risk arises when hedging a financial derivative with an instrument different from its underlying asset. This risk can significantly impair hedging effectiveness and must therefore be properly managed. This article develops a discrete-time hedging framework for European-style derivatives that explicitly accounts for basis risk while incorporating key empirical properties of asset returns, including time-varying volatilities, leverage effects, and a flexible dependence structure between assets. Using a covariance-dependent pricing kernel, we derive semi-closed-form solutions for the optimal risk-minimizing hedge ratio. Empirical analyses using S&P 500 index data, its futures contracts, and the VIX demonstrate that our proposed strategy consistently outperforms conventional benchmarks across various maturities and moneyness levels, providing an effective approach to managing basis risk in derivative hedging.

The Bachelier implied volatility: A Malliavin calculus approach.
2025-09-05 12:00 - 13:00 | via Zoom
Speaker: Prof. Elisa Alos, Dept. of Economics and Business, University of Pompeu Fabra, Barcelona
Abstract: We introduce the main tools of Malliavin calculus and show how to use them to study the short-end behavior of skew and curvature of the implied volatility surface. This methodology allows us to obtain general formulas in terms of Malliavin derivatives that can be applied to a wide class of models including local, stochastic and rough volatilities. Numerical examples are given.

Rough Heston model as the scaling limit of bivariate cumulative heavy-tailed INAR( ∞) processes and applications
2025-09-12 14:00 - 15:00 | via Zoom
Speaker: Prof. Zhenyu Cui, School of Business, Stevens Institute of Technology, Hoboken NJ
Abstract: We establish a novel link between nearly unstable cumulative heavy-tailed integer-valued autoregressive (INAR(∞)) processes and the rough Heston model via discrete scaling limits. We prove that a sequence of bivariate cumulative INAR(∞) processes converge in law to the rough Heston model under appropriate scaling conditions, providing a rigorous mathematical foundation for understanding how microstructural order flow drives macroscopic prices following rough volatility dynamics. Our theoretical framework extends the scaling limit techniques from Hawkes processes to the INAR(∞) setting.
Hence, we can carry out efficient Monte Carlo simulation of the rough Heston model through simulating the corresponding approximating INAR(∞) processes, which provides an alternative discrete-time simulation method to the Euler-Maruyama method. Extensive numerical experiments illustrate the improved accuracy and efficiency of the proposed simulation scheme as compared to the literature, in the valuation of European options, and also path-dependent options such as arithmetic Asian options, lookback options and barrier options.

Recent advances in stochastic volatility jump diffusions: Calibration and exotic option pricing
2025-09-19 14:00 - 15:00 | via Zoom
Speaker: Dr. Jean-Phillipe Aguilar, Head of Pricing Models Audit, Societe Generale, Paris La Defense
Abstract:Stochastic Volatility Jump Diffusion (SVJ) models combine the advantages of both stochastic volatility and jump models, while addressing some of their well-known limitations; moreover, they often calibrate well in equity and FX markets. In this talk we will focus on a particular class of SVJ models, namely the Heston Kou Double Exponential (HKDE) model, that has recently been investigated in detail and shown to outperform challenger models possessing similar features. We will discuss the main properties of the HKDE model as well has its calibration to single stock and FX option data, demonstrating a better fit of the volatility smile when compared to several challenger models; we will also discuss the smile sensitivity to the HKDE model parameters as well as their econometrics interpretations. Last, we will provide application to the pricing and analysis of several generations of exotic contracts by means of advanced Fourier pricing (PROJ method in particular).
Joint work with Gaetano Agazzotti, Claudio Aglieri Rinella and Justin Lars Kirkby.

Risk-aware Trading Portfolio Optimization
2025-09-26 12:00 - 13:00 | via Zoom
Speakers: Dr. Marco Bianchetti, Head of Market and Counterparty Risk IMA Methodologies, Intesa Sanpaolo, Milan, Italy
Dr Fabio Vitale, Senior Researcher, CENTAI Institute, Turin, Italy
Abstract: We investigate portfolio optimization in financial markets from a trading and risk management perspective. We term this task Risk-Aware Trading Portfolio Optimization (RATPO), formulate the corresponding optimization problem, and propose an efficient Risk-Aware Trading Swarm (RATS) algorithm to solve it. The key elements of RATPO are a generic initial portfolio P, a specific set of Unique Eligible Instruments (UEIs), their combination into an Eligible Optimization Strategy (EOS), an objective function, and a set of constraints. RATS searches for an optimal EOS that, added to P, improves the objective function respecting the constraints. RATS is a specialized Particle Swarm Optimization method that leverages the parameterization of P in terms of UEIs, enables parallel computation with a large number of particles, and is fully general with respect to specific choices of the key elements, which can be customized to encode financial knowledge and needs of traders and risk managers. We showcase two RATPO applications involving a real trading portfolio made of hundreds of different financial instruments, an objective function combining both market risk (VaR) and profit & loss measures, constraints on market sensitivities and UEIs trading costs. In the case of small-sized EOS, RATS successfully identifies the optimal solution and demonstrates robustness with respect to hyper-parameter tuning. In the case of large-sized EOS, RATS markedly improves the portfolio objective value, optimizing risk and capital charge while respecting risk limits and preserving expected profits. Our work bridges the gap between the implementation of effective trading strategies and compliance with stringent regulatory and economic capital requirements, allowing a better alignment of business and risk management objectives.

New runs-based approach to testing value at risk forecasts
2025-10-03 12:00 - 13:00 | via Zoom
Speaker: Prof. Marta Malecka, Dept. of Statistical Methods, Univ. of Lodz, Lodz, Poland
Abstract: The reformed Basel framework has left value at risk (VaR) as a basic tool of validating risk models. Within this framework, VaR independence tests have been regarded as critical to ensuring stability during periods of financial turmoil. However, until now, there is no consent among researchers regarding the choice of the appropriate test. The available procedures are either inaccurate in finite samples or need to rely on Monte Carlo simulations. To remedy these problems, we propose a new method for testing VaR models, based on the distribution of the number of runs. It outperforms the existing methods in two main aspects: First, it is exact in finite samples and thus allows for perfect control over the Type 1 error; second, its distribution is available in a closed form, so it does not require simulations before implementation. We show that it is the most adequate current procedure for testing low-level VaR series, which corresponds to today’s regulatory standards.

Beyond Traditional Models: Assessing the Role of LSTM Networks in Volatility Prediction
2025-10-10 12:00 - 13:00 | via Zoom
Speaker: Prof. Massimo Guidolin, Baffi Carefin Center, Bocconi Univ., Milan
Abstract: This paper examines the out-of-sample accuracy of recurrent artificial neural networks (ANNs) compared to traditional econometric models for the prediction of realized volatility. We focus on a horserace between the heterogeneous autoregressive (HAR) model, its Markov-switching extension (MS-HAR), multi-layer perceptrons (MLP), and long short-term memory (LSTM) networks across 31 international equity indices. Using high-frequency realized volatility data, we evaluate predictive performance based on four loss functions and test for equal accuracy using Diebold-Mariano tests. Our results suggest that the HAR and MS-HAR models often deliver the most accurate forecasts, outperforming LSTMs. However, differences in out-of-sample accuracy between LSTM, HAR, and MS-HAR models are not always statistically significant. We conclude that ANNs do not consistently outperform HAR-based models in equity volatility forecasting.

Multi-hypothesis prediction for portfolio optimization: A structured ensemble learning approach to risk diversification
2025-10-17 12:00 - 13:00 | via Zoom
Speaker: Dr. Alejandro Rodriguez Dominguez, Director of Quantitative Analysis and Artificial Intelligence, Miralta Finance Bank, Madrid.
Abstract: We introduce a novel framework for portfolio construction, covering both selection and optimization, based entirely on ensemble learning theory. A portfolio is modelled as an ensemble in a multi-hypothesis prediction setting, with each constituent (base learner) focused on a specific hypothesis. This formulation connects the Bias–Variance–Diversity trade-off in ensemble models with out-of-sample portfolio performance. Diversity in the training of base learners translates to out-of-sample diversification, allowing control over portfolio diversification via model training.
Portfolio optimization is reframed as a supervised learning task, where the target portfolio follows an ensemble combiner rule derived from Bregman divergences and ensemble model properties. When using Mean Squared Error, the equal-weighted portfolio emerges as the target. Also,it enables the use of alternative loss functions—treating the problem as classification or regression, where targets follow ensemble combiner rules defined by Bregman divergences. A second source of out-of-sample diversification is also identified: the diversity in return predictions across base learners. Controlling this diversity at decision time further improves performance. When base learners exhibit similar error levels, portfolios built from asset sets with more diverse return predictions, but lower average sets forecasts, outperform those with higher average sets predictions but less diversity. This defines a diversity-quality trade-off in predicted returns. Together, these two sources of diversification expand the traditional boundaries of portfolio construction, enabling meaningful diversification even within single-asset portfolios, benefiting constrained strategies and redefining conventional notions of diversification. Theoretical results are empirically validated using full historical data from all S&P 500 constituents and a globally diversified set of 1,300 bonds across multiple categories, spanning over two decades and diverse market regimes. The diversity-quality trade-off is shown to be applicable across a wide range of portfolio optimization methods.

Option Pricing with a Compound CARMA(p,q)-Hawkes
2025-10-24 12:00 - 13:00 | via Zoom
Speaker: Prof. Lorenzo Mercuri, Dept of Economics, Management and Quantitative Methods, Univ. of Milan
Abstract: A self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p,q)-Hawkes model, has recently been introduced. The model generalizes the Hawkes process by substituting the Ornstein-Uhlenbeck intensity with a CARMA(p,q) model where the associated state process is driven by the counting process itself. The proposed model preserves the same degree of tractability as the Hawkes process, but it can reproduce more complex time-dependent structures observed in several market data. The paper presents a new model of asset price dynamics based on the CARMA(p,q) Hawkes model. It is constructed using a compound version of it with a random jump size that is independent of both the counting and the intensity processes and can be employed as the main block for pure jump and (stochastic volatility) jump-diffusion processes. The numerical results for pricing European options illustrate that the new model can replicate the volatility smile observed in financial markets. Through an empirical analysis, which is presented as a calibration exercise, we highlight the role of higher order autoregressive and moving average parameters in pricing options.

A general framework for pricing and hedging under local viability
2025-10-31 12:00 - 13:00 | via Zoom
Speaker: Prof. Huy Chau, Dept. Mathematics, University of Manchester
Abstract: In this paper, a new approach for solving the problems of pricing and hedging derivatives is introduced in a general frictionless market setting. The method is applicable even in cases where an equivalent local martingale measure fails to exist. Our main results include a new superhedging duality for American options when wealth processes can be negative and trading strategies are subject to a cone constraint. This answers one of the questions raised by Fernholz, Karatzas and Kardaras.

Robust Bayesian Portfolio Optimization
2025-11-07 14:00 - 15:00 | via Zoom
Speaker: Dr. Carlos Andres Zapata Quimbayo, ODEON, Universidad Externado de Colombia, Bogota
Abstract: We implement a robust Bayesian framework for portfolio optimization that integrates Bayesian inference with robust optimization techniques. The model considers parameter uncertainty in expected returns and covariances by combining normal-inverse-Wishart and gamma distributions through ellipsoidal uncertainty sets. We apply this methodology to a stock portfolio from the Dow Jones Industrial Average and compare its performance with traditional mean-variance and robust portfolio models.
