Mathematical Finance

Semi-analytic pricing of American options in some time-dependent jump-diffusion models
2024-04-19 12:00 - 13:00 (America/Chicago) | via Zoom
Speaker: Prof. Andrey Itkin, Department of Risk and Financial Engineering, Tandon School of Engineering, NYU
Abstract: In this paper we propose a semi-analytic approach to pricing American options for some time-dependent jump-diffusions models. The idea of the method is to further generalize our approach developed for pricing barrier, [Itkin et al., 2021], and American, [Carr and Itkin, 2021; Itkin and Muravey, 2023], options in various time-dependent one factor and even stochastic volatility models. Our approach i) allows arbitrary dependencies of the model parameters on time; ii) reduces solution of the pricing problem for American options to a simpler problem of solving an algebraic nonlinear equation for the exercise boundary and a linear Fredholm-Volterra equation for the the option price; iii) the options Greeks solve a similar Fredholm-Volterra linear equation obtained by just differentiating Eq. (25) by the required parameter.

Portfolio selection under non-gaussianity and systemic risk: A machine learning based forecasting approach
2024-04-19 14:00 | via Zoom
Speaker: Prof. Abderrahim Taamouti, Management School, University of Liverpool
Abstract: The Sharpe-ratio-maximizing portfolio becomes questionable under non-Gaussian returns, and it rules out, by construction, systemic risk, which can negatively affect its out-of-sample performance. In the present work, we develop a new performance ratio that simultaneously addresses these two problems when building optimal portfolios. To robustify the portfolio optimization and better represent extreme market scenarios, we simulate a large number of returns via a Monte Carlo method. This is done by obtaining probabilistic return forecasts through a distributional machine learning approach in a big data setting and then combining them with a fitted copula to generate return scenarios. Based on a large-scale comparative analysis conducted on the US market, the backtesting results demonstrate the superiority of our proposed portfolio selection approach against several popular benchmark strategies in terms of both profitability and minimizing systemic risk. This outperformance is robust to the inclusion of transaction costs.

Hedging with temporary price impact
2024-04-26 12:00 - 13:00 | via Zoom
Speaker: Prof. Peter Bank, Department of Mathematics, Technical University of Berlin
Abstract: We consider the problem of hedging a European contingent claim in a Bachelier model with temporary price impact as proposed by Almgren and Chriss (J Risk 3:5–39, 2001). Following the approach of Rogers and Singh (Math Financ 20:597–615, 2010) and Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), the hedging problem can be regarded as a cost optimal tracking problem of the frictionless hedging strategy. We solve this problem explicitly for general predictable target hedging strategies. It turns out that, rather than towards the current target position, the optimal policy trades towards a weighted average of expected future target positions. This generalizes an observation of Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b) from their homogenous Markovian optimal investment problem to a general hedging problem. Our findings complement a number of previous studies in the literature on optimal strategies in illiquid markets as, e.g., Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b), Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), Rogers and Singh (Math Financ 20:597–615, 2010), Almgren and Li (Option hedging with smooth market impact. Preprint, 2015), Moreau et al. (Math Financ. doi:10.1111/mafi.12098, 2015), Kallsen and Muhle-Karbe (High-resilience limits of block-shaped order books. Preprint, 2014), Guasoni and Weber (Mathematical Financ. doi:10.1111/mafi.12099, 2015a; Nonlinear price impact and portfolio choice. Preprint, 2015b), where the frictionless hedging strategy is confined to diffusions. The consideration of general predictable reference strategies is made possible by the use of a convex analysis approach instead of the more common dynamic programming methods.

Gold-backed cryptocurrencies: A hedging tool against categorical and regional financial stress
2024-05-01 08:00 - 17:00, 2024-08-30 14:00 - 15:00 | via Zoom
Speaker: Prof. Md. Rayfayet Alam, Dept. of Finance and Economics, University of Tennessee at Chattanooga
Abstract: This study evaluates the potential of gold-backed cryptocurrencies, such as Tether Gold and PAX Gold, as a hedge and safe haven against global, regional, and categorical financial stresses. Hedge and safe haven properties of gold-backed cryptocurrencies are also compared with those of gold and Bitcoin. For the analyses, dynamic conditional correlation (DCC) and quantile coherency techniques are applied to daily data from February 2020 to March 2023. The results show that Tether Gold and PAX Gold are strong safe havens against the US and equity-valuation-related financial stress but weak safe havens against global financial stress. Tether Gold is a weak safe haven against credit-related financial stress as well. Tether Gold is a strong hedge against US financial stress but a weak hedge against aggregate financial stress of developed economies and that of emerging economies. In our sample, gold-backed cryptocurrencies usually outperform gold and Bitcoin as a hedge and safe haven against financial stresses. The Quantile coherency analysis shows that Tether Gold is a hedge against low to moderate financial stress and a safe haven against extreme financial stresses. These findings have important implications for investors, risk-managers and policy makers.

Elementary function solutions to the Bachelier model generated by Lie point symmetries
2024-05-03 12:00 - 13:00 | via Zoom
Speaker: Dr. Evangelos Melas, Department of Mathematics, University of Thessaly
Abstract: Under the recent negative interest rate situation, the Bachelier model has been attracting attention and adopted for evaluating the price of interest rate options. In this paper we find the Lie point symmetries of the Bachelier partial differential equation (PDE) and use them in order to generate new classes of denumerably infinite elementary function solutions to the Bachelier model from elementary function solutions to it, which we derived in a previous publication.

Quanto Option Pricing on a Multivariate Lévy Process Model with Generative Artificial Intelligence
2024-08-23 14:00 - 15:00 | via Zoom
Speaker: Prof. Aaron YS Kim, College of Business, Stony Brook University
Abstract: In this study, we discuss a machine learning technique to price exotic options with two underlying assets based on a non-Gaussian Levy process model. We introduce a new multivariate Levy process model named the generalized normal tempered stable (gNTS) process, which is defined by time-changed multivariate Brownian motion. Since the gNTS process does not provide a simple analytic formula for the probability density function (PDF), we use the conditional real-valued non-volume preserving (CRealNVP) model, which is a type of flow-based generative network. Then, we discuss the no-arbitrage pricing on the gNTS model for pricing the quanto option whose underlying assets consist of a foreign index and foreign exchange rate. We present the training of the CRealNVP model to learn the PDF of the gNTS process using a training set generated by Monte Carlo simulation. Next, we estimate the parameters of the gNTS model with the trained CRealNVP model using the empirical data observed in the market. Finally, we provide a method to find an equivalent martingale measure on the gNTS model and to price the quanto option using the CRealNVP model with the risk-neutral parameters of the gNTS model.

Optimal Portfolios with Sustainable Assets - Aspects for Life Insurers
2024-09-13 14:00 - 15:00 | via Zoom
Speaker: Prof. Ralf Korn, Dept. of Mathematics, RPTU Kaiserslautern-Landau
Abstract: Since August 2022 customers have to be asked if they are interested in sustainable investment when entering a pension contract. Hence, the provider has to be prepared to offer suitable investment opportunities. Further, the provider has to manage the new risks and chances of those assets in the whole portfolio. We therefore especially look at possible consequences for optimal portfolio decisions of a life insurer and suggest modeling approaches for the evolution of the demand and the sustainability ratings for sustainable assets. We will solve various portfolio problems under sustainability constraints explicitly and suggest further research topics. As a special feature for a life insurer, we particularly look at the role of the actuarial reserve fund and the annual declaration of its return.

To hedge or not to hedge? Cryptocurrencies, gold and oil against stock market risk
2024-09-20 12:00 - 13:00 | via Zoom
Speaker: Prof. Agata Kliber, Dept of Applied Mathematics, Poznan University of Economics & Business
co-Authors: Prof. Krzysztof Echaust, Dept. of Operations Research & Mathematical Economics, Poznan University of Economics & Business
Prof. Małgorzata Just, Dept. of Finance & Accounting, Poznan University of Life Sciences
Abstract: The article aims to determine whether any hedging strategy against stock market risk, performed using instruments popular in the literature (gold, cryptocurrencies and oil), can beat index futures. As a hedging strategy, we understand a pair-wise portfolio consisting of a long position in stocks and a short position in a hedging instrument put together to minimise the portfolio variance. As a benchmark, we analyse optimal and naive hedging strategies with futures contracts. We demonstrate that, regardless of the stock market, the best hedging strategy focused on variance minimisation requires using index futures. Both strategies: the optimisation-based one and the naive one, beat the dynamic strategies utilising the remaining hedging assets. Therefore, from a risk-minimisation point of view, investors have no motivation to implement cryptocurrencies, gold or oil in hedging strategy against stock market risk. The results are robust with respect to hedging against tail risk.

ESG performance and investment efficiency: The impact of information asymmetry
2024-09-27 12:00 - 13:00 | via Zoom
Speaker: Prof. Seda Erdogan, Dept. International Trade & Finance, Kadir Has University
Abstract: This paper investigates the relationship between firms’ engagement in environmental, social, and governance (ESG) activities and corporate investment efficiency, using 1,094 firms from 21 countries in Europe, covering the years 2002–2019. We conduct our estimations using fixed effects panel data techniques and address potential endogeneity with instrumental variables (IV) estimations. We provide evidence that overall ESG engagement is positively and significantly associated with investment efficiency. Analyzing overinvestment and underinvestment scenarios shows that ESG engagement decreases only overinvestment problems. Within the underinvestment scenario, we observe that ESG engagement is beneficial only for firms with higher information asymmetries. Thus, information asymmetry matters in the underinvestment case. We next show that four firm-level channels—information asymmetry, financial constraints, cash flows, and risk—link ESG performance to investment inefficiency. Additional analysis shows that firms with extreme ESG scores (i.e., very low and very high) do not experience significant reductions in investment inefficiency. Altogether, our findings draw attention to the critical role of ESG performance and information asymmetry in determining corporate investment efficiency.

Option Pricing under a Generalized Black–Scholes Model with Stochastic Interest Rates, Stochastic Strings, and Lévy Jumps
2024-10-04 14:00 - 15:00 | via Zoom
Speaker: Prof. Steven P. Clark, Dept. of Finance, UNC Charlotte
Abstract: We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes.

Seminar Cancelled
2024-10-11 14:00 - 15:00 | via Zoom
Title: Time changes, Fourier transforms and the joint calibration to the S&P500/VIX smiles
Speaker: Prof. Laura Ballotta, Bayes Business School, City University of London
Abstract: We develop a model based on time changed Lévy processes and study its ability of reproducing the joint S&P500/VIX implied volatility smiles and the VIX futures prices – a problem known in the literature as the `joint calibration problem’. The model admits semi-analytical characteristic functions for the key quantities, and therefore efficient Fourier based pricing schemes can be deployed. We focus on a specification of the proposed general setting which uses purely discontinuous processes. Results from the application to market data show satisfactory performances in solving the joint calibration problem, and therefore demonstrate that the class of affine processes can provide a workable fit.

Elicitability and identifiability of tail risk measures
2024-10-18 13:00 - 14:00 | 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.
