Joint QF-STAT PhD Webinars

Speaker: Jack Peters and Taras Vorobets

Title: Pricing European Cryptocurrency Options using Numerical Replication.

Date/Time: 10 Feb. 2023, Friday, 10:00 AM - 11:00 AM

Abstract: In this case study, using the methodical approach of Ryabchenko, Sarykalin, and Uryasev, we price European style options for Bitcoin and Ethereum. This approach involves approximating the value of an option by using a portfolio consisting of the underlying and a risk-free bond. Using quadratic programming, we produce tables of call and put prices based on the price of the underlying. We model the price of an asset using a set of sample-paths generated from historical prices which we massage to reflect the current volatility of the market.

Speaker: Anton Malandii

Title: SVR Quadrangle

Date/Time: 24 Feb. 2023, Friday, 10:00 AM - 11:00 AM

Abstract: Support Vector Regression (SVR) is investigated in the context of the fundamental risk quadrangle paradigm. It is shown that both formulations of SVR, $\varepsilon$-SVR and $\nu$-SVR, correspond to the minimization of equivalent regular error measures (Vapnik error and superquantile (CVaR) norm, respectively) with a regularization penalty. These error measures, in turn, give rise to corresponding risk quadrangles. Additionally, the technique used for the construction of quadrangles serves as a powerful tool in proving the equivalence between $\varepsilon$-SVR and $\nu$-SVR. In general, the Support Vector (SV) algorithm, which is firmly grounded in the framework of Vapnik-Chervonenkis (VC) theory, is proven to be a highly effective classification tool and a generalization of regression. In the context of VC theory, a problem of function estimation relies on the so-called principle of empirical risk minimization, which is essentially a minimization of the expected value of the loss function of the regression residual. The fundamental risk quadrangle theory takes another approach. The concept of generalized regression in this paradigm is developed through the regular measure of error, which is defined axiomatically and, therefore, takes it beyond the expected loss types of error. However, it turns out that errors of expectation type play a significant role in statistical estimation. In particular, regression with respect to a regular error measure of expectation type estimates the corresponding conditional statistic from the same quadrangle (e.g., least-squares regression estimates conditional mean, quantile regression estimates conditional quantile). By constructing the fundamental risk quadrangle, which corresponds to SVR, we show that SVR is the asymptotically unbiased estimator of the average of two symmetric conditional quantiles. Additionally, SVR is formulated as a regular deviation minimization problem with a regularization penalty by invoking Error Shaping Decomposition of Regression. Finally, the dual formulation of SVR in the risk quadrangle framework is derived.

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Date/Time: 10 Mar. 2023, Friday, 10:00 AM - 11:00 AM

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Date/Time: 31 Mar. 2023, Friday, 10:00 AM - 11:00 AM

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Date/Time: 14 Apr. 2023, Friday, 10:00 AM - 11:00 AM

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Date/Time: 28 Apr. 2023, Friday, 10:00 AM - 11:00 AM

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Speaker: Eash Naik, Som Naik

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Date/Time: 9 Sep. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: Inflation Uncertainty: ETF Risk Model, Structural Change, and Breakeven Inflation: We present a predictive risk model for a popular Treasury Inflation Protected Securities (TIPS) ETF. The model is based on ARMA-GARCH and a heavy-tailed volatility model. Its assessment based on standard VaR, CVaR, and Kolmogorov-Smirnov statistics is very encouraging. We also study structural breaks in the CPI-based inflation rate. The structural breaks correlate with key inflation related external events. Inflation expectations are expressed through the breakeven inflation (BEI) rate. We infer distinctive market motivations of TIPS investors based on BEI expectations across TIPS maturities.

TIPS ETF: An explanatory model using CPI: This paper investigates the relationship between ETFs composed of Treasury Inflation Protected Securities (TIPS) and inflation as indicated by the CPI. The iShares TIPS ETF and the Consumer Price Index for All Urban Consumers (CPIAUCSL) metric are selected for analysis. Our main result is to establish the rationale which governs the behavior of participants in this market. Strong upwards or strong downwards movements of inflation, or the absence of either, are the major factors governing participants’ behavior. This insight leads to the identification of three distinct regimes of TIPS ETF price movements during varying types of shocks in the CPIAUCSL. A model is then constructed using insights from the three regimes. The model is tested by out-of-sample data and provides an excellent agreement with observations. An R-squared value of 0.989 is achieved when the model is trained on the first half of the data. The data and the model both suggest an inverse relationship between iShares TIPS ETF price data and the CPIAUCSL metric during strong price shocks.

Speaker: Zhikang Dong

Title: CP-PINNs: Changepoints Detection in PDEs using Physics Informed Neural Networks with Total-Variation Penalty

Date/Time: 23 Sep. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: We consider the inverse problem for the Partial Differential Equations (PDEs) such that the parameters of the dependency structure can exhibit random changepoints over time. This can arise, for example, when the physical system is either under malicious attack (e.g., hacker attacks on power grids and internet networks) or subject to extreme external conditions (e.g., weather conditions impacting electricity grids or large market movements impacting valuations of derivative contracts). For that purpose, we employ Physics Informed Neural Networks (PINNs) -- universal approximators that can incorporate prior information from any physical law described by a system of PDEs. This prior knowledge acts in the training of the neural network as a regularization that limits the space of admissible solutions and increases the correctness of the function approximation. We show that when the true data generating process exhibits changepoints in the PDE dynamics, this regularization can lead to a complete miss-calibration and a failure of the model. Therefore, we propose an extension of PINNs using a Total-Variation penalty which accommodates (multiple) changepoints in the PDE dynamics. These changepoints can occur at random locations over time, and they are estimated together with the solutions. We propose an additional refinement algorithm that combines changepoints detection with a reduced dynamic programming method that is feasible for the computationally intensive PINNs methods, and we demonstrate the benefits of the proposed model empirically using examples of different equations with changes in the parameters. In case of no changepoints in the data, the proposed model reduces to the original PINNs model. In the presence of changepoints, it leads to improvements in parameter estimation, better model fitting, and a lower training error compared to the original PINNs model. Link: https://arxiv.org/abs/2208.08626

Speaker: Benjamin Larah

Title: Modeling Your Future Path: A Perspective on a Quant Finance Career

Date/Time: 7 Oct. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: Ben Larah, Senior Manager at PwC, will speak about his quantitative finance career journey. He will provide insights around how models are used in practice throughout the financial industry, and share perspectives on the evolution of skills needed to further your quantitative finance career.

Affiliation: PwC

Speaker: Dimitri Bianco

Title: Quant Career Landscape Presentation

Date/Time: 21 Oct. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: Sell Side, Buy Side, Crypto, and Fintech. Understanding the quantitative finance landscape, current roles, and the skills needed to built a long term career. Insights and perspective from a head of quant risk and research as well as a discussion on resumes and interviews.

Affiliation: Agora Data

Speaker Bio Dimitri Bianco is currently the Head of Quantitative Risk and Research at Agora Data. He received his bachelors degree in Finance from Washington State University and his Masters of Applied Economics from the University of Michigan. His career has been focused on risk management for eight years working at both regional and global banks doing model development, model validation, model implementation, and internal audit. He has covered credit, operations, market, and regulatory risks across the firms with a focus in time-series. He is also an industry disruptor pushing for an academic approach to using both statistical and machine learning models to solve problems in finance. His current role in fintech is to bring about rigor to modeling methods which provide new technology to the finance industry. He also runs the largest YouTube channel and podcast focused solely on quantitative finance with over 2 million views and nearly 25,000 subscribers. Much of his focus is on career development from students just starting out to more senior positions looking for new opportunities. His life experiences and relationships with both universities and practitioners provides a unique perspective not found elsewhere.

Speaker: Weichuan Deng

Title: Dynamic Financial Factors Model

Date/Time: 4 Nov. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: We consider the problem of estimating a regression problem such as dynamic financial factor model where the contribution of the individual factors evolves smoothly over time. In this general setup under proper canonical scaling that ensures functional spaces embedding, we show that the minimax risk of the estimator with total variation regularization is lower than the minimax risk of any linear smoother. Encouraged by these results we develop primal-dual optimization algorithm for fitting the proposed model. Further extensions to local adaptivity, potential curse of dimensionality, and links to deep neural networks will be discussed.

Speaker: Xiaoqi Dong

Title: Deep Hedging with Regularization

Date/Time: 18 Nov. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: Deep hedging is referred to as deep reinforcement machine learning methods that hedges portfolios of derivatives in the presence of market frictions. To stablize the hedging paths, we consider a regularized deep hedging method which adds L2 panelty to the convex risk measure of the portfolio. Our current studies show that the regularized hedging path has less variation than un-regularized hedging path and the induced transac- tion cost is also reduced. (This is a work in progress)

Speaker: Konstantin Kalinchenko

Title: Career in Data Science and Quantitative Finance

Date/Time: 11 Feb. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: We will discuss the strategy that a graduate with determination to pursue a career in data intensive profession should follow. We will talk about the landscape of opportunities in various industries, skills that are currently in demand, and what would be the optimal allocation of efforts while you are a student.

Speaker Bio:Dr. Konstantin Kalinchenko has over 12 years of professional experience in various roles concentrated in applications of Statistics, Optimization and Risk Management in Banking, Trading and Data Science Consulting. He currently works for private equity firm Cerberus Capital Management, in its Cerberus Technology Solutions consulting subsidiary. Previously, he was a Vice President in Trading Analytics and Risk Management at hedge fund WorldQuant LLC, a Trading Associate at Deutsche Bank, and Internal Auditor at Sberbank. He defended his PhD dissertation "Optimization with Generalized Deviation Measures in Risk Management" at University of Florida and holds a Specialist degree in Mathematics from M.Lomonosov Moscow State University.

Speaker: Rui Ding

Title: Risk Sensitivity and Model Uncertainty in Sequential Decision Making

Date/Time: 25 Feb. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: In this work we study sequential decision making problems under uncertainty. In particular we are concerned with risk-sensitive MDPs, distributionally robust MDPs where the model parameters are unknown a priori and specified through uncertainty sets, and relevant reinforcement learning algorithms. We highlight a deep connection between risk sensitivity and model uncertainty. This work is two-fold. First, we study CVaR optimization for MDPs and connections with distributionally robust MDPs. The standard CVaR MDP problem can be reformulated through an augmented space where the problem can be interpreted as a distributionally robust MDP with nature playing as an adversary. We provide a better structural formulation using a sufficient statistic to be the augmented state in our value iteration algorithm, hence resolving the possible ambiguity in identifying the assigned risk state. There is a strong relation between risk-sensitive MDPs and distributionally robust MDPs where the uncertainty sets are specified by confidence balls defined through some statistical distances. A particular robust MDP problem under R-contamination uncertainty sets has an interesting connection with a specific nested mean-CVaR mixed criterion MDP. Second, we discuss recent results on the family of f-divergence induced coherent risk measures that draws a direct connection between risk measures and distributional robustness. Building on this new family of risk measures and their properties, we demonstrate equivalence between a class of distributionally robust MDP problems based on statistical distance/divergence uncertainty sets and their corresponding risk sensitive MDPs based on nested conditional construction of f-divergence induced coherent risk measures. In particular, we propose to use the squared Hellinger distance for epistemic uncertainty sets and propose to study the Hellinger robust MDPs through those perspectives. Finally, we discuss some problems from other domains of reinforcement learning that make important use of trust region type methods, which share a similar flavor as the distributional robustness problems in previous sections.

Speaker: Eric Werneburg

Title: Training Neural Networks Using Reproducing Kernel Space Interpolation

Date/Time: 25 Mar. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: We introduce and study the theory of training neural networks using interpolation techniques from reproducing kernel Hilbert space theory. We generalize the method to Krein spaces, and show that widely-used neural network architectures are subsets of reproducing kernel Krein spaces. We introduce the concept of “associated Hilbert spaces” of such conventional neural networks. Using such machinery results in networks with the same expressivity, but which tend to generalize better after being trained. Next, we introduce Agler’s theorem in the context of neural network theory to show that there is one activation function, the expressivity of which is superior to all other desirable activation functions. Finally, we show the successful application of our theory in the field of neurourology and urodynamics.

Speaker: Yuhang Liu and Weihao Wang

Title: On the Effectiveness of Non-Pharmaceutical Interventions for COVID-19

Date/Time: 8 Apr. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: Worldwide, governments imposed a wide range of non-pharmaceutical interventions (NPIs) in the wake of the COVID-19 pandemic. Two years later today, pandemic fatigue has set in among the world’s population as the virus attack continues in waves. To help governments contain the pandemic more effectively and to ease the burden on the population, we examined the effectiveness of individual NPI among the 42 states in the US where the death count exceeded 100 during the first wave of the COVID-19 pandemic (February 1 to June 15, 2020). Two types of analyses were performed. Firstly, a prototypical Bayesian hierarchical model is employed to estimate the effectiveness of 5 commonly imposed NPIs in the US, including gathering restriction, restaurant capacity restriction, business closure, school closure, and stay-at-home. Secondly, the effectiveness of facemask mandate, the most controversial policy among states, is studied through counterfactual modeling, a variant of the prototypical Bayesian hierarchical model.

Speaker: El Mehdi Ainasse

Title: Multiple Changepoint Detection in Latent Signals and Processes

Date/Time: 22 Apr. 2022, Friday, 10:00 AM - 11:00 AM

Abstract: This work introduces a new method for detecting change-points in latent signals indirectly using consistent estimators with arbitrary rates and under a general class of heavy-tailed noise (sub-Weibull). Following the LSTV-LARS algorithm introduced by Leduc-Harchaoui (2010), we use a least-squares criterion with an L1 penalty. We show that despite not using LSTV on the underlying signal (which is assumed to be observed in the case of Leduc-Harchaoui) but using it on the estimator instead, our approach consistently estimates the breakpoint locations and the corresponding underlying latent signal. We also show that our indirect method and the direct approach are, in fact, asymptotically equivalent—both for the breakpoint location estimates and for the estimates of the underlying signal. Our empirics demonstrate that the method performs well even if the breakpoint location is close to the end of the sample and has been used to detect change-points in the mean, the variance, the mean, and the variance simultaneously, as well as the distribution. We will briefly touch upon how this method can be extended, through the introduction of kernels, to a more general functional-analytic setting that is suitable for various other applications.

Speaker: Teng Chen

Title: Estimation of Heavy Tails

Date/Time: 10 Sep. 2021, Friday, 10:00 AM - 11:00 AM

Abstract: In extreme value theory, the tail index is a critical measure for assessing the heavy-tailed behavior of a distribution. In this talk, we propose a new class of Pickands-type estimators based on conditional value-at-risk (CVaR) for the tail index. The CVaR-based estimators not only inherit the universal consistency, the location and scale invariant properties of Pickands estimator but also significantly improve the asymptotic efficiency and reduce the sensitivity to the choice of the intermediate order statistics. We prove the weak and strong consistency, and the asymptotic normality of these estimators under quite general conditions. A detailed investigation of the asymptotic behavior of the estimators in the family is carried out in order to identify which members of the family perform optimally. A simulation study involving a wide range of distributions shows the CVaR-based estimators have good finite-sample performance and compare favorably with the other estimators.

Speaker: Jiaju Miao

Title: Sector Rotation Strategy via Machine Learning

Date/Time: 24 Sep. 2021, Friday, 10:00 AM - 11:00 AM

Abstract: Asset-specific factors have been widely used to explain financial returns and measure asset-specific risk premia. In this paper, we employ these factors in various machine learning models to measure sector risk premia. We initially start with a comparison of the prediction of different models and demonstrate large economic gains from using machine learning for sector forecasting. We develop an assembling algorithm that combines different models based on the history of their performance, and we prove that the risk premia of the resulting meta-algorithm are not much worse than the risk premia of the infeasible optimal assembling. The resulting meta-strategy is used for portfolio investment that substantially outperforms the market.

Speaker: Qinyun Zhao

Title: Learning and control of time-varying linear quadratic regulator

Date/Time: 8 Oct. 2021, Friday, 10:00 AM - 11:00 AM

Abstract: Economic agents are hard to obtain complete information about all the parameters which could affect the payoffs that they receive. However, they could get feedback from observing the rewards of their actions. There is a voluminous literature on learning and control with unknown parameters. In this talk, we first introduce the work in Wieland's paper about his numeric method to get optimal control in a linear process with unknown parameters. After that, I would like to show my on-going work of applying a more efficient method, rollout algorithm to obtain approximate optimal control under more complicate time-varying environments.

Speaker: Xiaoqi Dong

Title: Survey on multi-agent reinforcement learning

Date/Time: 22 Oct. 2021, Friday, 10:00 AM - 11:00 AM

Abstract: In recent years, reinforcement learning (RL) has been witnessed to have magnificent advances. Most of the RL real-world applications, however, involve the participation of more than one agent, and fall into the realm of multi-agent RL (MARL). Although multi-agent learning (MAL) was first discussed in 1999 and is relatively less popular in 2000s, due to advances in single-agent RL (SARL) techniques and improvements of computation performance, this realm has recently re-merged. In this survey, we pro- vide a selective overview of algorithms in MARL. In specific, we review the algorithms in two representative frameworks, Markov games and extensive-form games, in accordance with the types of learning goals, which are fully cooperative, fully competitive, and a mix of the two. (This talk is a review of Zhang, Kaiqing, Zhuoran Yang, and Tamer Başar. "Multi-agent reinforcement learning: A selective overview of theories and algorithms." Handbook of Reinforcement Learning and Control(2021): 321-384).

Speaker: Ryan Kaufman and Prof. James Glimm

Title: GA1.2: An Intraday and Overnight Risk Model and Interest Rate Risk

Date/Time: 5 Nov. 2021, Friday, TBD

Abstract: Both daily and intraday risk models miss one of the key elements of a day's risk: the overnight jump. Intraday risk models will underestimate the day's risk when using time series analysis without a model for the overnight step, during which new information becomes available to traders, but prices freeze, a feature not captured in the time series representation of the data. Daily risk models will also underestimate the risk. Daily time series does capture the overnight step within the data, but averages it in with the risk of the whole day. Interest rate forecasting also comes with some caveats for modeling, most notably is the effect of political actions. We incorporate this into our model by including information about the present and future federal reserve rate into the model for bond prices, which is used to calculate risk. We show models for both of these phenomena and present some results.

Speaker: Greeshma Balabhadra

Title: Breakpoints in High Frequency Volatility

Date/Time: 19 Nov. 2021, Friday, 10:00 AM - 11:00 PM

Abstract: We introduce two new high-frequency volatility estimators that account for possible breakpoints in the spot volatility process. They are l1-penalized versions of classical estimators—the quadratic variation, and, jump robust version of it, bipower variation. We show that in the presence of a mean-square error of order op(1) achieved by these classical estimators, detecting breakpoints using the volatility estimator is asymptotical equivalent to detecting them using the infeasible (latent) volatility path. The proposed estimators are evaluated in simulations and on real data. They are fast in computations, and they accurately detect breakpoints that are close to the end of the sample—both properties are very desirable for financial applications. In terms of out-of-sample volatility prediction, qualitatively, the new estimators provide more smooth and realistic forecasts; quantitatively, they outperform the aforementioned competitors and their extensions at various frequencies and forecasting horizons.

Speaker: Jin Huang

Title: Convergence Analysis of Natural Policy Gradient Algorithms

Date/Time: 3 Dec. 2021, Friday, 10:00 AM - 11:00 AM

Abstract: When solving the problem of reinforcement learning, we often use optimization methods such as gradient descent. In this study, we are committed to studying the convergence of the Natural Policy Gradient under multiple iterations. Besides, we continue to discuss the possibility of convergence based on Natural Actor-Critic algorithm. The purpose of the research is to achieve faster convergence and theoretically establish the premise of high algorithm efficiency.