Mathematical Finance
Department of Mathematics and Statistics
Texas Tech University
Algorithmic trading requires the trading machines to consider the reasonably
expected near term order flows (i.e., RENTOF) in trading.
To manage the price impact and transaction cost associated with large orders
submitted to an order driven market,
trading machine must determine their trading styles (aggressive, neutral, or passive)
based on the market liquidity in response to RENTOF, particularly for trading a large size of stocks.
In this work we introduce an adaptive learning algorithm for considering different trading styles
to satisfy the predictive near-term market liquidity
(i.e., order flows) with respect to an optimal order submission strategy based on
different market situations.
We show some analytical properties and numerical performances of our algorithm
in search of optimal solutions. We evaluate the performances of our algorithm with simulations
run over a set of experiments in comparison with two alternative strategies.
Our results suggest that the proposed algorithmic trading strategy illustrates superiority in performance.Abstract: We argue that media slant constitutes a source of ambiguity and show
that the uncertainty stemming from slanted news is priced in the cross section of US stocks.
Our identification of slanted news stocks is based on a combination of a news proxy using
Wikipedia page view data and mutual fund managers' aggregated portfolio positions.
We find that slanted news stocks earn a premium of roughly 1% in announcement months
over their unslanted peers, which peaks on the announcement day itself.
Our results further show that the premium is compensating for the exposure to a slanted
news mimicking factor.
This is joint work with Prof. Marliese Uhrig-Homburg
In our study, the exposure to equity markets is measured by a convex risk measure,
and the stock returns follow normal variance-mean mixture distributions.
We convert the high-dimensional problem into a two-dimensional one by using a scheme motivated by Shi and Kim (2001).
We further prove the dimension reduction scheme can preserve the convexity of the problem.
An empirical study will be presented for illustration.This presentation reviews the significant progress in academic research on economic impact of climate change
and explores the implications for expected returns and strategic portfolio allocations across major public asset classes.
There have been numerous efforts to measure the environmental impact within a broader ESG framework with
a focus on microeconomic and firm-level implications. In this presentation, we assess the impact of climate change
on long-term expected returns across asset classes from a top-down macroeconomic perspective.
We use well-accepted climate risk scenarios to assess the potential impact of alternative climate scenarios on economic growth,
inflation, and asset returns for major asset classes.
Finally, we design hypothetical portfolios given these top-down assumptions and explore portfolio allocation implications.
Bio:
Yesim Tokat-Acikel, PhD, is a Managing Director, Head of Multi-Asset Research and Portfolio Manager for PGIM
Quantitative Solutions working within the Global Multi-Asset Solutions team.
In this capacity, she is responsible for the research, development, and portfolio management of systematic total
and absolute return investment solutions. She is also an investment lead for our global solutions efforts.
Prior to PGIM Quantitative Solutions, Yesim worked as a Senior Quantitative Analyst developing GTAA strategies at AllianceBernstein,
and as a Senior Investment Analyst for the Vanguard Group, where she built tactical and strategic asset
allocation models for retirement and private client markets.
Yesim’s articles have appeared in the Journal of Portfolio Management, the Journal of Investment Management,
Journal of Investing, Journal of Risk and Financial Management, the Journal of Economic Dynamics and Control,
the Strategic Management Journal, and the Journal of Financial Planning, among other leading publications.
She earned a BS in industrial engineering from Bilkent University in Turkey, an MS in industrial engineering
from the University of Arizona, Tucson, and a PhD in economics from the University of California, Santa Barbara.
The persistence of low interest rates is spurring research on the question how to increase yields,
while limiting the variability of long-term investment payouts.
Under the benchmark approach it is possible to achieve attractive, almost riskless,
non-fluctuating long-term investment results.
Payouts of savings account units that achieve an almost riskless outcome over a long time period
can be hedged reliably as contingent claims by using a stock index and a savings account.
This dynamic asset allocation can be performed in a less expensive manner than by traditional valuation methods.
The benchmark approach is using real-world pricing,
which provides the least expensive hedging strategy for replicable contingent claims. This talk will cover the Bachelier model of asset pricing, its extensions and option pricing.
Note: The Bachelier model uses a normal price distribution rather than the Black-Scholes
log-normal distribution and has applications when option prices can be negative.
Stochastic orders formalize preferences among random outcomes and are widely used in statistics and economics.
We analyze stochastic optimization problems involving stochastic-order relations as constraints,
which compare performance functionals, depending on our decisions, to benchmark random outcomes.
We discuss the relation of univariate and multivariate stochastic orderings to utility functions,
conditional value at risk, and to coherent measures of risk.
Necessary and sufficient conditions of optimality and duality theory for problems with stochastic order
constraints involve expected utility theory, dual (rank-dependent) utility theory, and coherent measures of risk.
The model provides a link between various approaches for risk-averse optimization.
Some attention will be paid to the numerical solution of the problems and their applications.
The growing interest for sustainable investing calls for an axiomatic approach to characterize risk
and reward measures for investors that do not focus uniquely on financial returns,
but also for environmental and social sustainability.
We propose definitions of ESG-coherent risk and reward measures, as well as ESG risk-reward ratios.
Such measures are defined as functions of bivariate random variables:
the financial returns, and ESG scores (a proxy for sustainability).
We provide examples of such functions, describing families of measures that can be derived from
traditional univariate risk and reward measures.
We then show an empirical example in which we use an ESG-adjusted CVaR in portfolio optimization.Asset-specific factors have been widely used to explain financial returns and measure asset-specific risk premia.
We employ these factors in various machine learning models to measure sector risk premia.
First, we make a comparison of the prediction of different models and demonstrate large economic gains from
using machine learning for sector forecasting.
Second, we develop an ensemble algorithm that combines different models based on the history of their risk premia
prediction performance, and we prove that the prediction accuracy of the resulting meta-algorithm is not much
worse than the prediction accuracy of an infeasible optimal ensemble.
The proposed ensemble achieves out-of-sample R2 of 1.54%, and the resulting meta-prediction is used in a sector
rotation investment strategy that substantially outperforms the market, individual models, and other naive ensembles.
The annual Sharpe ratio of the proposed long-short sector rotation strategy is 1.83,
and the portfolio performance survives many robustness checks against other factors and subperiods,
it does not die out in more recent years, and the strategy is profitable even at very conservative transaction cost levels.
Our results show that individual stock characteristics, when used in a well designed ensemble of machine learning algorithms,
are highly relevant for the prediction of sector risk premia, and for the construction of profitable sector rotation strategy.One criticism of the classical Black-Scholes-Merton option pricing formulation
is its use of a Gaussian price process for the asset underlying the option.
As a result, various observed (“stylized”) facts of financial price processes
remain uncaptured by the BSM model.
These behaviors, which are observed in the return process
(fractional change in price over time) and in the distribution of those returns over time,
include volatility clustering, skewness and heavy tails.
Going beyond a Gaussian model presents challenges,
for example existing formalisms for option pricing cannot accommodate distributions
with power-law tails such as Student’s t.
In this talk I discuss the use of double subordinated Levy processes within
established option pricing formalisms.
In particular, inverse Gauss processes
(https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution)
are used to capture five stylized behaviors: the mean, volatility,
skewness and kurtosis of the distribution of asset returns,
as well as to capture the fact that information driving asset prices arrives at discrete,
random intervals.
This work will be presented in the context of European call and put options
whose underlying asset is a portfolio.
The specific portfolio consists of holdings in real estate investment trusts (REITs).
A by-product of the use of subordinated methods is the natural definition of a
new measure for the volatility of asset returns.The Generalized Hyperbolic (GH) distribution is a multivariate heavy tailed distribution that has been widely used in finance.
In this presentation we review its properties and show that some popular techniques based on Gaussian
distribution (i) shrinkage estimator, (ii) online parameter updating, (iii) portfolio optimization via quadratic programming,
and (iv) measuring portfolio diversification can be extended to the GH distribution as well. While environmental, social, and governance (ESG) trading activity has been a distinctive feature of financial markets,
the debate if ESG scores can also convey information regarding a company’s riskiness remains open.
Regulatory authorities, such as the European Banking Authority (EBA), have acknowledged that ESG factors can contribute to risk.
Therefore, it is important to model such risks and quantify what part of a company’s riskiness can be attributed to the ESG scores.
This paper aims to question whether ESG scores can be used to provide information on (tail) riskiness.
By analyzing the (tail) dependence structure of companies with a range of ESG scores, that is within an ESG rating class,
using high-dimensional vine copula modelling, we are able to show that risk can also depend on and be directly associated with
a specific ESG rating class.
Empirical findings on real-world data show positive not negligible ESG risks determined by ESG scores, especially during the 2008 crisis.