Special Issue "Mathematical and Empirical Finance"

A special issue of Journal of Risk and Financial Management (ISSN 1911-8074). This special issue belongs to the section "Mathematics and Finance".

Deadline for manuscript submissions: 1 December 2022 | Viewed by 11061

Special Issue Editors

Prof. Dr. W. Brent Lindquist
E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA
Interests: mathematical and empirical finance; computational applied mathematics
Prof. Dr. Svetlozar (Zari) Rachev
E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA
Interests: mathematical and empirical finance; probability metrics; mass transportation problems

Special Issue Information

Dear Colleagues,

High-frequency finance is a relatively new and exciting field of rational finance. When studying this field, the wealth of high-frequency data is both a blessing and a curse. Market microstructure phenomena often make the use of the classical semimartingale approach to high-frequency asset pricing obsolete. Still, the current host of market microstructure models lack the mathematical beauty of dynamic asset pricing theory and its jewel, the Fundamental Theorem of Asset Pricing. This Special Issue of JRFM is an attempt to bring together recent work in the areas of high-frequency asset pricing, market microstructure, high-frequency econometrics, risk assessment and risk management , and derivative pricing in an effort to seek an unified approach to dynamic asset pricing and market microstructure in high-frequency traded markets.

This Special Issue is aimed at reconciling dynamic asset pricing theory and market microstructure in high-frequency traded financial markets. We seek contributions on novel approaches to high-frequency finance, approaches that capture market microstructure phenomena in high-frequency trading but remain consistent with dynamic asset pricing theory, or its novel extensions. We strongly encourage contributions whose findings are backed by solid empirical studies. We would like to see articles which try to resolve the divide between dynamic asset pricing and market microstructure—a divide described in Joel Hasbrouck’s working paper “Modeling Market Microstructure Time Series (February 1996) as follows: “At the level of transaction prices, however, the random-walk conjecture is a straw man, a hypothesis that is very easy to reject in most markets even in small data samples. In microstructure, the question is not ‘whether’ transaction prices diverge from random walk, but rather ‘how much?’ and ‘why?’.”

We encourage possibly controversial papers seeking new dynamic asset pricing models possibly beyond the semimartingale approach to rational finance but having empirical findings consistent with market microstructure theory. We are in search of the Holy Grail of high-frequency finance—a Fundamental Asset Pricing and Market Microstructure Theorem.

Prof. Dr. W. Brent Lindquist
Prof. Dr. Svetlozar (Zari) Rachev
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • high frequency finance
  • dynamic asset pricing theory
  • market microstructure
  • risk management
  • derivative pricing

Published Papers (14 papers)

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Research

Article
National Governance Index, Corruption Index and Growth Rate—International Evidence from Sub-Saharan and MENA Countries
J. Risk Financial Manag. 2022, 15(6), 261; https://doi.org/10.3390/jrfm15060261 - 09 Jun 2022
Viewed by 359
Abstract
In an international setting of developing countries, applying advanced statistical estimation approaches such as the system generalized method of moments (GMM), two-stage least square (2SLS) regressions, and cluster analysis, this paper revisits the impact of macro-level governance quality and the corruption index on [...] Read more.
In an international setting of developing countries, applying advanced statistical estimation approaches such as the system generalized method of moments (GMM), two-stage least square (2SLS) regressions, and cluster analysis, this paper revisits the impact of macro-level governance quality and the corruption index on the economic growth rate. We use cross-country panel data for 40 sub-Saharan and the Middle Eastern and North African (MENA) countries over the period of 2009–2020. The empirical results document the positive and negative effects of the national governance index and the corruption index on the economic growth rate. Additionally, foreign direct investment and population have a positive impact on the economic growth rate and trade openness has a negative impact. The study evaluates the robustness of these associations through a series of tests. These findings have important policy implications for policymakers and regulators in developing countries. In particular, the study recommends the implementation of an anti-corruption campaign and improving country-level governance quality that could encourage increased foreign direct investment for an accelerated economic growth rate. These will further enhance accountability, transparency, the rule of law, social responsibility, the public voice, and government effectiveness. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
Article
The Pricing Model of Pension Benefit Guaranty Corporation Insurance with Regime-Switching Processes
J. Risk Financial Manag. 2022, 15(6), 258; https://doi.org/10.3390/jrfm15060258 - 09 Jun 2022
Viewed by 293
Abstract
This paper aims to evaluate Pension Benefit Guaranty Corporation (PBGC) insurance values through regime-switching models. We separate periods of the economy with faster growth from those with slower growth to observe long-term trends in the economy. We derive a fair PBGC insurance pricing [...] Read more.
This paper aims to evaluate Pension Benefit Guaranty Corporation (PBGC) insurance values through regime-switching models. We separate periods of the economy with faster growth from those with slower growth to observe long-term trends in the economy. We derive a fair PBGC insurance pricing formula under distress termination and intervention termination using regime-switching processes. We set parameters by estimating the S&P 500 index and one-year treasury bills via expectation maximization particle swarm optimization (EM-PSO)-Gradient, which is an extension of the EM-Gradient method. Then, we conduct sensitivity analysis to investigate the impact of model parameters on insurance values. According to the maximum likelihood estimation results, the Akaike information criterion (AIC) and Bayesian information criterion (BIC) estimators show that the regime-switching process has better goodness of fit than the geometric Brownian motion. Scenario analysis also supports the adequacy of our pricing formula. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
Article
The Generalized Gamma Distribution as a Useful RND under Heston’s Stochastic Volatility Model
J. Risk Financial Manag. 2022, 15(6), 238; https://doi.org/10.3390/jrfm15060238 - 26 May 2022
Viewed by 372
Abstract
We present the Generalized Gamma (GG) distribution as a possible risk neutral distribution (RND) for modeling European options prices under Heston’s stochastic volatility (SV) model. We demonstrate that under a particular reparametrization, this distribution, which is a member of the scale-parameter family of [...] Read more.
We present the Generalized Gamma (GG) distribution as a possible risk neutral distribution (RND) for modeling European options prices under Heston’s stochastic volatility (SV) model. We demonstrate that under a particular reparametrization, this distribution, which is a member of the scale-parameter family of distributions with the mean being the forward spot price, satisfies Heston’s solution and hence could be used for the direct risk-neutral valuation of the option price under Heston’s SV model. Indeed, this distribution is especially useful in situations in which the spot’s price follows a negatively skewed distribution for which Black–Scholes-based (i.e., the log-normal distribution) modeling is largely inapt. We illustrate the applicability of the GG distribution as an RND by modeling market option data on three large market-index exchange-traded funds (ETF), namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long-term US Treasury bonds). As of the writing of this paper (August 2021), the option chain of each of the three market-index ETFs shows a pronounced skew of their volatility ‘smile’, which indicates a likely distortion in the Black–Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion in the volatility ‘smile’ appears not to exist in the TLT option data. We provide a thorough modeling of the option data we have on each ETF (with the 15 October 2021 expiration) based on the GG distribution and compare it to the option pricing and RND modeling obtained directly from a well-calibrated Heston’s SV model (both theoretically and also empirically, using Monte Carlo simulations of the spot’s price). All three market-index ETFs exhibited negatively skewed distributions, which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black–Scholes modeling in such instances, which involves negatively skewed distribution, is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. Similarly, the closely related Inverse Generalized Gamma distribution (IGG) is also proposed as a possible RND for Heston’s SV model in situations involving positively skewed distribution. In all, utilizing the Generalized Gamma distributions as possible RNDs for direct option valuations under the Heston’s SV is seen as particularly useful to the retail traders who do not have the numerical tools or the know-how to fine-calibrate this SV model. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Portfolio Optimization on Multivariate Regime-Switching GARCH Model with Normal Tempered Stable Innovation
J. Risk Financial Manag. 2022, 15(5), 230; https://doi.org/10.3390/jrfm15050230 - 23 May 2022
Viewed by 386
Abstract
This paper uses simulation-based portfolio optimization to mitigate the left tail risk of the portfolio. The contribution is twofold. (i) We propose the Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) to accommodate fat tails, volatility clustering and regime switch. [...] Read more.
This paper uses simulation-based portfolio optimization to mitigate the left tail risk of the portfolio. The contribution is twofold. (i) We propose the Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) to accommodate fat tails, volatility clustering and regime switch. The volatility of each asset independently follows the regime-switch GARCH model, while the correlation of joint innovation of the GARCH models follows the Hidden Markov Model. (ii) We use tail risk measures, namely conditional value-at-risk (CVaR) and conditional drawdown-at-risk (CDaR), in the portfolio optimization. The optimization is performed with the sample paths simulated by the MRS-MNTS-GARCH model. We conduct an empirical study on the performance of optimal portfolios. Out-of-sample tests show that the optimal portfolios with tail measures outperform the optimal portfolio with standard deviation measure and the equally weighted portfolio in various performance measures. The out-of-sample performance of the optimal portfolios is also more robust to suboptimality on the efficient frontier. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Dynamic and Static Volatility Interruptions: Evidence from the Korean Stock Markets
J. Risk Financial Manag. 2022, 15(3), 105; https://doi.org/10.3390/jrfm15030105 - 25 Feb 2022
Viewed by 572
Abstract
We conducted a comprehensive analysis on the sequential introductions of dynamic and static volatility interruptions (VIs) in the Korean stock markets. The Korea Exchange introduced VIs to improve price formation, and to limit risk to investors from brief periods of abnormal volatility for [...] Read more.
We conducted a comprehensive analysis on the sequential introductions of dynamic and static volatility interruptions (VIs) in the Korean stock markets. The Korea Exchange introduced VIs to improve price formation, and to limit risk to investors from brief periods of abnormal volatility for individual stocks. We found that dynamic VI is effective in price stabilization and discovery, while the effect of static VI is limited. The static VI functions similarly to the pre-existing price-limit system; this accounts for its limited incremental benefit. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
The Dynamic Relationship between Investor Attention and Stock Market Volatility: International Evidence
J. Risk Financial Manag. 2022, 15(2), 66; https://doi.org/10.3390/jrfm15020066 - 01 Feb 2022
Viewed by 692
Abstract
This paper investigates the role of investor attention in forecasting realized volatility for fourteen international stock markets, by means of Google Trends data, over the sample period January 2004 through November 2021. We devise an augmented Empirical Similarity model that combines three volatility [...] Read more.
This paper investigates the role of investor attention in forecasting realized volatility for fourteen international stock markets, by means of Google Trends data, over the sample period January 2004 through November 2021. We devise an augmented Empirical Similarity model that combines three volatility components, defined over different time horizons, using the similarity measure between lagged Google search queries and volatility. Results show that investor attention positively affects future volatility in the short-run. The effect of investor attention is likely to reverse in the long-run, consistently with the price pressure hypothesis. The proposed model demonstrates important gains in terms of volatility forecast accuracy and outperforms highly competitive models. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Maximum Drawdown, Recovery, and Momentum
J. Risk Financial Manag. 2021, 14(11), 542; https://doi.org/10.3390/jrfm14110542 - 11 Nov 2021
Viewed by 537
Abstract
We empirically test predictability on asset price using stock selection rules based on maximum drawdown and its consecutive recovery. In various equity markets, monthly momentum- and weekly contrarian-style portfolios constructed from these alternative selection criteria are superior not only in forecasting directions of [...] Read more.
We empirically test predictability on asset price using stock selection rules based on maximum drawdown and its consecutive recovery. In various equity markets, monthly momentum- and weekly contrarian-style portfolios constructed from these alternative selection criteria are superior not only in forecasting directions of asset prices but also in capturing cross-sectional return differentials. In monthly periods, the alternative portfolios ranked by maximum drawdown measures exhibit outperformance over other alternative momentum portfolios including traditional cumulative return-based momentum portfolios. In weekly time scales, recovery-related stock selection rules are the best ranking criteria for detecting mean-reversion. For the alternative portfolios and their ranking baskets, improved risk profiles in various reward-risk measures also imply more consistent prediction on the direction of assets in future. Moreover, turnover rates of these momentum/contrarian portfolios are also reduced with respect to the benchmark portfolios. In the Carhart four-factor analysis, higher factor-neutral intercepts for the alternative strategies are another evidence for the robust prediction by the alternative stock selection rules. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Multi-Asset Value Payoff: Is Recent Underperformance Cyclical?
J. Risk Financial Manag. 2021, 14(10), 477; https://doi.org/10.3390/jrfm14100477 - 11 Oct 2021
Viewed by 631
Abstract
Recent value factor underperformance has called into question whether the value factor payoff is cyclically low, or if there are more structural challenges. We use a new approach to explore a link between the well-known macroeconomic exposures of traditional asset classes and those [...] Read more.
Recent value factor underperformance has called into question whether the value factor payoff is cyclically low, or if there are more structural challenges. We use a new approach to explore a link between the well-known macroeconomic exposures of traditional asset classes and those of value premia in a multi-asset context, focusing on country equities, bonds, and currencies in developed markets. Taking advantage of the cross-country inflation and growth expectations implicit in every value portfolio, we derive the net inflation and real growth characteristics embedded in each asset class carry portfolio at each point in time. Our analysis provides several insights: (1) Multi-asset value payoff is only weakly related to the global business cycle. (2) However, we find that the payoff to value portfolios is strongly linked to relative growth and inflation expectations across countries. (3) Over the last decade, we find that cheaper assets have had much lower net relative macro exposures compared to earlier time periods. This characteristic coincides with the period of unconventional central bank policies designed to lift global growth after the Global Financial Crisis (GFC). Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Global Index on Financial Losses Due to Crime in the United States
J. Risk Financial Manag. 2021, 14(7), 315; https://doi.org/10.3390/jrfm14070315 - 09 Jul 2021
Viewed by 708
Abstract
Despite the potential importance of crime rates in investments, there are no indices dedicated to evaluating the financial impact of crime in the United States. As such, this paper presents an index-based insurance portfolio for crime in the United States by utilizing the [...] Read more.
Despite the potential importance of crime rates in investments, there are no indices dedicated to evaluating the financial impact of crime in the United States. As such, this paper presents an index-based insurance portfolio for crime in the United States by utilizing the financial losses reported by the Federal Bureau of Investigation. The objective of our paper is to introduce new risk hedging financial contracts for crime, consistent with dynamic asset pricing. Underlying the index, we hedge the investments by issuing marketable European call and put options and providing risk budgets. These budgets show that real estate, ransomware, and government impersonation are the main risk contributors in our index. Next, we evaluate the performance of our index via stress testing to determine its resilience to economic crisis. Of all the factors considered in this study, unemployment rate has the potential to demonstrate the highest systemic risk to the portfolio. Our portfolio will help investors envision risk exposure in the market, gauge investment risk based on their desired risk level, and hedge strategies for potential losses due to economic crashes. In conclusion, we provide a basis for the securitization of insurance risk from certain crimes that could forewarn investors to transfer their risk to capital market investors. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Systemic Risk Modeling with Lévy Copulas
J. Risk Financial Manag. 2021, 14(6), 251; https://doi.org/10.3390/jrfm14060251 - 05 Jun 2021
Cited by 2 | Viewed by 1317
Abstract
We investigate a systemic risk measure known as CoVaR that represents the value-at-risk (VaR) of a financial system conditional on an institution being under distress. For characterizing and estimating CoVaR, we use the copula approach and introduce the normal tempered stable (NTS) copula [...] Read more.
We investigate a systemic risk measure known as CoVaR that represents the value-at-risk (VaR) of a financial system conditional on an institution being under distress. For characterizing and estimating CoVaR, we use the copula approach and introduce the normal tempered stable (NTS) copula based on the Lévy process. We also propose a novel backtesting method for CoVaR by a joint distribution correction. We test the proposed NTS model on the daily S&P 500 index and Dow Jones index with in-sample and out-of-sample tests. The results show that the NTS copula outperforms traditional copulas in the accuracy of both tail dependence and marginal processes modeling. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Insuring Hollywood: A Movie Returns Index and the American Stock Market
J. Risk Financial Manag. 2021, 14(5), 189; https://doi.org/10.3390/jrfm14050189 - 21 Apr 2021
Viewed by 1219
Abstract
The aim of this paper is the definition of a daily index representing the risk-return on investments in the American film industry. The index should be used to predict the riskiness and the expected return of movie projects at the level of the [...] Read more.
The aim of this paper is the definition of a daily index representing the risk-return on investments in the American film industry. The index should be used to predict the riskiness and the expected return of movie projects at the level of the overall industry and then to determine a premium for insurance for such an investment. Such an index can inform the decision making in relation to risk but also timing. Though not currently legal in the United States, such an index may be relevant at some point in the future or in other countries for film production companies as well as venture capitalists interested in investing in one or a slate of motion picture productions or more broadly in the holdings of a media conglomerate, an exhibition chain, or some other aspect of the media landscape. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Sample Path Generation of the Stochastic Volatility CGMY Process and Its Application to Path-Dependent Option Pricing
J. Risk Financial Manag. 2021, 14(2), 77; https://doi.org/10.3390/jrfm14020077 - 15 Feb 2021
Cited by 1 | Viewed by 803
Abstract
This paper proposes the sample path generation method for the stochastic volatility version of the CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to the American style S&P 100 [...] Read more.
This paper proposes the sample path generation method for the stochastic volatility version of the CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to the American style S&P 100 index options market, using the least square regression method. Moreover, we discuss path-dependent options, such as Asian and Barrier options. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
An Artificial Intelligence Approach to the Valuation of American-Style Derivatives: A Use of Particle Swarm Optimization
J. Risk Financial Manag. 2021, 14(2), 57; https://doi.org/10.3390/jrfm14020057 - 02 Feb 2021
Cited by 1 | Viewed by 790
Abstract
In this paper, we evaluate American-style, path-dependent derivatives with an artificial intelligence technique. Specifically, we use swarm intelligence to find the optimal exercise boundary for an American-style derivative. Swarm intelligence is particularly efficient (regarding computation and accuracy) in solving high-dimensional optimization problems and [...] Read more.
In this paper, we evaluate American-style, path-dependent derivatives with an artificial intelligence technique. Specifically, we use swarm intelligence to find the optimal exercise boundary for an American-style derivative. Swarm intelligence is particularly efficient (regarding computation and accuracy) in solving high-dimensional optimization problems and hence, is perfectly suitable for valuing complex American-style derivatives (e.g., multiple-asset, path-dependent) which require a high-dimensional optimal exercise boundary. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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Article
Option Pricing Incorporating Factor Dynamics in Complete Markets
J. Risk Financial Manag. 2020, 13(12), 321; https://doi.org/10.3390/jrfm13120321 - 15 Dec 2020
Cited by 1 | Viewed by 973
Abstract
Using the Donsker–Prokhorov invariance principle, we extend the Kim–Stoyanov–Rachev–Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the Cherny–Shiryaev–Yor invariance principles, we formulate a new binomial path-dependent pricing model for discrete- and continuous-time complete [...] Read more.
Using the Donsker–Prokhorov invariance principle, we extend the Kim–Stoyanov–Rachev–Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the Cherny–Shiryaev–Yor invariance principles, we formulate a new binomial path-dependent pricing model for discrete- and continuous-time complete markets where the stock price dynamics depends on the log-return dynamics of a market influencing factor. In the discrete case, we extend the results of this new approach to a financial market with informed traders employing a statistical arbitrage strategy involving trading of forward contracts. Our findings are illustrated with numerical examples employing US financial market data. Our work provides further support for the conclusion that any option pricing model must preserve valuable information on the instantaneous mean log-return, the probability of the stock’s upturn movement (per trading interval), and other market microstructure features. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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