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Frank J. Fabozzi

Publications and source records attributed to Frank J. Fabozzi.

At least 19 recordsLinked to original sources

Portfolio Optimization under Heavy Tails and Asymmetric Volatility: Evidence from Taiwan-Exposed ETFs

Taiwan's central role in global semiconductor manufacturing exposes Taiwan-related ETFs to technology concentration, geopolitical uncertainty, and supply-chain disruptions, resulting in return distributions characterized by heavy tails, volatility clustering, and asymmetric responses to negative shocks. This paper analyzes thirty U.S.-listed ETFs with Taiwan exposure from February 2015 to February 2025 using tail-risk diagnostics, asymmetric volatility modeling, and portfolio optimization under mean--variance and conditional value-at-risk (CVaR) criteria. Hill tail-index estimates document heavy-tailed behavior across the ETF universe. Although the ETFs exhibit broadly similar asymptotic tail-decay behavior, semiconductor-focused ETFs produce substantially larger VaR and CVaR estimates than diversified benchmarks, indicating that cross-sectional differences in extreme downside risk are driven primarily by differences in return scale rather than tail-index estimates. GJR-GARCH estimates reveal persistent, asymmetric volatility, and the apparent long memory in squared returns is largely attributable to conditional heteroskedasticity rather than genuine fractional integration. CVaR optimization produces substantially more concentrated allocations than mean--variance optimization, with the CVaR tangent portfolio allocating a large weight to SMH during the post-COVID AI-driven expansion. Portfolio rankings depend on the performance measure: the Sharpe ratio and STARR measure favor the equally weighted portfolio, whereas the Rachev ratio favors CVaR-based portfolios. Overall, the results suggest that variance-based frameworks alone provide an incomplete characterization of risk in technology-concentrated investment environments and that variance-based and tail-sensitive performance measures may favor different portfolios over the same sample period.

q-fin.PM

Portfolio Optimization and Tail-Risk Analytics of Actively Managed ETFs

This paper examines portfolio optimization and tail-risk analytics for a heterogeneous universe of actively managed investment funds. Using daily Bloomberg data for 30 funds from 4 December 2020 to 24 December 2025, the study evaluates buy-and-hold, mean--variance, CVaR-based, and tangency-type strategies under long-only and long--short constraints. The sample consists predominantly of actively managed ETFs, with PTTRX retained as an actively managed fixed-income mutual-fund comparator. The results show substantial heterogeneity across thematic equity, fixed-income, income-oriented, multi-asset, and alternative strategies, creating both diversification opportunities and meaningful differences in volatility, drawdown behavior, downside exposure, and tail risk. Historical results indicate that tangency-type portfolios are generally the strongest competitors to the buy-and-hold benchmark in cumulative and risk-adjusted terms, while minimum-variance and CVaR-minimizing portfolios sacrifice upside participation for stronger downside control. Dynamic allocation does not improve all strategies uniformly: the long-only dynamic CVaR-95 portfolio is consistently attractive across several risk-adjusted criteria, whereas long--short dynamic tangency-CVaR portfolios perform strongly but are more sensitive to turnover and implementation costs. Tail-risk diagnostics based on empirical VaR, Expected Shortfall, maximum drawdown, left-tail Hill estimators, and POT--GPD methods show that downside tail exposure remains meaningful after portfolio aggregation. Overall, actively managed ETFs are best evaluated as components of a joint investment opportunity set in which dependence structure, portfolio design, dynamic allocation, implementation frictions, and tail-risk exposure jointly shape performance.

q-fin.PM

Innovative Extensions to Option Pricing: Asymmetric Brownian Motion and Random Walk Approaches

Classical option pricing models, such as Bachelier and Black--Scholes--Merton, postulate symmetric Brownian diffusion, which limits their capacity to reflect empirical phenomena including return skewness, heavy tails, and volatility asymmetry. This paper develops an innovative extension: the Geometric Asymmetric Brownian Motion (GABM), unifying asymmetric Brownian motion and random walk methodologies within the Bachelier--Black--Scholes--Merton framework. The approach harnesses the Cherny--Shiryaev--Yor invariance principle (CSYIP) to define asymmetric random walk integrals, where local time at the origin generates skewness and state-dependent risk. Closed-form option pricing formulas are derived, and a discrete-time binomial tree algorithm is constructed and shown to converge rigorously to the GABM limit. By incorporating a smoothed functional form based on the normal inverse Gaussian distribution, the model allows for flexible, state-dependent volatility calibration. Numerical experiments demonstrate the resulting option price and implied volatility surfaces, highlighting the framework's enhanced ability to capture persistent market asymmetry and complex risk behaviors observed in empirical data.

q-fin.MF

Option Pricing under Stochastic Volatility and Jumps:A PIDE Framework with Empirical Evidence

We develop a partial integro-differential equation (PIDE) framework for option pricing under joint stochastic volatility and jump dynamics, and evaluate its empirical content using the S&P500 index option contracts across three maturities. The framework is derived from the infinitesimal generator of an affine Lévy-type process and implemented via finite-difference discretization with FFT-based treatment of the nonlocal jump operator. Calibration via GMM reveals that stochastic volatility accounts for the dominant share of pricing improvement, where relative to Black-Scholes, the Heston specification reduces implied-volatility RMSE by 39%. Jump augmentation via either Merton or CGMY specifications yields marginal improvements concentrated at short maturities and in the deep out-of-the-money region. The calibrated CGMY activity index supports a compound-Poisson structure, consistent with high-frequency evidence on S&P500 index returns.

q-fin.PR

Probability Weighting Meets Heavy Tails: An Econometric Framework for Behavioral Asset Pricing

We develop an econometric framework integrating heavy-tailed Student's $t$ distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we demonstrate Student's $t$ specifications outperform Gaussian models in 88.4\% of cases. Bounded probability-weighting transformations preserve mathematical properties required for dynamic pricing. Gaussian models underestimate 99\% Value-at-Risk by 19.7\% versus 3.2\% for our specification. Joint estimation procedures identify tail and behavioral parameters with established asymptotic properties. Results provide robust inference for asset-pricing applications where heavy tails and behavioral distortions coexist.

q-fin.MF

Binary Tree Option Pricing Under Market Microstructure Effects: A Random Forest Approach

We propose a machine learning-based extension of the classical binomial option pricing model that incorporates key market microstructure effects. Traditional models assume frictionless markets, overlooking empirical features such as bid-ask spreads, discrete price movements, and serial return correlations. Our framework augments the binomial tree with path-dependent transition probabilities estimated via Random Forest classifiers trained on high-frequency market data. This approach preserves no-arbitrage conditions while embedding real-world trading dynamics into the pricing model. Using 46,655 minute-level observations of SPY from January to June 2025, we achieve an AUC of 88.25% in forecasting one-step price movements. Order flow imbalance is identified as the most influential predictor, contributing 43.2% to feature importance. After resolving time-scaling inconsistencies in tree construction, our model yields option prices that deviate by 13.79% from Black-Scholes benchmarks, highlighting the impact of microstructure on fair value estimation. While computational limitations restrict the model to short-term derivatives, our results offer a robust, data-driven alternative to classical pricing methods grounded in empirical market behavior.

q-fin.CP

Behavioral Probability Weighting and Portfolio Optimization under Semi-Heavy Tails

This paper develops a unified framework that integrates behavioral distortions into rational portfolio optimization by extracting implied probability weighting functions (PWFs) from optimal portfolios modeled under Gaussian and Normal-Inverse-Gaussian (NIG) return distributions. Using DJIA constituents, we construct mean-CVaR99 frontiers, alongwith Sharpe- and CVaR-maximizing portfolios, and estimate PWFs that capture nonlinear beliefs consistent with fear and greed. We show that increasing tail fatness amplifies these distortions and that shifts in the term structure of risk-free rates alter their curvature. The results highlight the importance of jointly modeling return asymmetry and belief distortions in portfolio risk management and capital allocation under extreme-risk environments.

econ.GN

Winners vs. Losers: Momentum-based Strategies with Intertemporal Choice for ESG Portfolios

This paper introduces a state-dependent momentum framework that integrates ESG regime switching with tail-risk-aware reward-risk metrics. Using a dynamic programming approach and solving a finite-horizon Bellman equation, we construct long-short momentum portfolios that adjust to changing ESG sentiment regimes. Unlike traditional momentum strategies based on historical returns, our approach incorporates the Stable Tail Adjusted Return ratio and Rachev ratio to better capture downside risk in turbulent markets. We apply this framework across three asset classes, Russell 3000 equities, Dow Jones~30 stocks, and cryptocurrencies, under both pro- and anti-ESG market regimes. We find that ESG-loser portfolios significantly outperform ESG-winner portfolios in pro-ESG regimes, a counterintuitive result suggesting that market overreaction to ESG sentiment creates short-term pricing inefficiencies. This pattern is robust across tail-sensitive performance metrics and is most pronounced under a two-week formation and holding period. Our framework highlights how ESG considerations and sentiment regimes alter return dynamics, offering practical guidance for investors seeking to implement responsive momentum strategies under sustainability constraints. These findings challenge conventional assumptions about ESG investing and underscore the importance of dynamic, regime-aware portfolio construction in environments shaped by regulatory signals, investor flows, and behavioral biases.

econ.GN

Multivariate Affine GARCH with Heavy Tails: A Unified Framework for Portfolio Optimization and Option Valuation

This paper develops and estimates a multivariate affine GARCH(1,1) model with Normal Inverse Gaussian innovations that captures time-varying volatility, heavy tails, and dynamic correlation across asset returns. We generalize the Heston-Nandi framework to a multivariate setting and apply it to 30 Dow Jones Industrial Average stocks. The model jointly supports three core financial applications: dynamic portfolio optimization, wealth path simulation, and option pricing. Closed-form solutions are derived for a Constant Relative Risk Aversion (CRRA) investor's intertemporal asset allocation, and we implement a forward-looking risk-adjusted performance comparison against Merton-style constant strategies. Using the model's conditional volatilities, we also construct implied volatility surfaces for European options, capturing skew and smile features. Empirically, we document substantial wealth-equivalent utility losses from ignoring time-varying correlation and tail risk. These findings underscore the value of a unified econometric framework for analyzing joint asset dynamics and for managing portfolio and derivative exposures under non-Gaussian risks.

econ.EM

Risk-Adjusted Performance of Random Forest Models in High-Frequency Trading

Because of the theoretical challenges posed by the Efficient Market Hypothesis to technical analysis, the effectiveness of technical indicators in high-frequency trading remains inadequately explored, particularly at the minute-level frequency, where effects of the microstructure of the market dominate. This study evaluates the integration of traditional technical indicators with random forest regression models using minute-level SPY data, analyzing 13 distinct model configurations. Our empirical results reveal a stark contrast between in-sample and out-of-sample performance, with $R^2$ values deteriorating from 0.749--0.812 during training to negative values in testing. A feature importance analysis demonstrates that primary price-based features dominate the predictions made by the model, accounting for over 60% of the importance, while established technical indicators, such as RSI and Bollinger Bands, account for only 14%--15%. Although the indicator-enhanced models achieved superior risk-adjusted metrics, with Rachev ratios between 0.919 and 0.961, they consistently underperformed a simple buy-and-hold strategy, generating returns ranging from -2.4% to -3.9%. These findings challenge conventional assumptions about the usefulness of technical indicators in algorithmic trading, suggesting that in high-frequency contexts, they may be more relevant to risk management rather than to predicting returns. For practitioners and researchers, our findings indicate that successful high-frequency trading strategies should focus on adaptive feature selection and regime-specific modeling rather than relying on traditional technical indicators, as well as indicating the critical importance of robust out-of-sample testing in the development of a model.

q-fin.CP

Advancing Portfolio Optimization: Adaptive Minimum-Variance Portfolios and Minimum Risk Rate Frameworks

This study presents the Adaptive Minimum-Variance Portfolio (AMVP) framework and the Adaptive Minimum-Risk Rate (AMRR) metric, innovative tools designed to optimize portfolios dynamically in volatile and nonstationary financial markets. Unlike traditional minimum-variance approaches, the AMVP framework incorporates real-time adaptability through advanced econometric models, including ARFIMA-FIGARCH processes and non-Gaussian innovations. Empirical applications on cryptocurrency and equity markets demonstrate the proposed framework's superior performance in risk reduction and portfolio stability, particularly during periods of structural market breaks and heightened volatility. The findings highlight the practical implications of using the AMVP and AMRR methodologies to address modern investment challenges, offering actionable insights for portfolio managers navigating uncertain and rapidly changing market conditions.

econ.EM

Optimizing Portfolios with Pakistan-Exposed ETFs: Risk and Performance Insight

This study examines the investment landscape of Pakistan as an emerging and frontier market, focusing on implications for international investors, particularly those in the United States, through exchange-traded funds (ETFs) with exposure to Pakistan. The analysis encompasses 30 ETFs with varying degrees of exposure to Pakistan, covering the period from January 1, 2016, to February 2024. This research highlights the potential benefits and risks associated with investing in these ETFs, emphasizing the importance of thorough risk assessments and portfolio performance comparisons. By providing descriptive statistics and performance metrics based on historical optimization, this paper aims to equip investors with the necessary insights to make informed decisions when optimizing their portfolios with Pakistan-exposed ETFs. The second part of the paper introduces and assesses dynamic optimization methodologies. This section is designed to explore the adaptability and performance metrics of dynamic optimization techniques in comparison with conventional historical optimization methods. By integrating dynamic optimization into the investigation, this research aims to offer insights into the efficacy of these contrasting methodologies in the context of Pakistan-exposed ETFs. The findings underscore the significance of Pakistan's market dynamics within the broader context of emerging markets, offering a pathway for diversification and potential growth in investment strategies.

q-fin.PM

An Empirical Implementation of the Shadow Riskless Rate

We address the problem of asset pricing in a market where there is no risky asset. Previous work developed a theoretical model for a shadow riskless rate (SRR) for such a market in terms of the drift component of the state-price deflator for that asset universe. Assuming asset prices are modeled by correlated geometric Brownian motion, in this work we develop a computational approach to estimate the SRR from empirical datasets. The approach employs: principal component analysis to model the effects of the individual Brownian motions; singular value decomposition to capture the abrupt changes in condition number of the linear system whose solution provides the SRR values; and a regularization to control the rate of change of the condition number. Among other uses (e.g., for option pricing, developing a term structure of interest rate), the SRR can be employed as an investment discriminator between asset classes. We apply the computational procedure to markets consisting of groups of stocks, varying asset type and number. The theoretical and computational analysis provides not only the drift, but also the total volatility of the state-price deflator. We investigate the time trajectory of these two descriptive components of the state-price deflator for the empirical datasets.

q-fin.MF

Beyond the Traditional VIX: A Novel Approach to Identifying Uncertainty Shocks in Financial Markets

We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures market expectations of future volatility, but traditional methods based on second-moment shocks and time-varying volatility of the VIX often fail to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this, we construct a revised VIX by fitting a double-subordinated Normal Inverse Gaussian Levy process to S&P 500 option prices, providing a more comprehensive measure of volatility that reflects the extreme movements and heavy tails observed in financial data. Using an axiomatic approach, we introduce a general family of risk-reward ratios, computed with our revised VIX and fitted over a fractional time series to more accurately identify uncertainty shocks in financial markets.

econ.EM

Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model

We present a unified, market-complete model that integrates both the Bachelier and Black-Scholes-Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natural world that experiences the possibility of negative security prices or riskless rates. In contrast to classical Black-Scholes-Merton, we show that option pricing in the unified model displays a difference depending on whether the replicating, self-financing portfolio uses riskless bonds or a single riskless bank account. We derive option price formulas and extend our analysis to the term structure of interest rates by deriving the pricing of zero-coupon bonds, forward contracts, and futures contracts. We identify a necessary condition for the unified model to support a perpetual derivative. Discrete binomial pricing under the unified model is also developed. In every scenario analyzed, we show that the unified model simplifies to the standard Black-Scholes-Merton pricing under specific limits and provides pricing in the Bachelier model limit. We note that the Bachelier limit within the unified model allows for positive riskless rates. The unified model prompts us to speculate on the possibility of a mixed multiplicative and additive deflator model for risk-neutral option pricing.

q-fin.MF

The Financial Market of Environmental Indices

This paper introduces the concept of a global financial market for environmental indices, addressing sustainability concerns and aiming to attract institutional investors. Risk mitigation measures are implemented to manage inherent risks associated with investments in this new financial market. We monetize the environmental indices using quantitative measures and construct country-specific environmental indices, enabling them to be viewed as dollar-denominated assets. Our primary goal is to encourage the active engagement of institutional investors in portfolio analysis and trading within this emerging financial market. To evaluate and manage investment risks, our approach incorporates financial econometric theory and dynamic asset pricing tools. We provide an econometric analysis that reveals the relationships between environmental and economic indicators in this market. Additionally, we derive financial put options as insurance instruments that can be employed to manage investment risks. Our factor analysis identifies key drivers in the global financial market for environmental indices. To further evaluate the market's performance, we employ pricing options, efficient frontier analysis, and regression analysis. These tools help us assess the efficiency and effectiveness of the market. Overall, our research contributes to the understanding and development of the global financial market for environmental indices.

q-fin.CP

Option pricing using a skew random walk pricing tree

Motivated by the Corns-Satchell, continuous time, option pricing model, we develop a binary tree pricing model with underlying asset price dynamics following Itô-Mckean skew Brownian motion. While the Corns-Satchell market model is incomplete, our discrete time market model is defined in the natural world; extended to the risk neutral world under the no-arbitrage condition where derivatives are priced under uniquely determined risk-neutral probabilities; and is complete. The skewness introduced in the natural world is preserved in the risk neutral world. Furthermore, we show that the model preserves skewness under the continuous-time limit. We provide numerical applications of our model to the valuation of European put and call options on exchange-traded funds tracking the S&P Global 1200 index.

q-fin.MF

Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis

Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk. The GJR pricing tree exhibits skewness and kurtosis in both the natural and risk-neutral world. We construct implied surfaces for the parameters determining the GJR tree. Motivated by Merton's pricing tree incorporating transaction costs, we extend the GJR pricing model to include a hedging cost. We demonstrate ways to fit the GJR pricing model to a market driver that influences the price dynamics of the underlying asset. We supplement our findings with numerical examples.

q-fin.MF