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 1 January 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.

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 the market expectations of future volatility, but traditional methods based on second-moment shocks and the time-varying volatility of the VIX often do not effectively to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this, we constructed a revised VIX by fitting a double-subordinated Normal Inverse Gaussian Lévy process to S&P 500 log returns, to provide a more comprehensive measure of volatility that captures the extreme movements and heavy tails observed in financial data. Using an axiomatic framework, we developed a family of risk–reward ratios that, when computed with our revised VIX and fitted to a long-memory time series model, provide a more precise identification of 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 Lévy 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.

This article provides an educational demonstration of how transformer-based natural language processing models, specifically FinBERT, can be used to generate actionable sentiment indicators from financial news. The focus is on pedagogy, showing portfolio managers, risk officers, and students how unstructured textual data can be systematically converted into interpretable signals. The article outlines a replicable workflow for classifying firm-specific headlines, aggregating sentiment scores and aligning them with intraday stock price movements. Examples illustrate how negative or positive sentiment clusters correspond with short-term price behavior, making sentiment analysis an intuitive complement to established portfolio management tools. The goal is to demystify AI-driven sentiment analytics, providing a transparent and practical entry point for incorporating narrative-driven risks and opportunities into the investment process.

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.

Traditional short-rate lattice models assume that interest rates move up or down with equal risk-neutral probability. This symmetry is a convenient modeling device, but it does not reflect how markets actually price risk. We recover contract-level risk-neutral probabilities using option data and find persistent and systematic departures from the 50/50 benchmark. These option-implied asymmetries vary across maturities and market conditions, particularly during volatile episodes such as the onset of the COVID-19 crisis. Embedding the recovered probabilities into bond valuation reveals significant consequences for practitioners. Symmetric models consistently misprice bonds by several basis points, bias expected holding-period returns, and generate hedge ratios that lead to larger tracking errors, higher turnover, and greater transaction costs. Models disciplined by option-implied probabilities produce bond valuations more consistent with market prices, return forecasts that better capture term premiums, and hedges that perform more effectively. The results demonstrate that the symmetry assumption underlying standard short-rate trees is empirically false and economically costly to ignore.