arXiv subjects

Svetlozar T. Rachev

Publications and source records attributed to Svetlozar T. Rachev.

At least 37 records · Page 2Linked to original sources

arXiv2025

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↗

arXiv2025

Iterated Poisson Processes for Catastrophic Risk Modeling in Ruin Theory

This paper studies the properties of the Multiply Iterated Poisson Process (MIPP), a stochastic process constructed by repeatedly time-changing a Poisson process, and its applications in ruin theory. Like standard Poisson processes, MIPPs have exponentially distributed sojourn times (waiting times between jumps). We explicitly derive the probabilities of all possible jump sizes at the first jump and obtain the Laplace transform of the joint distribution of the first jump time and its corresponding jump size. In ruin theory, the classical Cramér-Lundberg model assumes that claims arrive independently according to a Poisson process. In contrast, our model employs an MIPP to allow for clustered arrivals, reflecting real-world scenarios, such as catastrophic events. Under this new framework, we derive the corresponding scale function in closed form, facilitating accurate calculations of the probability of ruin in the presence of clustered claims. These results improve the modeling of extreme risks and have practical implications for insurance solvency assessments, reinsurance pricing, and capital reserve estimation.

math.PR↗

arXiv2025

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↗

arXiv2025

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↗

arXiv2024

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↗

arXiv2024

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↗

arXiv2024

Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis

We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets consist of a stock and a perpetual derivative of that stock. The option has the stock and its derivative as its underlying. Using a replicating portfolio, we develop prices for European options and generate the unique relationships between the risk-neutral and real-world parameters of the model. We discuss calibration of the model to empirical data in the cases in which the risky asset returns are treated as either arithmetic or logarithmic. From historical price and call option data for select large cap stocks, we develop implied parameter surfaces for the real-world parameters in the model.

q-fin.MF↗

arXiv2024

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↗

arXiv2024

Hedonic Models Incorporating ESG Factors for Time Series of Average Annual Home Prices

Using data from 2000 through 2022, we analyze the predictive capability of the annual numbers of new home constructions and four available environmental, social, and governance factors on the average annual price of homes sold in eight major U.S. cities. We contrast the predictive capability of a P-spline generalized additive model (GAM) against a strictly linear version of the commonly used generalized linear model (GLM). As the data for the annual price and predictor variables constitute non-stationary time series, to avoid spurious correlations in the analysis we transform each time series appropriately to produce stationary series for use in the GAM and GLM models. While arithmetic returns or first differences are adequate transformations for the predictor variables, for the average price response variable we utilize the series of innovations obtained from AR(q)-ARCH(1) fits. Based on the GAM results, we find that the influence of ESG factors varies markedly by city, reflecting geographic diversity. Notably, the presence of air conditioning emerges as a strong factor. Despite limitations on the length of available time series, this study represents a pivotal step toward integrating ESG considerations into predictive real estate models.

q-fin.CP↗

arXiv2024

Alternatives to classical option pricing

We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The second approach does use a riskless asset. However, by ensuring equality between real-world and risk-neutral price-change probabilities, the second approach enables the computation of risk-neutral option prices utilizing expectations under the natural world probability P. This produces the same option prices as the classical approach in which prices are computed under the risk neutral measure Q. The second approach and the two specific examples of the first approach require the introduction of new, marketable asset types, specifically perpetual derivatives of a stock, and a stock whose cumulative return (rather than price) is deflated.

q-fin.PR↗

arXiv2024

Unifying Market Microstructure and Dynamic Asset Pricing

We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include moving average or autoregressive behavior. Our model is market-complete, arbitrage-free, and preserves all of the parameters governing the historical (natural world) price dynamics when passing to an equivalent martingale (risk-neutral) measure. Specifically, this includes the instantaneous mean and variance of the asset return and the instantaneous probabilities for the direction of asset price movement. We believe this is the first paper to demonstrate the ability to include market microstructure effects in dynamic asset/option pricing in a market-complete, no-arbitrage, format.

q-fin.MF↗

arXiv2024

Moment Matching Method for Pricing Spread Options with Mean-Variance Mixture Lévy Motions

The paper Borovkova et al. [4] uses moment matching method to obtain closed form formulas for spread and basket call option prices under log normal models. In this note, we also use moment matching method to obtain semi-closed form formulas for the price of spread options under exponential Lévy models with mean-variance mixture. Unlike the semi-closed form formulas in Caldana and Fusai [5], where spread prices were expressed by using Fourier inversion formula for general price dynamics, our formula expresses spread prices in terms of the mixing distribution. Numerical tests show that our formulas give accurate spread prices also

q-fin.PR↗

arXiv2023

Enhancing CVaR portfolio optimisation performance with GAM factor models

We propose a discrete-time econometric model that combines autoregressive filters with factor regressions to predict stock returns for portfolio optimisation purposes. In particular, we test both robust linear regressions and general additive models on two different investment universes composed of the Dow Jones Industrial Average and the Standard & Poor's 500 indexes, and we compare the out-of-sample performances of mean-CVaR optimal portfolios over a horizon of six years. The results show a substantial improvement in portfolio performances when the factor model is estimated with general additive models.

q-fin.PM↗

arXiv2023

Bitcoin Volatility and Intrinsic Time Using Double Subordinated Levy Processes

We propose a doubly subordinated Levy process, NDIG, to model the time series properties of the cryptocurrency bitcoin. NDIG captures the skew and fat-tailed properties of bitcoin prices and gives rise to an arbitrage free, option pricing model. In this framework we derive two bitcoin volatility measures. The first combines NDIG option pricing with the Cboe VIX model to compute an implied volatility; the second uses the volatility of the unit time increment of the NDIG model. Both are compared to a volatility based upon historical standard deviation. With appropriate linear scaling, the NDIG process perfectly captures observed, in-sample, volatility.

q-fin.ST↗

arXiv2023

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↗

arXiv2023

Portfolio analysis with mean-CVaR and mean-CVaR-skewness criteria based on mean-variance mixture models

The paper Zhao et al. (2015) shows that mean-CVaR-skewness portfolio optimization problems based on asymetric Laplace (AL) distributions can be transformed into quadratic optimization problems under which closed form solutions can be found. In this note, we show that such result also holds for mean-risk-skewness portfolio optimization problems when the underlying distribution is a larger class of normal mean-variance mixture (NMVM) models than the class of AL distributions. We then study the value at risk (VaR) and conditional value at risk (CVaR) risk measures on portfolios of returns with NMVM distributions. They have closed form expressions for portfolios of normal and more generally elliptically distributed returns as discussed in Rockafellar & Uryasev (2000) and in Landsman & Valdez (2003). When the returns have general NMVM distributions, these risk measures do not give closed form expressions. In this note, we give approximate closed form expressions for VaR and CVaR of portfolios of returns with NMVM distributions. Numerical tests show that our closed form formulas give accurate values for VaR and CVaR and shortens the computational time for portfolio optimization problems associated with VaR and CVaR considerably.

q-fin.PM↗

arXiv2022

Hedonic Models of Real Estate Prices: GAM and Environmental Factors

We consider the use of P-spline generalized additive hedonic models for real estate prices in large U.S. cities, contrasting their predictive efficiency against linear and polynomial based generalized linear models. Using intrinsic and extrinsic factors available from Redfin, we show that GAM models are capable of describing 84% to 92% of the variance in the expected ln(sales price), based upon 2021 data. As climate change is becoming increasingly important, we utilized the GAM model to examine the significance of environmental factors in two urban centers on the northwest coast. The results indicate city dependent differences in the significance of environmental factors. We find that inclusion of the environmental factors increases the adjusted R-squared of the GAM model by less than one percent.

q-fin.CP↗

arXiv2022

ESG-valued discrete option pricing in complete markets

We consider option pricing using replicating binomial trees, with a two fold purpose. The first is to introduce ESG valuation into option pricing. We explore this in a number of scenarios, including enhancement of yield due to trader information and the impact of the past history of a market driver. The second is to emphasize the use of discrete dynamic pricing, rather than continuum models, as the natural model that governs actual market practice. We further emphasize that discrete option pricing models must use discrete compounding (such as risk-free rate compounding of $1+r_f Δt$) rather than continuous compounding (such as $e^{r_f Δt})$.

q-fin.PR↗