The occurrence of extreme observations in a time series depends on the heaviness of the distribution's tails. This paper proposes a score-driven framework for detecting and modelling time-varying tail behaviour. The framework is based on the t conditional distributions and is extended to allow for asymmetric tails with distinct dynamic behaviour. In addition, the paper introduces a novel Lagrange Multiplier test to detect the presence of dynamics in the tail index parameters. The paper examines the properties of the test and demonstrates that it is more effective than existing methodologies at detecting tail variation. The framework is then applied to the tail behaviour of market returns from Equity Indices and Credit Default Swaps. The implications of neglecting dynamic tail features are assessed in terms of conditional density forecasts. The paper shows that allowing for a dynamic tail index, where appropriate, improves the forecasting accuracy of expected shortfalls and value-at-risk.
This paper investigates the relationship between the utilization ratio of central bank digital currency (CBDC) and bank lending returns. We extend the traditional credit rationing framework by including CBDC utilization and show that the relationship between the CBDC utilization ratio and bank lending returns can be negative, U-shaped, or positive, depending on the relative magnitude of the income, risk, and cost-saving effects associated with CBDC. Numerical simulations reveal varied trends in lending returns under different market conditions, with a U-shaped relationship observed in a neutral market. Sensitivity analysis further indicates a non-linear impact of key parameters on returns. These findings highlight the complex dynamics between CBDC utilization and bank lending returns, underscoring the need for further empirical research as more data becomes available.
Understanding the dependencies among financial assets is critical for portfolio optimization. Traditional approaches based on correlation networks often fail to capture the nonlinear and directional relationships that exist in financial markets. In this study, we construct directed and weighted financial networks using the Mixture Transition Distribution (MTD) model, offering a richer representation of asset interdependencies. We apply local assortativity measures-metrics that evaluate how assets connect based on similarities or differences-to guide portfolio selection and allocation. Using data from the Dow Jones 30, Euro Stoxx 50, and FTSE 100 indices constituents, we show that portfolios optimized with network-based assortativity measures consistently outperform the classical mean-variance framework. Notably, modalities in which assets with differing characteristics connect enhance diversification and improve Sharpe ratios. The directed nature of MTD-based networks effectively captures complex relationships, yielding portfolios with superior risk-adjusted returns. Our findings highlight the utility of network-based methodologies in financial decision-making, demonstrating their ability to refine portfolio optimization strategies. This work thus underscores the potential of leveraging advanced financial networks to achieve enhanced performance, offering valuable insights for practitioners and setting a foundation for future research.
We introduce a new Monte Carlo based method to evaluate American options under parameter uncertainty within a multifactor framework. The classical approach, referred to as the Longstaff-Schwartz Monte Carlo method, cannot deal with such a setup. Our proposed method, therefore, provides a significant extension of the computational toolbox relevant to American options and optimal stopping problems. We first reformulate the underlying American option price as the solution of a reflected backward stochastic differential equation (RBSDE) with a uniformly Lipschitz continuous generator and propose an algorithm based on stratified sampling. The proposed algorithm allows parallelization on graphics processing units (GPUs), and provides accurate and computationally efficient estimates of option prices under different multifactor models. Through extensive numerical experiments using calibrated models, we demonstrate the convergence of the proposed scheme. Finally, using our algorithm, we quantify the loss of premium due to parameter uncertainty for financial options, which can be useful when looking at the impact of model calibration error.
The crypto-assets markets are notoriously volatile and risky. In this context, market-neutral type strategies, such as pair-trading, may be relevant. In this paper, we focus on the implementation of pair-trading strategies with a wide range of crypto-assets over periods between August 2021 and January 2024. To carry out this study, we combine econometric and machine learning techniques which differ from those used in existing literature on the subject. By using cointegration tests and error correction models, we identify a sample of 229 pairs suitable for pair-trading strategies. Using a genetic algorithm and pair clustering, we test four strategies using standard and optimized thresholds. The results highlight the existence of profitable cointegrating relationships, and, therefore, short-term market inefficiencies in the crypto-assets market. Indeed, though still risky, the best strategy identified in terms of risk-return trade-off, with a median maxdrawdown of 15.29%, delivers an average annual Sharpe ratio per pair of 0.69 over the out-of-sample period.
This research unifies active portfolio selection through (1) Subjective Allocation Rule (SAR)-based allocation and (2) Minimum Tracking Error (MTE)-guided mimicking within a Bayesian Allocation Framework that integrates qualitative and quantitative beliefs into alpha-generating portfolios. Portfolio selection is modelled as view-driven, feedback-responsive rationality that reconciles normative and descriptive paradigms, with diverse investor behaviours emerging as local optima shaped by cognition, skill, and subjectivity. Empirical results show that when subjectivity aligns with predictive skill, portfolios outperform mean-variance benchmarks. This second paper focuses on the empirical validation.
This article proposes a simple primal-dual Monte Carlo algorithm for approximating the prices of American and Bermudan options. The algorithm calculates the dual (upper bound) price of an option by applying least squares linear regression to extract the Doob martingale part of the Snell envelope from a set of primal (lower bound) paths generated by a stopping time approximation estimator. This allows for straightforward and fast approximations of upper bounds on the true option price, without the need for nested simulations. The key to the algorithm is the use of orthogonal projections to approximate both the value process and the conditional expectations along each path by projecting the primal paths at each timestep onto the subspace spanned by the same set of basis functions, evaluated one timestep apart. Numerical results for a variety of option pricing problems are presented, allowing for direct comparison with other algorithms found in the literature. The results suggest wide applicability of the algorithm to practical problems in option pricing.
This research unifies active portfolio selection through (1) Subjective Allocation Rule (SAR)-based allocation and (2) Minimum Tracking Error (MTE)-guided mimicking within a Bayesian Allocation Framework that integrates qualitative and quantitative beliefs into alpha-generating portfolios. Portfolio selection is modelled as view-driven, feedback-responsive rationality that reconciles normative and descriptive paradigms, with diverse investor behaviours emerging as local optima shaped by cognition, skill, and subjectivity. Empirical results show that when subjectivity aligns with predictive skill, portfolios outperform mean-variance benchmarks. This first paper focuses on the structural formulation.
A quanto option is a type of multivariate option whose payoff is determined by the product of a standard option and a stochastic multiplier such as trading volume. In this study, we extend this concept to swing options, which allow multiple exercises within a specified period, and introduce the 'multifactor swing quanto option' to mitigate cash flow fluctuation risks driven by the product of price and volume in electricity markets. First, we model the underlying asset prices and volume indices using deterministic time trends and vector autoregressive (VAR) processes. The least-squares Monte Carlo (LSMC) method is then applied to compute option prices based on generated sample paths and estimated continuation value functions, with tensor product spline basis functions enhancing flexibility in multidimensional modeling. To assess the hedging performance of the proposed swing quanto option, we conduct numerical experiments using Japanese electricity market data, including Japan Electric Power Exchange (JEPX) spot prices and area demand. Conventional comparisons indicate that swing quanto options achieve better hedging performance than European quanto options; however, this advantage may simply reflect their higher initial cost. To examine cost-effectiveness, we adjust the holding quantity of swing quanto options to match the initial cost of European quanto options and compare their hedging performance under an equal investment constraint. Even after this adjustment, swing quanto options still provide superior loss-risk mitigation, demonstrating greater cost-effectiveness. This also suggests that the flexibility in selecting exercise timing, while inherently valuable, enables effective hedging even when its associated cost is reduced.
We study a call auction model with general demand and supply curves. Buy and sell orders arrive randomly and, on average, generate these curves. The model generalizes several existing models. While only conditional distributions of the clearing price and traded volume have been mathematically described in the literature, we derive both the exact and asymptotic unconditional distributions of these quantities. We demonstrate the rapid convergence of the asymptotic distributions to the exact ones. The model is able to reproduce fat-tailed behaviour of the clearing price. In particular, we show that the quotes (bid and ask) inherit the tail behaviour of the demand and/or supply curves, and that fat tails in the price distribution may alternatively be caused by order imbalance.
Risk capital allocation involves the decomposition of the overall portfolio risk in a credit portfolio into marginal risk contributions associated with individual obligors. The Value-at-Risk contribution (VaRC) measures how much each obligor contributes to the overall portfolio VaR. We propose two forms of simulation-analytical approach to calculate VaRC in Gaussian copula credit portfolios with correlation between probability of default (PD) and loss given default (LGD). Our method resolves the challenge of computing the expectation of the default loss of an individual obligor conditional on an event with zero probability mass. By employing ingenious analytical and simulation procedures, we recast the VaRC calculation to involve simulating the distribution function of the random portfolio loss, thereby avoiding numerical instabilities in the common kernel estimation method of computing expectations conditional on a zero-probability event. The inclusion of an analytical component in our algorithms helps reduce simulation effort when compared with the full simulation algorithms. Numerical experiments demonstrate that our proposed algorithms perform favorably well in terms of accuracy and computational efficiency, outperforming typical direct Monte Carlo simulation methods such as the iterative cross entropy method.
This paper introduces a novel approach to improving the precision and adaptability of trading signals in pairs trading. Our method derives the full conditional distribution of the hedge ratio and utilizes its quantiles as confirmation thresholds for trading signals generated within the standard cointegration framework. We apply this approach to 41 selected asset pairs across the U.S. and Brazilian markets, evaluating its effectiveness through empirical analysis. Our findings indicate that the proposed Bayesian hierarchical model improves trading performance and risk management in the majority of analyzed pairs, with particularly strong results in dual-class share configurations. The method achieves these improvements while reducing trading frequency by approximately 24%, which implies less exposure to transaction costs in practical implementations. By adopting a distribution-based framework, our approach not only enables more timely and adaptive trading signals but also enhances pair selection by effectively filtering out false positives in cointegration tests, as demonstrated through simulations.
A green bond is a widely utilised financial instrument designed for the purpose of funding environmentally friendly projects. The green bond's positive environmental effects are documented by previous investigations that largely rely on the Differences-in-Differences method to assess its overall impacts. In contrast, this paper employs a Controlled Interrupted Time Series model to investigate the influence of corporate green bonds on the environmental performance of issuers at the individual level. We perform two sequential experiments. Firstly, we probe into the factors that could influence the issuance of green bonds to produce a statistically significant effect on environmental performance. Secondly, we examine the interrelations between company characteristics, issuer characteristics, and the magnitude of the effects released by green bonds. For the first and second experiments, we implement random-forest-based and generalised-additive-based modelling approaches, respectively. These approaches allow us to explore non-linear relationships. We examine the various factors that are deemed to contribute to the efficacy of the green bonds. The effects on companies' environmental performance are assessed after issuing the green bonds in comparison to conventional bond issuers. Our findings reinforce the existing literature in which the environmental performance of most issuers improves following the issuance of green bonds. Whilst both bond and company characteristics influence the impact of green bonds, it is the company characteristics that play a more pivotal role. We show that the issuance of green bonds positively affects companies' environmental performance. Thus, policymakers must develop and implement policies that promote and support green financing to benefit the environment. It must be kept in mind that the characteristics of issuers are an important consideration alongside with the issuance of green bonds. So, company-wide strategies are necessary in addition to financial innovation to improve environmental performance.
We propose a new model for the simulation of both the implied volatility surfaces and the underlying asset price. In the spirit of [Guyon, J. and Lekeufack, J., Volatility is (mostly) path-dependent. Quant. Finance, 2023, 23(9), 1221-1258] who are interested in the dependence of volatility indices (e.g. the VIX) on the paths of the associated equity indices (e.g. the S&P 500), we first study how vanilla options implied volatility can be predicted using the past trajectory of the underlying asset price. Our empirical study reveals that a large part of the movements in the at-the-money-forward implied volatility for times-to-maturity of up to two years can be explained using the past returns and their squares. Moreover, we show that this feedback effect gets weaker when the time-to-maturity increases. Building on this new stylized fact, we fit to historical data a parsimonious version of the SSVI parameterization [Gatheral, J. and Jacquier, A., Arbitrage-free SVI volatility surfaces. Quant. Finance, 2014, 14(1), 59-71] of the implied volatility surface relying on only four parameters and show that the two parameters ruling the at-the-money-forward implied volatility as a function of the time-to-maturity exhibit a path-dependent behavior with respect to the underlying asset price. Finally, we propose a model for the joint dynamics of the implied volatility surface and the underlying asset price. The latter is modeled using a variant of the path-dependent volatility model of Guyon and Lekeufack and the former is obtained by adding a feedback effect of the underlying asset price onto the two parameters ruling the at-the-money-forward implied volatility in the parsimonious SSVI parameterization and by specifying Ornstein-Uhlenbeck processes for the residuals of these two parameters and Jacobi processes for the two other parameters. Thanks to this model, we are able to simulate highly realistic paths of implied volatility surfaces that are free from static arbitrage.
