Exploring non-analytical affine jump-diffusion models for path-dependent interest rate derivativesSilva, Allan Jonathan da; Baczynski, Jack
doi: 10.1007/s10287-024-00514-1pmid: N/A
This study introduces an adapted Fourier-cosine series (COS) method that focuses on numerically solving characteristic functions linked to interest rate processes. The adaptation extends to encompass models within the affine jump-diffusion niche to assess the impact of different probability distributions on path-dependent option prices, with emphasis on the influence of stochastic volatility models on skewness and kurtosis. This study leverages the COS method, modified to numerically address characteristic functions linked to interest rate processes, to calculate the price of path-dependent derivatives. It investigates diverse models within the affine jump-diffusion framework, encompassing elements such as stochastic volatility, jumps, and correlated Brownian motion. An innovative approach is introduced, wherein the characteristic function is generated from the integral of the interest rate, as opposed to the interest rate itself. The research generated notable findings, highlighting the adaptability and effectiveness of the modified COS method. This significantly expands the range of applicable models for those with analytically unsolved characteristic functions. Remarkably, even in cases with analytically solvable characteristic functions, an unexpectedly low number of terms can accurately priced options. This study introduces original contributions by adapting the COS method to address the characteristic functions associated with interest rate processes. The distinct approach of generating the characteristic function from the interest rate integral, rather than the interest rate itself, is a substantial original contribution. The application of Kibble’s bivariate gamma probability distribution to correlate interest rates and volatility jump sizes further enhances the originality of this research.
A constrained swarm optimization algorithm for large-scale long-run investments using Sharpe ratio-based performance measuresKaucic, Massimiliano; Piccotto, Filippo; Sbaiz, Gabriele
doi: 10.1007/s10287-023-00483-xpmid: N/A
We study large-scale portfolio optimization problems in which the aim is to maximize a multi-moment performance measure extending the Sharpe ratio. More specifically, we consider the adjusted for skewness Sharpe ratio, which incorporates the third moment of the returns distribution, and the adjusted for skewness and kurtosis Sharpe ratio, which exploits in addition the fourth moment. Further, we account for two types of real-world trading constraints. On the one hand, we impose stock market restrictions through cardinality, buy-in thresholds, and budget constraints. On the other hand, a turnover threshold restricts the total allowed amount of trades in the rebalancing phases. To deal with these asset allocation models, we embed a novel hybrid constraint-handling procedure into an improved dynamic level-based learning swarm optimizer. A repair operator maps candidate solutions onto the set characterized by the first type of constraints. Then, an adaptive ℓ1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell _1$$\end{document}-exact penalty function manages turnover violations. The focus of the paper is to highlight the importance of including higher-order moments in the performance measures for long-run investments, in particular when the market is turbulent. We carry out empirical tests on two worldwide sets of assets to illustrate the scalability and effectiveness of the proposed strategies, and to evaluate the performance of our investments compared to the strategy maximizing the Sharpe ratio.
A refinement of the gravity model for competitive facility locationDrezner, Zvi; Zerom, Dawit
doi: 10.1007/s10287-023-00484-wpmid: N/A
Most competitive location models assume that as the distance increases, the patronage of a facility declines at the same rate regardless of the facility attractiveness. We observed that the rate at which patronage declines is slower for more attractive facilities. Customers are willing to drive long distances to patronize an attractive facility. Less attractive facilities hardly attract customers from long distances. We propose to modify the effect of attractiveness on the appeal of the facility to customers. Many methods for estimating the market share captured by a facility can be modified to incorporate such property. We implemented the new modification on the gravity model and tested it on a real data set of shopping malls in Orange County, California. The approach was statistically validated and is computationally straightforward to implement with existing software such as R. Further, new facility location decisions are expected to be more accurate due to the improved market share estimates by the proposed model.
Evaluation of strategy portfoliosWang, Anlan; Kresta, Aleš; Tichý, Tomáš
doi: 10.1007/s10287-023-00497-5pmid: N/A
People usually create a portfolio in order to diversify the risk coming from individual investments. To get a high yield with a good level of diversification, investors usually seek professional advice from portfolio managers. However, the true performance of an optimized portfolio usually depends on the correctness of the estimates of the distribution of future returns, which is often a matter of luck rather than skill. Thus, the optimization models may not be better than randomly selected portfolios. Our aim is to find how the so-called strategy portfolios, i.e., portfolios obtained by some decision optimized for a long-run horizon, perform compared to a benchmark, namely, a random investment, under specific market conditions. For this purpose, we evaluate several portfolio strategies over two periods of crisis: the subprime mortgage crisis and the Covid-19 pandemic, as well as run a moving window analysis over a longer horizon. In each case, the results are compared with the performance of random-weight portfolios. We find that if the strategy is minimization, the portfolios perform well; however, for the maximization of the objectives, the results are rather mixed.
Distributional robustness, stochastic divergences, and the quadrangle of riskRockafellar, R. Tyrrell
doi: 10.1007/s10287-024-00516-zpmid: N/A
In the distributional robustness approach to optimization under uncertainty, ambiguity about which probability distribution to use is addressed by turning to the worst that might occur with respect to a specified set of alternative probability distributions. Such sets are often taken to be neighborhoods of some nominal distribution with respect to a stochastic divergence like that of Kullback–Leibler or Wasserstein. Here that approach is coordinated with the fundamental quadrangle of risk with its quantifications not only of risk, but also regret, deviation and error, along with the functionals that dualize them. Stochastic divergences are introduced axiomatically and shown to constitute the duals of risk measures in a special class. Rules are uncovered for how regret measures for those risk measures can be obtained by appropriate extensions of the divergence functional. This reveals clearly the pattern in which the robustness functionals coming from divergence neighborhoods can be provided with other formulas featuring minimization instead of maximization, which is beneficial for optimization schemes. To get everything to fit, however the aversity properties of risk and the rest that, until now, have been imposed in the quadrangle of relationships must be relaxed. A suitable substitute, called subaversity, is found that works while only differing from aversity for functionals that are not positively homogeneous.
A multiobjective optimization approach for threshold determination in extreme value analysis for financial time seriesChu, Carlin C. F.; Li, Simon S. W.
doi: 10.1007/s10287-023-00488-6pmid: N/A
The literature on the extreme value theory threshold optimization problem for multiple time series analysis does not consider determining a single optimal tail probability for all marginal distributions. With multiple tail probabilities, their discrepancy results in a differing number of exceedances, which may favour a particular marginal series. In this study, we propose a single optimal tail probability by integrating trade-offs among multiple time series within an MOO framework. Mathematically, our approach links the peaks-over-threshold technique and goal programming technique by developing a set of regression functions, which represent continuous paths of possible tail areas for multiple time series, and we formulate them at the desired levels within a multiobjective optimization framework. The optimal solution is found as the minimum Chebyshev variant weighted value. Our approach advances the development of the peaks-over-threshold method by considering the characteristics of a group of time series collectively instead of independently. The proposed optimal tail probability can be considered an optimal reference point for practical risk investment portfolio analysis that employs an identical tail size across multiple time series data. The daily log returns of four U.S. stock market indices, namely, S&P 500, NASDAQ Composite, NYSE Composite, and Russell 2000, from 1 July 1992 to 30 June 2022 are studied empirically.
Optimal investment by large consumers in an electricity market with generator market powerVerma, Pranjal Pragya; Hesamzadeh, Mohammad Reza; Rebennack, Steffen; Bunn, Derek; Swarup, K. Shanti; Srinivasan, Dipti
doi: 10.1007/s10287-024-00515-0pmid: N/A
The investment decisions of energy-intensive consumers can alter the balance of supply and demand in an electricity market. In particular, they can increase the market power of incumbent generators such that prices may increase as a consequence of their investments. Whilst it is therefore intuitive that such investors will wish to consider their effects on the market, it is a challenging problem analytically and one that has been under-researched. In general, the problem can be manifest in any supply chain where demand-side investments influence endogenous price formation in the intermediate product markets. Theoretically, we show how the presence of producer market power decreases demand-side investments and then, computationally we formulate a quad-level program to model the operational implications for a demand-side investor in more detail. With an innovative reduction in complexity to a bilevel model, an efficient solution algorithm for the optimal investment by a demand-side investor is facilitated. We demonstrate computability on a small scale electricity system and the results confirm the theory.
The Value of Shared Information for allocation of drivers in ride-hailing: a proof-of-concept studyLiberona, Gianfranco; Salas, David; von Niederhäusern, Léonard
doi: 10.1007/s10287-023-00487-7pmid: N/A
For drivers in ride-hailing companies, allocation within the city is paramount to get matched with rides. This decision depends on many factors, where some of them (such as demand and allocation of others) are unknown for the drivers, but are available for the company. In this work, we investigate whether it is beneficial or not for the ride-hailing company to share this information with their drivers. To do so, we study the problem through the lens of Stackelberg games, and we propose a new indicator called the Expected Value of Shared Information. We present a simplified model to conduct a proof-of-concept study: we provide explicit single-level reformulations of the bilevel programming problems derived from the model, and perform several simulations with randomly generated data. Our preliminary results suggest that sharing information could be beneficial and deserves to be further studied.