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This study aims to investigate the co-volatility patterns between cryptocurrencies and conventional asset classes across global markets, encompassing 26 global indices ranging from equities, commodities, real estate, currencies and bonds.

It used a multivariate factor stochastic volatility model to capture the dynamic changes in covariance and volatility correlation, thus offering empirical insights into the co-volatility dynamics. Unlike conventional research on price or return transmission, this study directly models the time-varying covariance and volatility correlation.

The study uncovers pronounced co-volatility movements between cryptocurrencies and specific indices such as GSCI Energy, GSCI Commodity, Dow Jones 1 month forward and U.S. 10-year TIPS. Notably, these movements surpass those observed with precious metals, industrial metals and global equity indices across various regions. Interestingly, except for Japan, equity indices in the USA, Canada, Australia, France, Germany, India and China exhibit a co-volatility movement. These findings challenge the existing literature on cryptocurrencies and provide intriguing evidence regarding their co-volatility dynamics.

This study significantly contributes to applying asset pricing models in cryptocurrency markets by explicitly addressing price and volatility dynamics aspects. Using the stochastic volatility model, the research adding methodological contribution effectively captures cryptocurrency volatility's inherent fluctuations and time-varying nature. While previous literature has primarily focused on bitcoin and a few other cryptocurrencies, this study examines the stochastic volatility properties of a wide range of cryptocurrency indices. Furthermore, the study expands its scope by examining global asset markets, allowing for a comprehensive analysis considering the broader context in which cryptocurrencies operate. It bridges the gap between traditional asset pricing models and the unique characteristics of cryptocurrencies.

This study aims to investigate how the gold return and its volatility respond to the COVID-19 pandemic.

Stochastic volatility (SV) models are conducted to examine the response of gold to the number of new confirmed cases and deaths.

The results indicate that an increase in the change rate of the number of COVID-19 infections or fatalities leads to heightened volatility in gold prices. Moreover, the results suggest that gold volatility is more sensitive to the impacts from high-income countries than by those from middle- and low-income countries. In addition, the asymmetric effect is detected in the gold price volatility, which is contrary to the typical asymmetric effect seen in the stock market. Furthermore, the results remain robust after accounting for the US dollar and the volatility index in relation to gold returns.

This study presents whether and to what extent gold is incorporated in the information related to the number of COVID-19 cases and deaths.

This study augments the existing literature by exploring how the number of COVID-19 infections and fatalities influences gold prices. In addition, it examines the day-of-the-week and asymmetric effects that may contribute to the volatility of gold prices. To the best of the authors’ knowledge, the evolution of gold has not yet been investigated using SV models.

Motivated by empirical features that characterize cryptocurrency volatility data, the authors develop a forecasting strategy that can account for both model uncertainty and heteroskedasticity of unknown form. The theoretical investigation establishes the asymptotic optimality of the proposed heteroskedastic model averaging heterogeneous autoregressive (H-MAHAR) estimator under mild conditions. The authors additionally examine the convergence rate of the estimated weights of the proposed H-MAHAR estimator. This analysis sheds new light on the asymptotic properties of the least squares model averaging estimator under alternative complicated data generating processes (DGPs). To examine the performance of the H-MAHAR estimator, the authors conduct an out-of-sample forecasting application involving 22 different cryptocurrency assets. The results emphasize the importance of accounting for both model uncertainty and heteroskedasticity in practice.

The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.

In this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.

As per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.

Based on the conclusion presented in this paper, there are several potential implications for research, practice and society.

This study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.

The accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.

It is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.

One of the crucial issues in the contemporary finance is the prediction of the volatility of financial assets. In this paper, the authors are interested in modelling the stochastic volatility of the MAD/EURO and MAD/USD exchange rates.

For this purpose, the authors have adopted Bayesian approach based on the MCMC (Monte Carlo Markov Chain) algorithm which permits to reproduce the main stylized empirical facts of the assets studied. The data used in this study are the daily historical series of MAD/EURO and MAD/USD exchange rates covering the period from February 2, 2000, to March 3, 2017, which represent 4,456 observations.

By the aid of this approach, the authors were able to estimate all the random parameters of the stochastic volatility model which permit the prediction of the future exchange rates. The authors also have simulated the histograms, the posterior densities as well as the cumulative averages of the model parameters. The predictive efficiency of the stochastic volatility model for Morocco is capable to facilitate the management of the exchange rate in more flexible exchange regime to ensure better targeting of monetary and exchange policies.

To the best of the authors’ knowledge, the novelty of the paper lies in the production of a tool for predicting the evolution of the Moroccan exchange rate and also the design of a tool for the monetary authorities who are today in a proactive conception of management of the rate of exchange. Cyclical policies such as monetary policy and exchange rate policy will introduce this type of modelling into the decision-making process to achieve a better stabilization of the macroeconomic and financial framework.

The aim of this study was to determine if there are asymmetries in the pass-through of West Texas Intermediate (WTI) crude oil prices to its derivatives (diesel and gasoline) in the Brazilian market.

Initially, the future WTI oil price series was analyzed using the self-exciting threshold autoregressive (SETAR) and logistic smooth transition autoregressive (LSTAR) non-linear models. Subsequently, the threshold autoregressive error-correction model (TAR-ECM) and Markov-switching model were used.

The findings indicated high prices throughout 2008 due to the subprime crisis. The findings indicated high prices throughout 2008 due to the subprime crisis. The results indicated that there is long-term pass-through of oil prices in both methods, suggesting an equilibrium adjustment in the prices of diesel and gasoline in the analyzed period. Regarding the short term, the variations in contemporary crude oil prices have positive effects on the variations in fuel prices. Lastly, this behavior can partly be explained by the internal price management structure adopted during almost all of the analyzed period.

This paper contributes to the literature at some points. The first contribution is the modeling of the oil price series through non-linear models, further enriching the literature on the recent behavior of this time series. The second is the simultaneous use of the TAR-ECM and Markov-switching model to capture possible short- and long-term asymmetries in the pass-through of prices, as few studies have applied these methods to the future price of oil. The third and main contribution is the investigation of whether there are asymmetries in the transfer of oil prices to the price of derivatives in Brazil. So far, no work has investigated this issue, which is very relevant to the country.

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

The current paper proposes a prediction model for a cryptocurrency that encompasses three properties observed in the markets for cryptocurrencies—namely high volatility, illiquidity, and regime shifts. As far as the authors’ knowledge extends, this paper is the first attempt to introduce a stochastic differential equation (SDE) for pricing cryptocurrencies while explicitly integrating the mentioned three significant stylized facts.

Cryptocurrencies are increasingly utilized by investors and financial institutions worldwide as an alternative means of exchange. To the authors’ best knowledge, there is no SDE in the literature that can be used for representing and evaluating the data-generating process for the price of a cryptocurrency.

By using Ito calculus, the authors provide a solution for the suggested SDE along with mathematical proof. Numerical simulations are performed and compared to the real data, which seems to capture the dynamics of the price path of two main cryptocurrencies in the real markets.

The stochastic differential model that is introduced and solved in this article is expected to be useful for the pricing of cryptocurrencies in situations of high volatility combined with structural changes and illiquidity. These attributes are apparent in the real markets for cryptocurrencies; therefore, accounting explicitly for these underlying characteristics is a necessary condition for accurate evaluation of cryptocurrencies.

We aim to clarify the effect of economic uncertainty on Chinese stock market fluctuations. We extend the understanding of the asymmetric connectedness between economic uncertainty and stock market risk and provide different characteristics of spillovers from economic uncertainty to both upside and downside risk. Furthermore, we aim to provide the different impact patterns of stock market volatility following several exogenous shocks.

We construct a Chinese economic uncertainty index using a Factor-Augmented Variable Auto-Regressive Stochastic Volatility (FAVAR-SV) model for high-dimensional data. We then examine the asymmetric impact of realized volatility and economic uncertainty on the long-term volatility components of the stock market through the asymmetric Generalized Autoregressive Conditional Heteroskedasticity-Mixed Data Sampling (GARCH-MIDAS) model.

Negative news, including negative return-related volatility and higher economic uncertainty, has a greater impact on the long-term volatility components than positive news. During the financial crisis of 2008, economic uncertainty and realized volatility had a significant impact on long-term volatility components but did not constitute long-term volatility components during the 2015 A-share stock market crash and the 2020 COVID-19 pandemic. The two-factor asymmetric GARCH-MIDAS model outperformed the other two models in terms of explanatory power, fitting ability and out-of-sample forecasting ability for the long-term volatility component.

Many GARCH series models can also combine the GARCH series model with the MIDAS method, including but not limited to Exponential GARCH (EGARCH) and Threshold GARCH (TGARCH). These diverse models may exhibit distinct reactions to economic uncertainty. Consequently, further research should be undertaken to juxtapose alternative models for assessing the stock market response.

Our conclusions have important implications for stakeholders, including policymakers, market regulators and investors, to promote market stability. Understanding the asymmetric shock arising from economic uncertainty on volatility enables market participants to assess the potential repercussions of negative news, engage in timely and effective volatility prediction, implement risk management strategies and offer a reference for financial regulators to preemptively address and mitigate systemic financial risks.

First, in the face of domestic and international uncertainties and challenges, policymakers must increase communication with the market and improve policy transparency to effectively guide market expectations. Second, stock market authorities should improve the basic regulatory system of the capital market and optimize investor structure. Third, investors should gradually shift to long-term value investment concepts and jointly promote market stability.

This study offers a novel perspective on incorporating a Chinese economic uncertainty index constructed by a high-dimensional FAVAR-SV model into the asymmetric GARCH-MIDAS model.

The authors consider the mutual benefits of the ceding company and reinsurance company in the design of reinsurance contracts. Two objective functions to maximize social expected utilities are established, which are to maximize the sum of the expected utilities of both the ceding company and reinsurance company, and to maximize their products. The first objective function, additive, emphasizes the total gains of both parties, while the second, multiplicative, accounts for the degree of substitution of gains of one party through the loss of the other party. The optimal price and retention of reinsurance are found by a grid search method, and numerical analysis is conducted. The results indicate that the optimal solutions for two objective functions are quite different. However, optimal solutions are sensitive to the change of the means and volatilities of the claim loss for both objective functions. The results are potentially valuable to insurance regulators and government entities acting as reinsurers of last resort.

In this paper, the authors apply relatively simple, but in the view significant, methods and models to discuss the optimization of excess loss reinsurance strategy. The authors only consider the influence of loss distribution on optimal retention and reinsurance price but neglect the investment factor. The authors also consider the benefits of both ceding company and reinsurance company to determine optimal premium and retention of reinsurance jointly based on maximizing social utility: the sum (or the product) of expected utilities of reinsurance company and ceding company. The authors solve for optimal solutions numerically, applying simulation.

This paper establishes two optimization models of excess-of-loss reinsurance contract against catastrophic losses to determine optimal premium and retention. One model considers the sum of the expected utilities of a ceding company and a reinsurance company's expected utility; another considers the product of them. With an example, the authors find the optimal solutions of premium and retention of excess loss reinsurance. Finally, the authors carry out the sensitivity analysis. The results show that increasing the means and the volatilities of claim loss will increase the optimal retention and premium. For objective function I, increasing the coefficients of risk aversion of or reducing the coefficients of risk aversion of will make the optimal retention reduced but the optimal premium increased, and vice versa. However, for objective function 2, the change of coefficient of risk aversion has no effect on optimal solutions.

Utility of the two partners: The ceding company and the reinsurance company, may have different weights and different significance. The authors have not studied their relative significance. The simulation approach in numerical methods limits us to the probability distributions and stochastic processes the authors use, based on, generally speaking, lognormal models of rates of return. This may need to be generalized to other returns, including possible models of shocks through jump processes.

In the recent two decades, reinsurance companies have played a great role in hedging mega-catastrophic losses. For example, reinsurance companies (and special loss sharing arrangements) paid as much as two-thirds of the insured losses for the September 11, 2001 tragedy. Furthermore, large catastrophic events have increased the role of governments and regulators as reinsurers of last resort. The authors hope that the authors provide guidance for possible balancing of the needs of two counterparties to reinsurance contracts.

Nearly all governments around the world are engaged in regulation of insurance and reinsurance, and some are reinsurers themselves. The authors provide guidance for them in these activities.

The authors believe this paper to be a completely new and original contribution in the area, by providing models for balancing the utility to the ceding insurance company and the reinsurance company.

我們探討分出公司和再保險公司在再保險合約的設計上、如何能達至互利互惠。研究確立了兩個目標函數，分別為把分出公司和再保險公司兩者之預期效用的總和最大化，以及把它們的產品最佳化。第一個目標函數是加法的，強調兩個參與方的總增益;而第二個目標函數則是乘法的，這個目標函數，闡釋參與方因另一方虧損而有所收益之取代度。再保險的最佳價格和自留額是利用網格搜索法找出的，數值分析也予以進行。研究結果顯示，兩個目標函數的最佳解決方案甚為不同。唯最佳解決方案會對就這兩個目標函數而言的追討損失的波動、以及其平均值之改變產生敏感反應。研究結果將會見其價值於作為在萬不得已的時候的再保險人的保險業規管機構和政府實體。

在這學術論文裡，我們採用了相對簡單、但我們認為是重要的方法和模型，來探討超額賠款再保險策略的優化課題。我們只考慮虧損分佈對最佳自留額和再保險價格的影響，而不去檢視投資因素。我們亦考慮對分出公司和再保險公司兩者的利益，來釐定最佳保費和再保險的自留額，而這兩者則共同建基於把社會效益最大化之上：再保險公司和分出公司的預期效益的總和 (或其積數) 。 我們採用類比模仿方法、來解決尋求在數字上最佳解決方案的問題。

本研究建立了就應對嚴重虧損而設的兩個超額賠款再保險合約的優化模型，來釐定最佳的保費和自留額。其中一個模型考慮了分出公司和再保險公司兩者各自的預期效益的總和。另外的一個模型則考慮了兩者的預期效益的積數。透過例子，我們找到了保費和超額虧損再保險自留額的最佳解決方案。最後，我們進行了敏感度分析。研究結果顯示、若增加追討損失的平均值和波動，則最佳自留額和保費也會隨之而增加。就第一個目標函數而言，若增加風險規避係數、或減少這個係數，則最佳自留額會隨之而減少，但最佳保費卻會隨之而增加，反之亦然。唯就第二個目標函數而言，風險規避係數的改變，對最佳解決方案是沒有影響的。

• – 有關的兩個夥伴之效用性：分出公司和再保險公司或有不同的份量和重要性。我們沒有探討兩者的相對重要性。

• – 我們以數值方法為核心的類比模仿研究法、使我們局限於機率分配和一般而言建基於投資報酬率對數常態模型之隨機過程的使用。我們或許需要調節研究法。以能概括其它回報收益，包括透過跳躍過程而可能達至之沖擊模型。

– 有關的兩個夥伴之效用性：分出公司和再保險公司或有不同的份量和重要性。我們沒有探討兩者的相對重要性。

– 我們以數值方法為核心的類比模仿研究法、使我們局限於機率分配和一般而言建基於投資報酬率對數常態模型之隨機過程的使用。我們或許需要調節研究法。以能概括其它回報收益，包括透過跳躍過程而可能達至之沖擊模型。

在過去20年裡，再保險公司在控制極嚴重災難性的損失上曾扮演重要的角色。例如、再保險公司 (以及特殊的損失分擔安排) 為了2001年9月11日的災難事件而支付多至保險損失的三分之二的費用。而且，重大的災難性事件使政府及作為最後出路再保險人的調控者得扮演更重要的角色。我們希望研究結果能為再保險合約兩對手提供指導，以平衡雙方的需要。

全球差不多每個政府都參與保險和再保險的管理工作，有部份更加本身就是再保險人。研究結果為他們的管理工作提供了指導。

我們相信本學術論文、提供了平衡分出保險公司和再保險公司效用性的模型，就此而言，本論文在相關的領域上作出了全新和獨創性的貢獻。