Search Results (69)

In this paper, we present a fast and accurate numerical approach applied to specific American-style derivatives, namely American power call and put options, whose main feature is that the underlying asset is raised to a power. The study is set in the Black–Scholes framework, and we consider continuously paying dividends assets and arbitrary positive values for the power. It is important to note that although a log-normal process raised to a power is again log-normal, the resulting change in variables may lead to a negative dividend rate, and this case remains largely understudied in the literature. We derive closed-form formulas for the perpetual options’ optimal boundaries and for the fair prices. For finite maturities, we approximate the optimal boundary using some first-hitting properties of the Brownian motion. As a consequence, we obtain the option price quickly and with relatively high accuracy—the error is at the third decimal position. We further provide a comprehensive analysis of the impact of the parameters on the options’ value, and discuss ordinary European and American capped options. Various numerical examples are provided. Full article

This paper presents a new model of the term structure of interest rates that is based on the continuous Ho–Lee one. In this model, we suggest that the drift and volatility coefficients depend additionally on a generalized inverse Gaussian (GIG) distribution. Analytical expressions for the bond price and its moments are found in the new GIG continuous Ho–Lee model. Also, we compute in this model the prices of European call and put options written on bond. The obtained formulas are determined by the values of the Humbert confluent hypergeometric function of two variables. A numerical experiment shows that the third and fourth moments of the bond prices differentiate substantially in the continuous Ho–Lee and GIG continuous Ho–Lee models. Full article

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. Full article

The Dupire formula is a very useful tool for pricing financial derivatives. This paper is dedicated to deriving the aforementioned formula for the European call option in the space of distributions by applying a mathematically rigorous approach developed in our previous paper concerning the case of the Margrabe option. We assume that the underlying asset is described by the Merton jump-diffusion model. Using this stochastic process allows us to take into account jumps in the price of the considered asset. Moreover, we assume that the instantaneous interest rate follows the Merton model (1973). Therefore, in contrast to the models combining a constant interest rate and a continuous underlying asset price process, frequently observed in the literature, applying both stochastic processes could accurately reflect financial market behaviour. Moreover, we illustrate the possibility of using the minimal entropy martingale measure as the risk-neutral measure in our approach. Full article

In this article, I argue that Eurafricans’ invisibility in Zambia’s national census, history, and social framework is an echo of colonial whiteness stemming from the destructive legacy of illegitimacy perpetuated by British officials in Northern Rhodesia (present-day Zambia) during the colonial era (1924–64), which continues to the present day. This is evidenced by the absence of Eurafricans in the Zambia national censuses. This contribution calls for the British government to apologise to the Eurafrican community for the legacy of illegitimacy and intergenerational racial trauma it bestowed on the community. Zambia’s tribal ‘ethnic’ and ‘linguistics’ census classification options prevent a comprehensive understanding of Zambia’s multi-racial history and the development of a hybrid space that embraces a ‘mixed-race’ Eurafrican (of European and African heritage) Zambian identity. Through an autoethnographic account of my Eurafrican uncle Aaron Milner, I reflect on Zambian Eurafricans’ historical racial positioning as ‘inferior interlopers’, which has contributed to their obscurity in Zambia’s national history and census. However, my reflection goes beyond Milner’s story in Zambia. It is my entryway to highlight how race and colonial whiteness interconnected and underpinned racial ideology in the wider British Empire, and to draw attention to its echoes in various contemporary sociopolitical contexts, including census terminology in Australia and Zambia and Western nations’ anti-Black immigration policies. Full article

Religion can often be very influential in the political system and political actors frequently take advantage of the leverage that it provides. In the Zambian case, Christianity in particular plays a crucial role in politics and policymaking, dating from the pre- to post-colonial era. Around 1880, Zambia, then Northern Rhodesia, became a British colony and, at the same time, Christianity was introduced within the context of the European culture. Later, 27 years after independence, Zambia was declared a Christian nation, and all Zambian political leaders have embraced Christianity as the nation’s identity. Thus, Christianity plays a critical function in Zambia’s political sphere. The main aim of this paper is to critically examine how Christianity seeks to direct the political agenda in Zambia’s national politics. It demonstrates the interplay between church and state relations linked to how the state seeks to govern the nation in a Godly manner and the implications on public policymaking in Zambia. This paper explores a multifaceted analysis of the existing literature and the ideas around the politics of the state and religion. It argues that (i) Christianity in Zambia is often used as a political weapon to gain political mileage and (ii) Christianity as a religion has been traditionalised in Zambia. It serves as a “national moral campus”, which compromises the nation’s position as a so-called “democratic” state and suppresses individual freedoms. Thus, it corrupts the very nature of fundamental practices of the religion itself, as it has simply blossomed into more of a norm than a religion. Understanding these dynamics is very crucial, especially in the context of how religion is perceived, experienced and exercised in the political arena to circumvent limited policy options for broader problem solving. Full article

This paper addresses the valuation of European options, which involves the complex and unpredictable dynamics of fractal market fluctuations. These are modeled using the $\alpha$-order time-fractional Black–Scholes equation, where the Caputo fractional derivative is applied with the parameter $\alpha$ ranging from 0 to 1. We introduce a novel, high-order numerical scheme specifically crafted to efficiently tackle the time-fractional Black–Scholes equation. The spatial discretization is handled by a tailored finite point scheme that leverages exponential basis functions, complemented by an L1-discretization technique for temporal progression. We have conducted a thorough investigation into the stability and convergence of our approach, confirming its unconditional stability and fourth-order spatial accuracy, along with $(2-\alpha )$-order temporal accuracy. To substantiate our theoretical results and showcase the precision of our method, we present numerical examples that include solutions with known exact values. We then apply our methodology to price three types of European options within the framework of the time-fractional Black–Scholes model: (i) a European double barrier knock-out call option; (ii) a standard European call option; and (iii) a European put option. These case studies not only enhance our comprehension of the fractional derivative’s order on option pricing but also stimulate discussion on how different model parameters affect option values within the fractional framework. Full article

In this paper, the use of artificial neural networks (ANNs) is proposed to approximate the option price sensitivities of Johannesburg Stock Exchange (JSE) Top 40 European call options in a classical and a modern multi-curve framework. The ANNs were trained on artificially generated option price data given the illiquid nature of the South African market, and the out-of-sample performance of the optimized ANNs was evaluated using an implied volatility surface constructed from published volatility skews. The results from this paper show that ANNs trained on artificially generated input data are able to accurately approximate the explicit solutions to the respective option price sensitivities of both a classical and a modern multi-curve framework in a real-world out-of-sample application to the South African market. Full article

This article traces the emergence of what is nowadays called “postsecular” religion from German-Jewish philosophy of the 1920s and 1930s. The three different cases of Franz Rosenzweig, Alexander Altmann, and Leo Strauss impel us to pay particular attention to a few recurring argumentative and rhetorical strategies. The emergence of postsecularism marks a shift in the epistemic foundations of Jewish religious thought, which had long been under pressure from secular European thought. Beginning with Rosenzweig, Jewish philosophy used secular categories of European philosophy to facilitate a return to the foundations of Judaism, eventually turning against what it sees as the epistemic weaknesses of secularism itself. This article traces the new phenomenon to Rosenzweig’s evolving view of secularism, especially to his ridicule of Siegfried Kracauer’s secular messianism, before examining a few key arguments in his book The Star of Redemption (1921). A brief discussion of Alexander Altmann’s writings of the early 1930s provides that even modern Orthodox Jewish thought, which had never been “secular”, used postsecular categories and arguments to make the philosophical case for orthodoxy. Leo Strauss’s introduction to his Philosophy and Law (1935) provides a far more elaborated form of Rosenzweig’s argument. As this article seeks to show, postsecular Jewish thought comes with a slight twist of epistemic relativism, particularly when it comes to the juxtaposition of the Biblical and scientific “world-views”. But here it merely draws the full consequences of modern science, beating scientism with its own weapons. Furthermore, religious thought in the 20th century had no other option than to rebuild itself on postsecular grounds. Full article

We develop a binary tree pricing model with underlying asset price dynamics following Itô–McKean skew Brownian motion. Our work was motivated by the Corns–Satchell, continuous-time, option pricing model. However, the Corns–Satchell market model is incomplete, while 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 empirical applications of our model to the valuation of European put and call options on exchange-traded funds tracking the S&P Global 1200 index. Full article

The last ten years have seen the development and publication of numerous national and international guidelines devoted to the diagnosis and treatment of insomnia. These include guidelines by the American College of Physicians (ACP), the American Academy of Sleep Medicine (AASM), the British Sleep Society (BSS), the German Sleep Society (GSS), and the European Sleep Research Society (ESRS). Though coming from very diverse authors and backgrounds, these guidelines by and large agree concerning the therapeutic recommendations: cognitive behavioral treatment of insomnia (CBT-I), a multicomponent psychotherapeutic intervention, is unequivocally recommended as a first-line treatment. In this report, we will focus on the most recent guideline update from the ESRS, which was published in November 2023. After suggesting a careful diagnostic procedure, CBT-I, both applied face to face (F2F) or digitally (dCBT-I), is again recommended as a first-line treatment based on the available evidence. Hypnotic medications like benzodiazepines (BZ), benzodiazepine receptor agonists (BZRA), sedating antidepressants, and others are approved for short-term-treatment of up to four weeks. Orexin receptor antagonists (i.e., daridorexant) and prolonged release melatonin are considered as options for longer-term treatment when carefully considering the advantages and disadvantages. Both light therapy and exercise regimens were viewed as promising; however, they still lack convincing evidence for the time being. Given the fact that not every patient responds satisfactorily or even remits following CBT-I or other treatment options, the research agenda calls for the development and evaluation of new therapeutic avenues and combination therapies. Full article

We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes. Full article

In this paper, the approximate stationarity of the second-order moment increments of the sub-fractional Brownian motion is given. Based on this, the pricing model for European options under the sub-fractional Brownian regime in discrete time is established. Pricing formulas for European options are given under the delta and mixed hedging strategies, respectively. Furthermore, European call option pricing under delta hedging is shown to be larger than under mixed hedging. The hedging error ratio of mixed hedging is shown to be smaller than that of delta hedging via numerical experiments. Full article

This study investigates the pricing formula for European options when the underlying asset follows a fuzzy mixed weighted fractional Brownian motion within a jump environment. We construct a pricing model for European options driven by fuzzy mixed weighted fractional Brownian motion with jumps. By converting the partial differential equation (PDE) into a Cauchy problem, we derive explicit solutions for both European call options and European put options. The figures and tables demonstrating the effectiveness of the results highlight the suitability of the fuzzy mixed weighted fractional Brownian motion with jump model for option pricing. Full article

The pace of the implementation of renewable electricity storage in Europe is disappointingly slow. Several factors influence this and there is a need to speed up the rate and increase the volumes in order to promote a 100% transition to renewable energy resources, expand the practice of using renewable energy, and contribute to the improvement of the quality of life of consumers. An important factor is significantly reducing impact on the environment and climate change. Electricity from renewable energy sources such as solar and wind has a seasonal nature that cannot provide the necessary electricity consumption and cover peak loads. The so-called “energy resource crisis” is also a very topical problem at the moment, which reinforces the global need to increase the share of renewable energy resources in the overall balance of primary energy resources. Practical wider integration of renewable electricity storage is what can help stimulate this. The availability of renewable electricity is constantly increasing, and the level of technological innovation is rapidly developing. Therefore, it is valuable to analyse, look for connections and for ways to accumulate electricity in order to promote its availability from private homes to the national scale and more broadly on the European scale. Therefore, this article analyses and compares the different options for renewable electricity storage, from small batteries to large storage systems, arriving at the best solution according to needs, using analysis methods such as multicriteria decision analysis (MCDA) and TOPSIS. After comparing nine criteria, such as the amount of investment required, existing power density, efficiency, duration of operation, and others in two groups (small and large accumulation systems), it was concluded that lithium-ion batteries are currently the best solution among batteries, while pumped hydro storage is the best solution among large accumulation systems. Full article