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In this study, we assume that stock prices follow piecewise geometric Brownian motion, a variant of geometric Brownian motion except the ex-dividend date, and find pricing formulas of American call options. While piecewise geometric Brownian motion can effectively incorporate discrete dividends into stock prices without losing consistency, the process results in the lack of closed-form solutions for option prices. We aim to resolve this by providing analytical approximation formulas for American call option prices under this process. Our work differs from other studies using the same assumption in at least three respects. First, we investigate the analytical approximations of American call options and examine European call options as a special case, while most analytical approximations in the literature cover only European options. Second, we provide both the upper and the lower bounds of option prices. Third, our solutions are equal to the exact price when the size of the dividend is proportional to the stock price, while binomial tree results never match the exact option price in any circumstance. The numerical analysis therefore demonstrates the efficiency of our method. Especially, the lower bound formula is accurate, and it can be further improved by considering second order approximations although it requires more computing time.

The purpose of this article is to propose a detailed methodology to estimate, model and incorporate the non-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination.

This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic.

Findings showed that in the proposed method with volatility tends to zero, the multiplicative binomial traditional method is a particular case, and results are comparable between these methodologies, as well as to the exact solution offered by the Black–Scholes model.

The originality of this paper lies in try to model the implicit (conditional) market volatility to assess, based on that, a real option using a quadrinomial tree, including into this valuation the stochastic volatility of the underlying asset. The main contribution is the formal derivation of a risk-neutral valuation as well as the market risk premium associated with volatility, verifying this condition via numerical test on simulated and real data, showing that our proposal is consistent with Black and Scholes formula and multiplicative binomial trees method.

This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50 Index, the paper shows that the pricing accuracy of these models is very satisfactory under four different pricing error functions. The result is that taking a position in a third moment swap considerably improves the performance of the standard hedge of a variance swap based on a static position in the log-contract and a dynamic trading strategy. The position in the third moment swap is taken by running a Monte Carlo simulation.

This paper undertook empirical tests of three parametric models. The aim of the paper is twofold: assess the pricing accuracy of these models and show how the classical hedge of the variance swap in terms of a position in a log-contract and a dynamic trading strategy can be significantly enhanced by using third-order moment swaps. The pricing accuracy was measured under four different pricing error functions. A Monte Carlo simulation was run to take a position in the third moment swap.

The results of the paper are twofold: the pricing accuracy of the Heston (1993) model and that of two Levy models with stochastic time and stochastic volatility are satisfactory; taking a position in third-order moment swaps can significantly improve the performance of the standard hedge of a variance swap.

The limitation is that these empirical tests are conducted on existing three parametric models. Maybe more critical insights could have been revealed had these tests been conducted in a brand new derivatives pricing model.

This work is 100 per cent original, and it undertook empirical tests of the pricing and hedging accuracy of existing three parametric models.

This paper measures different market risk impacts on options portfolios under the new Fundamental Review of the Trading Book (FRTB) regulation, issued in Basel and coming into effect in 2023.

This paper first suggests an algorithm for implementing the FRTB standardised approach via the sensitivities-based method to estimate a portfolio's risk capital and presents an illustration applied to an option position. Second, it proposes a methodology to estimate the expected shortfall in options portfolios from the FRTB internal models approach. In this regard, an application is developed to measure expected shortfall (ES) and value at risk (VaR) impacts under FRTB versus conventional VaR in a currency option position by considering stress scenarios from the 2007–9 and 2020–1 crises and back-testing procedures.

The suggested algorithm satisfactorily captures impacts via the sensitivities-based method, and higher risk capital demands are expected for emerging economies. Also, the planned FRTB methodology to measure ES and VaR is appropriate; in particular, historical metrics perform well. Astonishingly, their revealed impacts are more significant under the 2020–1 pandemic crisis than the 2007–9 financial crisis.

The proposals developed weave a communication bridge between the standardised and internal approaches of FRTB regulation, which can be scaled up technologically and institutionally.

This paper aims to present the theoretical and conceptual framework of a new method in public finance called “participation based tax increment financing (P-TIF)” by combining conventional tax increment financing (TIF) within the Sharīʿah-compliance structure.

This study develops a benchmark model for P-TIF, which offers a participative contract between both lender and borrower. With the help of this model, a financing schema in P-TIF is established by incorporating stochastic modelling. Possible implications and alternative options of application are also explored with a discussion of challenges.

The results mainly indicate that P-TIF promises lenders to be a part of increment from tax earnings, in return for a reduced interest rate. They show how a rise in participation of the lender in a given contract lowers the interest rate. Under the base case scenario, the interest rate is reduced to zero when the participation of the lender in tax increment is set at 50%.

With the feature of being interest-free, P-TIF can be implied also within the Sharīʿah-compliance framework, thanks to the model it is based on. Additionally, as the model in this paper is parametric, it can be applicable to various cases in Islamic finance.

To the best of our knowledge, this is the first paper in the literature in the sense that it provides a conceptual idea and respective model for TIF method within a Sharīʿah-compliance framework.

This study aims to develop a high-quality impairment loss allowance model in conformity with Indonesian Financial Accounting Standards 71 (PSAK 71) that has significant contribution to national interests and the banking industry.

The determination of the impairment loss allowance model is settled through 7 stages, using integration of some statistical methods such as Markov chain, exponential smoothing, time series analysis of behavioral inherent trends of probability of default, tail conditional expectation and Monte Carlo simulation.

The model which is developed by the authors is proven to be a high-quality and reliable model. By using the model, it can be shown that the implementation of the expected credit losses model on Indonesian Financial Accounting Standards 71 is more prudent than the implementation of the incurred loss model on Indonesian Financial Accounting Standards 55.

Determination of defaults was based on days past due, and the analysis in this study did not touch the aspects of hedge accounting in general.

This developed model will contribute significantly to national interests as a source of reference for other banks operating in Indonesia in calculating impairment loss allowance (CKPN) and can be used by the Financial Services Authority of Indonesia (OJK) as a guideline in assessing the formation of impairment loss allowance for banks operating in Indonesia.

As so far there is not yet an available standardized model for calculating impairment loss allowance on the basis of Indonesian Financial Accounting Standards 71, the model developed by the authors will be a new breakthrough in Indonesia.

Restrictions on social interaction and travel due to the COVID-19 pandemic have affected how researchers approach fieldwork and data collection. Whilst online focus groups have received attention since the 2000s as a method for qualitative data collection, relatively little of the relevant literature appears to have made use of now ubiquitous video calling software and synchronous, interactive discussion tools. Our own experiences in organising fieldwork aimed at understanding the impact of different “future-proofing” strategies for the European agri-food system during this period resulted in several methodological changes being made at short notice. We present an approach to converting in-person focus group to a virtual methodology and provide a checklist for researchers planning their own online focus groups. Our findings suggest data are comparable to in-person focus groups and factors influencing data quality during online focus groups can be safeguarded. There are several key steps, both before and during the focus groups, which can be taken to ensure the smooth running of such events. We share our reflections on this approach and provide a resource for other researchers moving to online-only data collection.

The purpose of this paper is to illustrate a profitable and original index options trading strategy.

The methodology is based on auto regressive integrated moving average (ARIMA) forecasting of the S&P 500 index and the strategy is tested on a large database of S&P 500 Composite index options and benchmarked to the generalized auto regressive conditional heteroscedastic (GARCH) model. The forecasts validate a set of criteria as follows: the first criterion checks if the forecasted index is greater or lower than the option strike price and the second criterion if the option premium is underpriced or overpriced. A buy or sell and hold strategy is finally implemented.

The paper demonstrates the valuable contribution of this option trading strategy when trading call and put index options. It especially demonstrates that the ARIMA forecasting method is a valid method for forecasting the S&P 500 Composite index and is superior to the GARCH model in the context of an application to index options trading.

The strategy was applied in the aftermath of the 2008 credit crisis over 60 months when the volatility index (VIX) was experiencing a downtrend. The strategy was successful with puts and calls traded on the USA market. The strategy may have a different outcome in a different economic and regional context.

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.

Regarding the retail internal supply chain (SC), both retailers and research are currently focused on reactive food waste reduction options in stores (e.g. discounting or donations). These options reduce waste after a surplus has emerged but do not prevent an emerging surplus in the first place. This paper aims to reveal how retailers can proactively prevent waste along the SC and why the options identified are impactful but, at the same time, often complex to implement.

The authors follow an exploratory approach for a nascent topic to obtain insights into measures taken in practice. Interviews with experts from retail build the main data source.

The authors identify and analyze 21 inbound, warehousing, distribution and store-related options applied in grocery retail. Despite the expected high overall impact on waste, prevention measures in inbound logistics and distribution and warehousing have not been intensively applied to date.

The authors provide a structured approach to mitigate waste within retailers' operations and categorize the types of barriers that need to be addressed.

This research provides a better understanding of prevention options in retail operations, which has not yet been empirically explored. Furthermore, this study conceptualizes prevention and reduction options and reveals implementation patterns.