BSM Model Research Articles

Technological Progress and Engineering Applications: Safety Impacts for Workplaces and Society

Technological innovations, embodied in Industry 4.0 and transhumanist developments, have essentially changed the nature of engineering practices and industrial operations. This paper discusses the bifacial impact of such changes on the safety of occupations and ethical values in society, emphasizing critical shortcomings in traditional risk assessment methodologies. This study proposes a new quantitative framework for dynamic risk assessment of safety in interconnected industrial environments by adopting and adapting the Black-Scholes-Merton model, originally developed for financial markets. The parameters of the model—namely, safety state, volatility, and time to expiration—were recalibrated to match the industrial safety metrics and later validated through simulations and empirical case studies across various sectors, including manufacturing and construction. The results show that the BSM model is effective in predicting violations of safety thresholds, being much more adaptable and objective than traditional methods like Failure Mode and Effects Analysis. Sensitivity analyses indicate that both fluctuations and safety thresholds are of importance for determining risk probabilities, thus showing that careful monitoring and recalibration are necessary. Ethical considerations, including equity in transhumanist technologies and ecological impact of IoT systems, were embedded into the methodology, ensuring the results to be aligned with societal values and sustainability objectives. This research marries theoretical advances with practical applications, providing pragmatic insights for policy makers, engineers, and leaders in industry. It advocates proactive risk management, real-time integration of IoT, and interdisciplinary research in order to further improve the predictive models of safety. While some limitations were noted, including data dependency and assumptions related to normal distribution, the research has shown that financial-based methodologies can be transformational in the area of industrial safety. This dissertation advances the ongoing discussion surrounding Industry 4.0 by proposing novel instruments designed to manage its intricacies, all the while encouraging ethical and sustainable advancements in technology.

Interpreting 95 GeV di-photon/bb¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b} $$\\end{document} excesses as a lightest Higgs boson of the MRSSM

The Minimal R-symmetric Supersymmetric Standard Model (MRSSM) is a well motivated BSM model which can accommodate the observed 125 GeV Higgs boson in agreement with electroweak precision observables, in particular with the W boson mass and T parameter. In the 2016 paper we showed that the SM-like 125 GeV Higgs state can be also realised as the second-to-lightest scalar of the MRSSM, leaving room for another sub-100 GeV state. Motivated by the recent ATLAS and CMS observation of the di-photon excess at a mass of around 95 GeV we investigate the possibility whether this could be the lightest CP-even MRSSM scalar in a variation of our benchmarks presented in the 2016 work. We show that such a state can also simultaneously explain the excess in the bb¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b} $$\\end{document} final state observed around the same mass value at LEP. Due to the R-symmetric nature of the model, a light singlet-like Higgs state leads necessarily to a light bino-singlino Dirac dark matter candidate, which can give a correct relic density while evading current experimental bounds. Dark matter and LHC searches place further bounds on this scenario and point to parameter regions which are viable and of interest for the LHC Run III and upcoming dark matter experiments.

State of the Commercial Stock of Rapa Whelk Rapana venosa in the Coastal Zone of the Northwestern Section of the Black Sea

The paper deals with the age and size-mass composition of the most important commercial object - veined rapa whelk <i>Rapana venosa </i>(Valenciennes, 1846) and spatial distribution of its population in the northwestern section of the Black Sea based on analysis of samples from 857 beam trawl catches and 7 diving sampling over 2018-2021. Maximal biomass of the mollusk is concentrated at the depths up to 25 m. Rapa whelk abundance decreased sharply below 25 m owing to insufficient food and low water temperature. The beam trawl surveys over 2020-2021 showed that in summer hypoxic zones were common in the bottom horizons in significant areas of the shelf water. The black sludge with a sharp smell of hydrogen sulfide often occurred in the catches. The mass death of the filtering mollusks and rapa whelk was registered as a consequence of these phenomena in the shelf zone. At the depths of 5-25 m, rapa whelk population comprised twelve age groups from 2+ to 13+ and the main portion consisted of the groups 6+-8+. At the same time, at the depth below 25 m, most specimens were 7-9 years old. Rapa whelk enters the deep-water zone due to migration from shallower areas where it reproduces. The stock of rapa whelk in the Ukrainian waters estimated by the direct trawl accounting varied within the range of 28.5-72.7 th. tons. At the same time stock assessment using the BSM model showed about 35.7 thousand tons. Intensification of the mollusk harvesting in recent years has not led to overexploitation of this stock. The size and age structure of the population did not significantly change. The areas accessible to fishermen are less than 15-20% of total shelf inhabited by rapa whelk. Its resource demonstrated high ability for sustainable reproduction due to good feeding conditions and constant migration of mollusks from areas where it is not harvested.

Comparison and Analysis of the Effectiveness of the State-of-the-Art in Option and Financial Pricing Models

Contemporarily, various models have been developed and used to price the returns of an asset or an option for decades. This paper will discuss and compare two option pricing models (the BSM model and the Monte Carlo Simulation) and three financial pricing models (the CAPM, the FF3 Model, and the FF5 Model). It will start with discussing the history, assumptions, and formulae of each model. Then, it will lead into how each model has changed over time, whether that be changes from the researchers themselves or other researchers within the community. Additionally, specifics of the change will be addressed, and the paper will outline what the new model has done to improve upon those concerns. Eventually, an empirical comparison will contrast the effectiveness and accuracy of each model. Ultimately, it will be seen that the BSM model and the MCS are useful in different time frames and the FF5 model is superior to the original financial pricing models as it builds on the original models’ limitations. Even so, the BSM model, MCS, and the FF5 model still have their own limitations that vary from reality and can be improved on in future research. These results shed light on guiding further exploration of newer and more refined models, methodologies, and approaches aimed to enhance our ability to make informed decisions and manage risks with greater precision.

Research on the option pricing of Amazon and Google based on B-S model and Monte Carlo simulation

The emergence of financial derivatives has helped people to effectively hedge the risks present in the financial markets while giving them the ability to make leveraged investments in the financial markets. Although derivatives did not originate in the financial market, it still has a huge role in the financial market so far. In recent years, science and technology innovation is known as a growing concern for governments due to factors such as environmental issues. In this paper, we choose to study the financial derivative, European call option pricing problem of technology-based companies AMZN and GOOGL. In this paper, the European call options of these two companies are priced by using the BSM model, and the results predicted by the BSM model are improved by using Monte Carlo Simulation. Ultimately, the paper finds that Monte Carlo Simulation prices European call options on technology-based firms nearly three times higher than those priced by the BSM model. The results suggest that using a single model to price European call options on technology-based firms is inaccurate. The purpose of this paper is to help investors in pricing European call options on technology-based firms and to warn investors about the inaccuracy of a single option pricing model.

Pricing of Shanghai stock exchange 50 ETF options based on different volatility models

On March 15, 2022, the volume of trade of the Shanghai Stock Exchange (SSE) 50 ETF option contracts and the CSI 300 ETF option contracts exceeded 10 million for the first time, of which 5,707,400 50 ETF options were traded, and SSE 50 ETF options, as the main force, has become one of the most active ETF option varieties in the world after seven years of vigorous development. The SSE 50 ETF options receive highlights in risk-free arbitrage, hedging, risk management and other aspects. In order to give full play to the function of the SSE 50 ETF options, it is necessary to conduct studies on their pricing. This paper adopts the traditional classical models for pricing European-style options, the BSM model and the volatility model, to price call options and put options of the SSE ETF, and meanwhile analyzes the volatility of the SSE 50 ETF. The empirical results suggest that (1) the volatility of SSE 50 ETF has a weak leverage effect or no leverage effect, which converges with the existence of the inverse leverage effect of the SSE index; (2) the BSM model will underestimate the price of SSE 50 ETF options and is only ideal for pricing in-the-money (ITM) options; while out-of-the-money (OTM) options are highly influenced by time value and therefore cannot be accurately priced.

Hide and seek: how PDFs can conceal new physics

The interpretation of LHC data, and the assessment of possible hints of new physics, require the precise knowledge of the proton structure in terms of parton distribution functions (PDFs). We present a systematic methodology designed to determine whether and how global PDF fits might inadvertently ‘fit away’ signs of new physics in the high-energy tails of the distributions. We showcase a scenario for the High-Luminosity LHC, in which the PDFs may completely absorb such signs of new physics, thus biasing theoretical predictions and interpretations. We discuss strategies to single out the effects in this scenario, and disentangle the inconsistencies that stem from them. Our study brings to light the synergy between the high luminosity programme at the LHC and future low-energy non-LHC measurements of large-x sea quark distributions. The analysis code used in this work is made public so that any users can test the robustness of the signal associated to a given BSM model against absorption by the PDFs.

Mixture-of-Theories training: can we find new physics and anomalies better by mixing physical theories?

Model-independent search strategies have been increasingly proposed in recent years because on the one hand there has been no clear signal for new physics and on the other hand there is a lack of a highly probable and parameter-free extension of the standard model. For these reasons, there is no simple search target so far. In this work, we try to take a new direction and ask the question: bearing in mind that we have a large number of new physics theories that go beyond the Standard Model and may contain a grain of truth, can we improve our search strategy for unknown signals by using them “in combination”? In particular, we show that a signal hypothesis based on a large, intermingled set of many different theoretical signal models can be a superior approach to find an unknown BSM signal. Applied to a recent data challenge, we show that “mixture-of-theories training” outperforms strategies that optimize signal regions with a single BSM model as well as most unsupervised strategies. Applications of this work include anomaly detection and the definition of signal regions in the search for signals of new physics.

Pricing of Asian Options on Tesla Based on BSM model

Due to the interaction of the changes in the world political situation and the influence of the global epidemic, the world economy has entered a period of instability and turmoil. This can be an opportunity for people who would like to make an investment. However, without adequate research and good preparation, they may face huge losses. Therefore, this research shows how to choose a reasonable investment approach for a particular market. To be more specific, the research topic of this paper is to show how Asian put options work well in Tesla Market, and the methods of this study include the BSM model, sensitivity analysis, and making a comparison of the Asian options with the European options. Then, the results could be seen that the Asian options will be a more affordable and less risky investment strategy for the Tesla market which is a market with high volatility. Thus, to invest in a market in the current society, it is better for investors to make a clear understanding of their target income and then make multifaceted research. As a result, the investor could reduce their unnecessary losses.

Research on The Lookback Option Pricing of Disney Based on BSM Model

The lookback option is a path-dependent option that enables holders to use the most advantageous pricing to execute the underlying asset. This paper adopts the BMS model to price the lookback option and takes risk factors into consideration to calculate the value of an option contract in the BMS model. The main variables in the BMS model are risk-free rate, current spot price, strike price, volatility, and time to maturity. The results are reliable enough for investors to make future decisions. However, the BMS model still has a few drawbacks which can make the prices derived from real future prices. When predicting future prices, using the BMS model can help investors make better decisions. The lookback option allows holders to minimize their regrets and exercise the underlying asset at the most beneficial price.

Dynamic Banking Systemic Risk Accumulation under Multiple-Risk Exposures.

Much of the existing research on banking systemic risk focuses on static single-risk exposures, and there is a lack of research on multiple-risk exposures. The reality is that the banking system is facing an increasingly complex environment, and dynamic measures of multiple-risk integration are essential. To reveal the risk accumulation process under the multi-risk exposures of the banking system, this article constructs a dynamic banking system as the research object and combines geometric Brownian motion, the BSM model, and the maximum likelihood estimate method. This article also aims to incorporate three types of exposures (interbank lending market risk exposures, entity industry credit risk exposures, and market risk exposures) within the same framework for the first time and builds a model of the dynamic evolution of banking systemic risk under multiple exposures. This study included the collection of a large amount of real data on banks, entity industries, and market risk factors, and used the ΔCoVaR model to evaluate the systemic risk of the China banking system from the point of view of the accumulation of risk from different exposures, revealing the dynamic process of risk accumulation under the integration of multiple risks within the banking system, as well as the contribution of different exposures to banking systemic risk. The results showed that the banking systemic risk of China first increased and then decreased with time, and the rate of risk accumulation is gradually slowing down. In terms of the impact of different kinds of exposures on system losses, the credit risk exposure of the entity industry had the greatest impact on the banking systemic risk among the three kinds of exposures. In terms of the contribution of the interbank lending market risk to the systemic risk, the Bank of Communications, China Everbright Bank, and Bank of Beijing contributed the most. In terms of the contribution of the bank-entity industry credit risk to the systemic risk, the financial industry, accommodation and catering industry, and manufacturing industry contributed the most. Considering the contribution of market risk to the systemic risk, the Shanghai Composite Index, the Hang Seng Composite Index, and the Dow Jones Index contributed the most. The research in this paper enriches the existing banking systemic risk research perspective and provides a reference for the regulatory decisions of central banks.

Comparative Analysis of the Application of Monte Carlo Model and BSM Model in European Option Pricing

At present, the expansion of China's domestic options market brings positive factors and risks, and in order to avoid risks, it is crucial to choose a suitable model for option pricing. This article provides an example of an option for the underlying asset of the SSE 50 ETF. Using the BSM model and the Monte Carlo model for the selected option pricing, and comparing the actual option price. It is found that the pricing efficiency of the Monte Carlo model is higher than that of the BSM model when the number of simulations reaches 30,000 times in the call option, and there is little difference between the two in the put option pricing. It is recommended to prefer the Monte Carlo model when pricing call options and the more convenient BSM model when pricing put options.

A Modified Black-Scholes-Merton Model for Option Pricing

Financial derivatives have grown in importance over the last 40 years with futures and options being actively traded on a daily basis throughout the world. The need to accurately price such financial instruments has, thus, also increased, which has given rise to several mathematical models among which is that of Black, Scholes, and Merton whose wide acceptance is partly justified by its ability to price derivatives in mature and well-developed markets. For instruments traded in emerging markets, however, the accurateness of the BSM model is unproven and new proposals need be made to face the pricing challenge. In this paper we develop a model, inspired in conformable calculus, providing greater flexibilities for these markets. After developing the theoretical aspects of the model, we present an empirical application.

The Impact of Market Liquidity on the Effectiveness of Option Valuation with the Black-Scholes-Merton Model Using the Example of the WIG20 Index

The Black-Scholes-Merton model is one of the most popular option pricing models used in market practice. This model is based on unrealistic assumptions, including the lack of transaction costs. While it is not possible to satisfy all the conditions of the model, it is logical to assume that perfectly liquid markets will meet them better, which will help to reduce the risk of error. The aim of the article was to measure the impact of liquidity to the divergence of the Black-Scholes-Merton model compared to real market closing prices. The result of the research demonstrates a moderate dependence between the volume of the WIG20 index, the volume of option transactions and a negative correlation with the ILLIQ illiquidity indicator introduced by Amihud (2002). The research led to the conclusion that there is a positive correlation between the liquidity and the divergence between BSM model and the market prices.

Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets

Abstract The pricing and hedging of financial derivatives have become one of the hot research issues in mathematical finance today. In the case of non-risk neutrality, this article uses the martingale method and probability measurement method to study the pricing method and hedging strategy of financial derivatives. This paper also further studies the hedging strategy of financial derivatives in the incomplete market based on the BSM model and converts the solution of this problem into solving a vector on the Hilbert space to its closure. The problem of space projection is to use projection theory to decompose financial derivatives under a given martingale measure. In the imperfect market, the vertical projection theory is used to obtain the approximate pricing method and hedging strategy of financial derivatives in which the underlying asset follows the martingale process; the projection theory is further expanded, and the pricing problem of financial derivatives under the mixed-asset portfolio is obtained. Approximate pricing of financial derivatives; in the discrete state, the hedging investment strategy of financial derivatives H in the imperfect market is found through the method of variance approximation.

ACROPOLIS: A generiC fRamework fOr Photodisintegration Of LIght elementS

The remarkable agreement between observations of the primordial light element abundances and the corresponding theoretical predictions within the standard cosmological history provides a powerful method to constrain physics beyond the standard model of particle physics (BSM). For a given BSM model these primordial element abundances are generally determined by (i) Big Bang Nucleosynthesis and (ii) possible subsequent disintegration processes. The latter potentially change the abundances due to late-time high-energy injections which may be present in these scenarios. While there are a number of public codes for the first part, no such code is currently available for the second. Here we close this gap and present ACROPOLIS, A generiC fRamework fOr Photodisintegration Of LIght elementS. The widely discussed cases of decays as well as annihilations can be run without prior coding knowledge within example programs. Furthermore, due to its modular structure, can easily be extended also to other scenarios.For the most recent version of this manual, please visit the GitHub repository at https://github.com/skumblex/acropolis.

How Much Is Your Strangle Worth? On the Relative Value of the Strangle under the Black-Scholes Pricing Model

Trading option strangles is a highly popular strategy often used by market participants to mitigate volatility risks in their portfolios. We propose a measure of the relative value of a delta-Symmetric Strangle and compute it under the standard Black-Scholes-Merton option pricing model. This new measure accounts for the price of the strangle, relative to the Present Value of the spread between the two strikes, all expressed, after a natural re-parameterization, in terms of delta and a volatility parameter. We show that under the standard BSM model, this measure of relative value is bounded by a simple function of delta only and is independent of the time to expiry, the price of the underlying security or the prevailing volatility used in the pricing model. We demonstrate how this bound can be used as a quick benchmark to assess, regardless the market volatility, the duration of the contract or the price of the underlying security, the market (relative) value of the strangle in comparison to its BSM (relative) price. In fact, the explicit and simple expression for this measure and bound allows us to also study in detail the strangle’s exit strategy and the corresponding optimal choice for a value of delta.

An Application of Extreme Value Theory to Finance – An Empirical Study of Whether Stock Shape Parameters and the Differences Between Corresponding Actual and BSM Put Option Values Are Positively Correlated

Large stock price movements and financial crises are a common occurrence relative to the belief of normality in markets, and they are becoming more common as the world becomes more interconnected and more technology driven. After large dips in prices and after crises the topic of risk management, specifically tail risk quantification, comes into the focus of not just researchers, but is also put into question by the general public. Recently, Extreme Value Theory, originally targeted at the study of weather and climate, entered the field of risk management and provided a new approach to measuring tail risk, letting the data speak for itself rather than underpinning distributional assumptions as most approaches had done thus far. This thesis employs Extreme Value Theory, specifically the Peaks over Threshold approach or Generalized Pareto Distribution approach, in order to quantify the tail thickness of the left tail of stock return distributions of the S&P 500 index and its constituents. The thesis then assesses the relationship between the tail fatness of the underlying stock and the absolute as well as relative difference between the actual put option value and the put option value according to Black Scholes Merton. The hypothesis is that thicker left tails imply that large negative movements are more probable than under the Gaussian assumption. This in turn could display itself in an undervaluation of put options, in particular deep out of the money put options, as calculated by traditional BSM. In the analysis, neither the absolute nor the relative differences seem to show a relationship to respective shape parameters. However, the averages of the absolute differences of deep out of the money put options do appear to be very small in size, indicating a valuation close to that of the BSM model, while the averages of the relative differences of deep out of the money put options are for the larger part close to 100%, indicating a complete undervaluation of these put options by BSM, regardless of the shape parameter. The lack of relationship between shape parameters and differences begs the question of whether buyers are valuing options correctly and the employed methodology is wrong or whether the thesis methodology is appropriate and buyers are mistaken. A short analysis provides evidence pointing to the latter.

Classical Option Pricing and Some Steps Further

This paper considers the asset price p as relations C=pV between the value C and the volume V of the executed transactions and studies the consequences of this definition for the option pricing equations. We show that the classical BSM model implicitly assumes that value C and volume V of transactions follow identical Brownian processes. Violation of this identity leads to 2-dimensional BSM-like equation with two constant volatilities. We show that agents expectations those approve execution of transactions can further increase the dimension of the BSM model. We study the case when agents expectations may depend on the option price data and show that such assumption can lead to the nonlinear BSM-like equations. We reconsider the Heston stochastic volatility model for the price determined by the value and the volume and derive 3-dimensional BSM-like model with stochastic value volatility and constant volume volatility. Variety of the BSM-like equations states the problem of reasonable balance between the accuracy and the complexity of the option pricing equations.

Efficacy of Nifty Index Options through BSM Model

Options are one of the products in financial derivatives, which gives the rights to buy and sell the product to an option holder in pre-fixed price which known as the strike price or exercise price at certain periods. Options contract was existed in various countries for long time, but it became very popular among the investors when the Fisher Black, Myron Scholes and Robert Merton were introduced the Black-Scholes Model in the year of 1973. This model was formerly developed by these three economists who were also receiving the Nobel prize for finding this innovative model. This model is mainly used to deal with the theoretical pricing challenge in options price determination. In India the trading in Index Options commenced on 4th June 2001 and Options on individual securities commenced on 2nd July 2001. There are many types in options contracts like stock options; Index options, weather options, real options and etc. This study has mainly been focusing on Nifty 50 index options which are effectively trade at NSE. This paper goes to describe about the importance of options pricing and how the BSM model has effectively used to find the optimum price of the theoretical value of call and put options.