Relevant bibliographies by topics / Multidimensional Black Scholes market

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  1. Journal articles
  2. Dissertations / Theses
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  5. Conference papers

Academic literature on the topic 'Multidimensional Black Scholes market'

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Published: 4 June 2021
Last updated: 8 February 2022

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Journal articles on the topic "Multidimensional Black Scholes market"

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ALBEVERIO, SERGIO, ALEX POPOVICI, and VICTORIA STEBLOVSKAYA. "A NUMERICAL ANALYSIS OF THE EXTENDED BLACK–SCHOLES MODEL." International Journal of Theoretical and Applied Finance 09, no. 01 (February 2006): 69–89. http://dx.doi.org/10.1142/s0219024906003469.

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In this article some numerical results regarding the multidimensional extension of the Black–Scholes model introduced by Albeverio and Steblovskaya [1] (a multidimensional model with stochastic volatilities and correlations) are presented. The focus lies on aspects concerning the use of this model for the practice of financial derivatives. Two parameter estimation methods for the model using historical data from the market and an analysis of the corresponding numerical results are given. Practical advantages of pricing derivatives using this model compared to the original multidimensional Black–Scholes model are pointed out. In particular the prices of vanilla options and of implied volatility surfaces computed in the model are close to those observed on the market.
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Dolinsky, Yan. "Shortfall Risk Approximations for American Options in the Multidimensional Black-Scholes Model." Journal of Applied Probability 47, no. 04 (December 2010): 997–1012. http://dx.doi.org/10.1017/s0021900200007312.

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We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black-Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path-dependent payoffs. In comparison to previous papers we consider the multiassets case for which we use the weak convergence approach.
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Dolinsky, Yan. "Shortfall Risk Approximations for American Options in the Multidimensional Black-Scholes Model." Journal of Applied Probability 47, no. 4 (December 2010): 997–1012. http://dx.doi.org/10.1239/jap/1294170514.

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We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black-Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path-dependent payoffs. In comparison to previous papers we consider the multiassets case for which we use the weak convergence approach.
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Bernard, Carole, Mateusz Maj, and Steven Vanduffel. "Improving the Design of Financial Products in a Multidimensional Black-Scholes Market." North American Actuarial Journal 15, no. 1 (January 2011): 77–96. http://dx.doi.org/10.1080/10920277.2011.10597610.

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Zimbidis, Alexandros A. "Optimal Management of a Variable Annuity Invested in a Black–Scholes Market Driven by a Multidimensional Fractional Brownian Motion." Stochastic Analysis and Applications 29, no. 1 (December 27, 2010): 61–77. http://dx.doi.org/10.1080/07362994.2011.532021.

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Guillaume, Tristan. "On the multidimensional Black–Scholes partial differential equation." Annals of Operations Research 281, no. 1-2 (August 11, 2018): 229–51. http://dx.doi.org/10.1007/s10479-018-3001-1.

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Munn, Luke. "From the Black Atlantic to Black-Scholes." Cultural Politics 16, no. 1 (March 1, 2020): 92–110. http://dx.doi.org/10.1215/17432197-8017284.

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Rather than being unprecedented, contemporary technologies are the most sophisticated instances of a long-standing dream: if space could be more comprehensively captured and coded, it could be more intensively capitalized. Two moments within this lineage are explored: maritime insurance of slave ships in the eighteenth century, and the Black-Scholes model of option pricing from the twentieth century. Maritime insurance rendered the unknown space of the ocean knowable and therefore profitable. By collecting information at Lloyds, merchants developed a map of threat within the Atlantic, and by writing a 10 percent buffer into slave-ship contracts they internalized contingency. This codification of risk pressured captains and established a logic for the violence enacted on the ship’s human “cargo.” The Black-Scholes formula of option pricing sought to codify the ocean of risk represented by the financial market. The formula mapped stock movements into a knowable stochastic equation. Traders could quantify and hedge against the unpredictable, rendering the stock market a space of riskless profit. However, the 2008 financial crash demonstrated the limits of spatial calculation. Taken together, these two moments demonstrate the historical continuity of a core imperative to exhaustively capitalize space. This historicization also foregrounds the racialized inequalities coded within these informatic logics. Against the bright innovation narratives of technology, this article stresses a longer and darker lineage based on inequality and dispossession.
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Dixit, Alok, and Shivam Singh. "Ad-Hoc Black–Scholes vis-à-vis TSRV-based Black–Scholes: Evidence from Indian Options Market." Journal of Quantitative Economics 16, no. 1 (February 15, 2017): 57–88. http://dx.doi.org/10.1007/s40953-017-0078-3.

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Özer, H. Ünsal, and Ahmet Duran. "The source of error behavior for the solution of Black–Scholes PDE by finite difference and finite element methods." International Journal of Financial Engineering 05, no. 03 (September 2018): 1850028. http://dx.doi.org/10.1142/s2424786318500287.

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Black–Scholes partial differential equation (PDE) is one of the most famous equations in mathematical finance and financial industry. In this study, numerical solution analysis is done for Black–Scholes PDE using finite element method with linear approach and finite difference methods. The numerical solutions are compared with Black–Scholes formula for option pricing. The numerical errors are determined for the finite element and finite difference applications to Black–Scholes PDE. We examine the error behavior and find the source of the corresponding errors under various market situations.
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Kermiche, Lamya. "Too Much Of A Good Thing? A Review Of Volatility Extensions In Black-Scholes." Journal of Applied Business Research (JABR) 30, no. 4 (June 30, 2014): 1171. http://dx.doi.org/10.19030/jabr.v30i4.8662.

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Since the seminal Black and Scholes model was introduced in the 1970s, researchers and practitioners have been continuously developing new models to enhance the original. All these models aim to ease one or more of the Black and Scholes assumptions, but this often results in a set of equations that is difficult if not impossible to use in practice. Nevertheless, in the wake of the financial crisis, an understanding of the various pricing models is essential to calm investors nerves. This paper reviews the models developed since Black and Scholes, giving the advantages and disadvantages of each type. It focuses on the main variable for which Black and Scholes gives results that differ widely from market data: implied volatility. This variable also forms the basis for the development of a new type of models, called market models.
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Dissertations / Theses on the topic "Multidimensional Black Scholes market"

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Maj, Mateusz. "Essays in risk management: conditional expectation with applications in finance and insurance." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209668.

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In this work we study two problems motivated by Risk Management: the optimal design of financial products from an investor's point of view and the calculation of bounds and approximations for sums involving non-independent random variables. The element that interconnects these two topics is the notion of conditioning, a fundamental concept in probability and statistics which appears to be a useful device in finance. In the first part of the dissertation, we analyse structured products that are now widespread in the banking and insurance industry. These products typically protect the investor against bearish stock markets while offering upside participation when the markets are bullish. Examples of these products include capital guaranteed funds commercialised by banks, and equity linked contracts sold by insurers. The design of these products is complex in general and it is vital to examine to which extent they are actually interesting from the investor's point of view and whether they cannot be dominated by other strategies. In the academic literature on structured products the focus has been almost exclusively on the pricing and hedging of these instruments and less on their performance from an investor's point of view. In this work we analyse the attractiveness of these products. We assess the theoretical cost of inefficiency when buying a structured product and describe the optimal strategy explicitly if possible. Moreover we examine the cost of the inefficiency in practice. We extend the results of Dybvig (1988a, 1988b) and Cox & Leland (1982, 2000) who in the context of a complete, one-dimensional market investigated the inefficiency of path-dependent pay-offs. In the dissertation we consider this problem in one-dimensional Levy and multidimensional Black-Scholes financial markets and we provide evidence that path-dependent pay-offs should not be preferred by decision makers with a fixed investment horizon, and they should buy path-independent structures instead. In these market settings we also demonstrate the optimal contract that provides the given distribution to the consumer, and in the case of risk- averse investors we are able to propose two ways of improving the design of financial products. Finally we illustrate the theory with a few well-known securities and strategies e.g. dollar cost averaging, buy-and-hold investments and widely used portfolio insurance strategies. The second part of the dissertation considers the problem of finding the distribution of a sum of non- independent random variables. Such dependent sums appear quite often in insurance and finance, for instance in case of the aggregate claim distribution or loss distribution of an investment portfolio. An interesting avenue to cope with this problem consists in using so-called convex bounds, studied by Dhaene et al. (2002a, 2002b), who applied these to sums of log-normal random variables. In their papers they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In the dissertation we prove that unlike the log-normal case the construction of a convex lower bound in explicit form appears to be out of reach for general sums of log-elliptical risks and we show how we can construct stop-loss bounds and we use these to construct mean preserving approximations for general sums of log-elliptical distributions in explicit form.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Nuugulu, Samuel Megameno. "Fractional black-scholes equations and their robust numerical simulations." University of the Western Cape, 2020. http://hdl.handle.net/11394/7612.

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Philosophiae Doctor - PhD
Conventional partial differential equations under the classical Black-Scholes approach have been extensively explored over the past few decades in solving option pricing problems. However, the underlying Efficient Market Hypothesis (EMH) of classical economic theory neglects the effects of memory in asset return series, though memory has long been observed in a number financial data. With advancements in computational methodologies, it has now become possible to model different real life physical phenomenons using complex approaches such as, fractional differential equations (FDEs). Fractional models are generalised models which based on literature have been found appropriate for explaining memory effects observed in a number of financial markets including the stock market. The use of fractional model has thus recently taken over the context of academic literatures and debates on financial modelling.
2023-12-02
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Nilsson, Oscar, and Okumu Emmanuel Latim. "Does Implied Volatility Predict Realized Volatility? : An Examination of Market Expectations." Thesis, Uppsala universitet, Nationalekonomiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-218792.

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The informational content of implied volatility and its prediction power is evaluated for time horizons of one month. The study covers the period of November 2007 to November 2013 for the two indices S&P500 and OMXS30. The findings are put in relation to the corresponding results for past realized volatility. We find results supporting that implied volatility is an efficient, although biased estimator of realized volatility. Our results support the common notion that implied volatility predicts realized volatility better than past realized volatility, and that it also subsumes most of the informational content of past realized volatility.
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Alston, Rowan Gilbert. "The efficiency of the South African market for rights issues: an application of the Black-Scholes model." Master's thesis, University of Cape Town, 1996. http://hdl.handle.net/11427/14414.

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Bibliography: leaves 87-93.
Capital market efficiency is an important aspect of modern financial theory. This is because in an efficient capital market, scarce resources are optimally allocated to productive investments in a way that is beneficial to market participants. Yet there appears to be a dearth of research into the market efficiency of rights issues in South Africa, despite the fact that the majority of equity issues on the JSE are via a rights issue. The problem is that if the market is inefficient it is failing in its role of being an efficient allocator of scarce resources. The objective of this study is to establish whether the South African market for rights issues is efficient.
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TEIXEIRA, THIAGO CARDOSO. "COMPARING BLACK-SCHOLES AND CORRADO-SU: A STUDY ON IMPLIED VOLATILITY APPLIED TO THE BRAZILIAN CALL OPTION MARKET." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2011. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19082@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
Algumas literaturas sugerem que a volatilidade implícita das opções de compra de ações não deve ser utilizada como estimador para a volatilidade futura. Contudo, estudos recentes e aplicados ao mercado brasileiro de ações comprovaram que em determinados casos existe relação entre a volatilidade implícita e a volatilidade real (ou realizada). Isso significa dizer que a primeira traz informações sobre a última. Nesse contexto, o objetivo deste estudo é comparar a volatilidade implícita de dois modelos de apreçamento de opções com a volatilidade realizada. Entre os modelos de Black-Scholes (1973) e Corrado-Su (1996), utilizando dados de opções de Petrobras e Vale do Rio Doce, foram calculados, através do erro quadrático, aqueles resultados que mais se aproximaram da volatilidade realizada. Estes resultados trazem indícios de que o modelo de Black-Scholes, em média, foi superior ao Corrado-Su no período que vai de janeiro de 2005 a julho de 2009. Porém, o último, por levar em consideração a assimetria e a curtose da distribuição de retornos, chegou mais perto da volatilidade realizada apenas em alguns momentos específicos das economias brasileira e mundial.
Several authors have proposed that implied volatility from purchase options should not be used as an estimate for future volatility. However, recent studies applied to the Brazilian stock market proved that in certain cases there is relation between implied volatility and realized volatility. This means that the first one provides information on the last. In this context, the objective of this study is to compare implied volatilities from two different option pricing models against the realized volatility. The models are Black-Scholes (1973) and Corrado-Su (1996). Working with purchase options on Petrobras and Vale do Rio Doce, it was calculated the difference, by quadratic error, between the implied volatility of these models and the realized volatility. After this, it was checked those results that came closer to the realized volatility. The results provide evidence that the Black-Scholes model, on average, has higher performance than Corrado-Su from January 2005 to July 2009. However, Corrado-Su by taking into account the asymmetry and kurtosis of the distribution of returns came closer to the realized volatility only in specific moments of the Brazilian and global economies.
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Ayana, Haimanot, and Sarah Al-Swej. "A review of two financial market models: the Black--Scholes--Merton and the Continuous-time Markov chain models." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55417.

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The objective of this thesis is to review the two popular mathematical models of the financialderivatives market. The models are the classical Black–Scholes–Merton and the Continuoustime Markov chain (CTMC) model. We study the CTMC model which is illustrated by themathematician Ragnar Norberg. The thesis demonstrates how the fundamental results ofFinancial Engineering work in both models.The construction of the main financial market components and the approach used for pricingthe contingent claims were considered in order to review the two models. In addition, the stepsused in solving the first–order partial differential equations in both models are explained.The main similarity between the models are that the financial market components are thesame. Their contingent claim is similar and the driving processes for both models utilizeMarkov property.One of the differences observed is that the driving process in the BSM model is the Brownianmotion and Markov chain in the CTMC model.We believe that the thesis can motivate other students and researchers to do a deeper andadvanced comparative study between the two models.
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Chen, Hung-Hsiang. "An examination of kurtosis of lognormality in the Black-Scholes option pricing formula in the South African warrants market." Master's thesis, University of Cape Town, 2005. http://hdl.handle.net/11427/5771.

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Includes bibliographical references.
The assumption of constant asset price volatility of classical Black-Scholes model hasbeen challenged continuously. The symmetrical distribution emphasises a lognormalized asset. This paper aims to investigate the volatility distribution (i.e. kurtosis) of the South African warrants market at Johannesburg Stock Exchange based on a comparison of option implied distributions of the terminal price of the TOP European Call option with lognormal distribution. The result indicates that the constant volatility of Black-Scholes model does not show in the selected warrant market.
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Zhao, Min. "Risk Measures Extracted from Option Market Data Using Massively Parallel Computing." Digital WPI, 2011. https://digitalcommons.wpi.edu/etd-theses/373.

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The famous Black-Scholes formula provided the first mathematically sound mechanism to price financial options. It is based on the assumption, that daily random stock returns are identically normally distributed and hence stock prices follow a stochastic process with a constant volatility. Observed prices, at which options trade on the markets, don¡¯t fully support this hypothesis. Options corresponding to different strike prices trade as if they were driven by different volatilities. To capture this so-called volatility smile, we need a more sophisticated option-pricing model assuming that the volatility itself is a random process. The price we have to pay for this stochastic volatility model is that such models are computationally extremely intensive to simulate and hence difficult to fit to observed market prices. This difficulty has severely limited the use of stochastic volatility models in the practice. In this project we propose to overcome the obstacle of computational complexity by executing the simulations in a massively parallel fashion on the graphics processing unit (GPU) of the computer, utilizing its hundreds of parallel processors. We succeed in generating the trillions of random numbers needed to fit a monthly options contract in 3 hours on a desktop computer with a Tesla GPU. This enables us to accurately price any derivative security based on the same underlying stock. In addition, our method also allows extracting quantitative measures of the riskiness of the underlying stock that are implied by the views of the forward-looking traders on the option markets.
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Gabih, Abdelali, Matthias Richter, and Ralf Wunderlich. "Dynamic optimal portfolios benchmarking the stock market." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501244.

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The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the Expected Utility Loss. We generalize the findings our previous papers to this case. Using the Black-Scholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.
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Kuys, Wilhelm Cornelis. "Black economic empowerment transactions and employee share options : features of non-traded call options in the South African market." Diss., University of Pretoria, 2011. http://hdl.handle.net/2263/27305.

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Employee share options and Black Economic Empowerment deals are financial instruments found in the South African market. Employee share options (ESOs) are issued as a form of non-cash compensation to the employees of the company in addition to their salaries or bonuses. Its value is linked to the share price and since there is no downside risk for the employee his share option is similar to owning a call option on the stock of his employer. Black economic empowerment (BEE) deals in this report refer to those types of transactions structured by listed South African companies to facilitate the transfer of a portion of their ordinary issued share capital to South African individuals or groups who qualify under the Broad-Based Black Economic Empowerment Act of 2003 (“the Act”). This Act requires a minimum percentage of the company to be black-owned in order to address the disproportionate distribution of wealth amongst racial groups in South Africa due to the legacy of Apartheid. These transactions are usually structured in such a way to allow the BEE partner to participate in the upside of the share price beyond a certain level but not in the downside which replicates a call option on the share price of the issuing company. The cost of both ESOs and BEE deals has to be accounted for on the balance sheet of the issuing company at its fair-value. Neither of these instruments can be traded and their extended option lifetimes are features that distinguish these deals significantly from regular traded options for which liquid markets exist. This makes pricing them a non-trivial exercise. A number of types of mathematical models have been developed to take the unique structure features into account to price them as accurately as possible. Research by Huddart&Lang (1995&1996) has shown that option holders often exercise their vested options long before the maturity of the transactions but are unable to quantify a measure that can be used. The wide variety of factors influencing option holders (recent stock price movements, market-to-strike ratio, proximity of vesting dates, time to maturity, share price volatility and wealth of option holder) as well as little exercise data publicly available prevents the options from being priced in a consistent manner. Various assumptions regarding the exercise behaviour of option holders are used that are not based on empirical observations even though the option prices are sensitive to this input. This dissertation provides an overview of the models, inputs and exercise behaviour assumptions that are recognized in pricing both ESOs and BEE deals under IFRS 2 in South Africa. This puts the reader in a position to evaluate all pricing aspects of these deals. Furthermore, their structuring are also analysed in order to identify the general issues related to them. A number of methods to manage the pricing issue surrounding exercise behaviour on ESOs have been considered for the South African market. The ESO Upper Bound-methodology showed that for each strike there is a threshold at which exercise will occur and the employee can invest the after-tax proceeds in a diversified portfolio with a higher expected return than that of the single equity option. This approach reduces the standard Black-Scholes option value without relying on assumptions about the employee’s exercise behaviour and is a viable alternative for the South African market. The derived option value represents the cost of the option. Seven large listed companies’ BEE transactions are dissected and compared against one another using the fair-value of the transaction as a percentage of the market capitalization of the company. The author shows how this measure is a more equitable way of assigning BEE credits to companies than the current practice which is shareholding-based. The current approach does not reward the effort (read cost) that a company has undertaken to transfer shares to black South Africans but only focuses on the amount that is finally owned by the BEE participants. This leaves the transaction vulnerable to a volatile share price and leads to transactions with extended lock-in periods that do not provide much economic benefit to the BEE participants for many years. Other inefficiencies in the type of BEE transactions that have emerged in reaction to the BEE codes that have been published by the South African government are also considered. Finally the funding model that is often used to facilitate these deals is assessed and the risks involved for the funder (bank) is reflected on.
Dissertation (MSc)--University of Pretoria, 2011.
Mathematics and Applied Mathematics
unrestricted
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Books on the topic "Multidimensional Black Scholes market"

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Option pricing: Black-scholes made easy : a visual way to understand stock options, option prices, and stock-market volatility. New York: Wiley, 2001.

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Book chapters on the topic "Multidimensional Black Scholes market"

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Koleva, Miglena N., and Lubin G. Vulkov. "Two-Grid Decoupled Method for a Black-Scholes Increased Market Volatility Model." In Numerical Methods and Applications, 271–78. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15585-2_30.

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"Derivatives in the Black–Scholes Market." In Lectures on Mathematical Finance and Related Topics, 201–63. WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811209574_0008.

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HU, YAOZHONG, BERNT ØKSENDAL, and AGNÈS SULEM. "OPTIMAL PORTFOLIO IN A FRACTIONAL BLACK & SCHOLES MARKET." In Mathematical Physics and Stochastic Analysis, 267–79. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792167_0021.

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"Deviations from the Black-Scholes paradigm II: market frictions." In Mathematical Methods for Foreign Exchange, 617–43. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812385307_0014.

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Björk, Tomas. "Completeness and Hedging." In Arbitrage Theory in Continuous Time, 119–27. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198851615.003.0008.

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The concept of market completeness is discussed in some detail and we prove that the Black–Scholes model is complete. We also discuss how completeness and absence of arbitrage is related to the number of risky assets and the number of random sources in the model.
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Osorio, Roberto, and Lisa Borland. "Distributions of High-Frequency Stock-Market Observables." In Nonextensive Entropy. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195159769.003.0023.

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Power laws and scaling are two features that have been known for some time in the distribution of returns (i.e., price fluctuations), and, more recently, in the distribution of volumes (i.e., numbers of shares traded) of financial assets. As in numerous examples in physics, these power laws can be understood as the asymptotic behavior of distributions that derive from nonextensive thermostatistics. Recent applications of the (Q-Gaussian distribution to returns of exchange rates and stock indices are extended here for individual U.S. stocks over very small time intervals and explained in terms of a feedback mechanism in the dynamics of price formation. In addition, we discuss some new empirical findings for the probability density of low volumes and show how the overall volume distribution is described by a function derived from q-exponentials. In March 1900 at the Sorbonne, a 30-year-old student—who had studied under Poincaré—submitted a doctoral thesis [2] that demonstrated an intimate knowledge of trading operations in the Paris Bourse. He proposed a probabilistic method to value some options on rentes, which were then the standard French government bonds. His work was based on the idea that rente prices evolved according to a random-walk process that resulted in a Gaussian distribution of price differences with a dispersion proportional to the square root of time. Although the importance of Louis Bachelier's accomplishment was not recognized by his contemporaries [24], it preceded by five years Einstein's famous independent, but mathematically equivalent, description of diffusion under Brownian motion. The idea of a Gaussian random-walk process (later preferably applied to logarithmic prices) eventually became one of the basic tenets of most twentieth-century quantitative works in finance, including the Black-Scholes [3] complete solution to the option-valuation problem—of which a special case had been solved by Bachelier in his thesis. In the times of the celebrated Black-Scholes solution, however, a change in perspective was already under way. Starting with the groundbreaking works of Mandelbrot [18] and Fama [11], it gradually became apparent that probability distribution functions of price changes of assets (including commodities, stocks, and bonds), indices, and exchange rates do not follow Bachelier's principle of Gaussian (or "normal") behavior.
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"EUROPEAN OPTION PRICING MODELS: THE PRECURSORS OF THE BLACK–SCHOLES–MERTON THEORY AND HOLES DURING MARKET TURBULENCE." In Derivatives, Risk Management & Value, 367–402. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812838636_0008.

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"The concept of continuous models. Limiting transitions from a discrete market to a continuous one. The Black-Scholes formula." In Translations of Mathematical Monographs, 93–97. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/mmono/184/10.

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Davis, Mark H. A. "6. Fund management." In Mathematical Finance: A Very Short Introduction, 94–105. Oxford University Press, 2019. http://dx.doi.org/10.1093/actrade/9780198787945.003.0006.

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‘Fund management’ discusses the objective to form portfolios of assets so as to maximize the investment return. A mathematical finance-oriented approach to optimal investment, in the context of the Black–Scholes price model, was proposed by Robert Merton in 1969. Fund management is a huge industry, and has become much more technical with the emergence of hedge funds deploying sophisticated strategies. There have been many attempts at constructing mathematical models for asset allocation that match real market behaviour more closely. The basic problem is that markets appear so erratic. Is there anything about them that is more invariant? The scenario tree model for long-term asset liability management is explained.
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Theodorou, Petros. "Business Strategy, Structure and IT Alignment." In Encyclopedia of Information Science and Technology, First Edition, 356–61. IGI Global, 2005. http://dx.doi.org/10.4018/978-1-59140-553-5.ch063.

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The structure of production during the last decade has been changed radically. The importance of design, flexibility, quality, and dependability increased. The main motive behind that restructuring seems to be the qualitative and quantitative diversification of demand (regulatory, technology, and other issues can be mentioned as well). The diversification of demand forced production to be more flexible in order to accommodate the environment’s variations. Information systems (IS) proved to be a perfect ‘partner’ for the enterprise who wants to move along at this pace: to increase competitive advantage and retain its competitive position in the market. The capabilities of information technology (IT) for increasing competitive advantage forced management to consider IT in the strategic planning process and to consider IT not as a mere tool of bolts and nuts, but as a strategic partner. The key for the successful IT-IS adoption is the strategic IT alignment model. According to this, IT should be aligned with organizations’ structure and employees’ culture in order to avoid resistance and increase core competence at the strategic level. But the strategic options offered by advanced IT investments are not appraised by using the usual hard financial criteria. Instead, Black and Scholes developed a financial formula to valuate derivative financial products and open the road to valuate options offered by real investments. Thus, the application of Black and Scholes’ formula offers an opportunity to valuate financially strategic IT investment.
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Conference papers on the topic "Multidimensional Black Scholes market"

1

Gnanavel, R., O. Pandithurai, K. S. Hareni, and K. Jayalakshmi. "Prophecy of share market price by using black scholes model." In 2017 Third International Conference on Science Technology Engineering & Management (ICONSTEM). IEEE, 2017. http://dx.doi.org/10.1109/iconstem.2017.8261296.

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2

Zhou, Wei, Meiying Yang, and Liyan Han. "Black-Scholes versus Artificial Neural Networks in Pricing Call Warrants: the Case of China Market." In Third International Conference on Natural Computation (ICNC 2007). IEEE, 2007. http://dx.doi.org/10.1109/icnc.2007.285.

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3

Yin, Xiangfei. "Is it reasonable to price options in China's stock market by Black-Scholes Option Pricing formula?" In 2011 International Conference on Electronics, Communications and Control (ICECC). IEEE, 2011. http://dx.doi.org/10.1109/icecc.2011.6066609.

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