• Title/Summary/Keyword: Greeks

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Asymptotic computation of Greeks under a stochastic volatility model

  • Park, Sang-Hyeon;Lee, Kiseop
    • Communications for Statistical Applications and Methods
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    • v.23 no.1
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    • pp.21-32
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    • 2016
  • We study asymptotic expansion formulae for numerical computation of Greeks (i.e. sensitivity) in finance. Our approach is based on the integration-by-parts formula of the Malliavin calculus. We propose asymptotic expansion of Greeks for a stochastic volatility model using the Greeks formula of the Black-Scholes model. A singular perturbation method is applied to derive asymptotic Greeks formulae. We also provide numerical simulation of our method and compare it to the Monte Carlo finite difference approach.

ACCURATE AND EFFICIENT COMPUTATIONS FOR THE GREEKS OF EUROPEAN MULTI-ASSET OPTIONS

  • Lee, Seunggyu;Li, Yibao;Choi, Yongho;Hwang, Hyoungseok;Kim, Junseok
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.18 no.1
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    • pp.61-74
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    • 2014
  • This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

A Study on the Dance Costume of Greece (그리이스 무용 형식에 관한 연구)

  • 임상임
    • Journal of the Korean Home Economics Association
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    • v.36 no.10
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    • pp.119-130
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    • 1998
  • This is on the dance costume of ancient Greece. The present study classified the characteristics of Greek dance and dance costume according to the silhouette, quality of material, color and ornaments. Materials of the study are the pictures and figures presented in literatures, sculptures, crockeries, murals, coins. The dances of Greece can be classified into religious dance, educational dance, recreational dance, dramatic dance and various forms of dance on each dances were developed. Especially, it is the greatest character that Greeks gave dances educational value and created composit art including song, lines and dance. As dance costume, Himation, Chiton, Chlamys which Greeks generally wore were widely worn. Also, the beauty of dance costume was maximized by the changes of basic costumes and development of various ways of wearing. Especially, professional dancers wore costumes shorter than knee-length ones forming a A-line silhouette different from a cylindrical one. Thin cloth revealing body silhouette such as fiax hemp, linen, silk were used as materials of dance costumes. As for colors, white was mainly used, But orange, blue and green were used, too. They wore band, scarf, bonnet on the head and seldom used any ornaments except for fibula. They wore the same sandals which Greeks wore, Crepis, front-heeled shoes which is thought to be the origin of modern ballet shoes for the technique of toe in dance. As mentioned above, as the dance costume of Greece were mainly worn as the similar forms of the dance costume of Greeks, various forms of costumes were worn with the development of dance and bold ways of wearing and silhouette were developed unlike the costume of common people.

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Fractal Interest Rate Model

  • Rhee, Joon-Hee;Kim, Yoon-Tae
    • Proceedings of the Korean Statistical Society Conference
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    • 2005.05a
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    • pp.179-184
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    • 2005
  • Empirical findings on interet rate dynamics imply that short rates show some long memories and non-Markovin. It is well-known that fractional Brownian motion(fBm) is a proper candidate for modelling this empirical phenomena. fBm, however, is not a semimartingale process. For this reason, it is very hard to apply such processes for asset price modelling. With some modifications, this paper investigate the fBm interest rate theory, and obtain a pure discount bond price and Greeks.

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THE GREEK CONCEPTION OF THE OTTOMAN ERA: ISLAMOPHOBIA AND MUSLIMS LABELED AS THE OTHER

  • OZSUER, ESRA
    • Acta Via Serica
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    • v.2 no.2
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    • pp.47-68
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    • 2017
  • To the Greeks, the Ottoman era was a "Dark Age" one that comprised a threat to their Greek Orthodox identity. The identities of Orthodox and Hellene were integral parts in the construction of their national history. In fact, the Morea Uprising, which began in 1821, was symbolized by a priest blessing the Greek flag in Aya Lavra Church. One of the most common national myths is religious oppression of the Christian population during the Ottoman Era, namely Turkokratia. They identified Ottomans as Asian barbarians who did not let Greeks practice their religion freely, and who furthermore forced them to change their religion. These kinds of beliefs, which might be taken as religious propaganda, are today still highlighted both in Greek textbooks and in publications supported by the church and books and newspapers published in their affiliated institutes. The underlying truth behind all these propagandist statements is Islamophobia. The existence of Islamophobia in the Balkans, where religious nationalism is intense, has caused nations to hold to these kinds of mythical beliefs. Most of the time the stories and narratives have been used for history building. The objective of this paper is to demonstrate the effect of the anti-Islam propaganda of the church in Greece on the state and the people using Greek sources. The references are Greek religious textbooks and books and newspapers published by church-supporting publishing houses.

The Default Risk of the Research Funding with Uncertain Variable in South Korea, Along with the Greeks (옵션민감도를 고려한 기술자금의 경제적 가치와 실패확률)

  • Sim, Jaehun
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.44 no.1
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    • pp.1-8
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    • 2021
  • As a nation experiencing rapid economic growth, South Korea and its government have made a continuous effort toward efficient research investments to achieve transformation of the Korean industry for the fourth industrial revolution. To achieve the maximum effectiveness of the research investments, it is necessary to evaluate its funding's worth and default risk. Thus, incorporating the concepts of the Black-Scholes-Merton model and the Greeks, this study develops a default-risk evaluation model in the foundation of a system dynamics methodology. By utilizing the proposed model, this study estimates the monetary worth and the default risks of research funding in the public and private sectors of Information and Communication technologies, along with the sensitivity of the R&D economic worth of research funding to changes in a given parameter. This study finds that the public sector has more potential than the private sector in terms of monetary worth and that the default risks of three types of research funding are relatively high. Through a sensitivity analysis, the results indicate that uncertainty in volatility, operation period, and a risk-free interest rate has trivial impacts on the monetary worth of research funding, while volatility has large impacts on the default risk among the uncertain factors.

An Improved Binomial Method using Cell Averages for Option Pricing

  • Moon, Kyoung-Sook;Kim, Hong-Joong
    • Industrial Engineering and Management Systems
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    • v.10 no.2
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    • pp.170-177
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    • 2011
  • We present an improved binomial method for pricing financial deriva-tives by using cell averages. After non-overlapping cells are introduced around each node in the binomial tree, the proposed method calculates cell averages of payoffs at expiry and then performs the backward valuation process. The price of the derivative and its hedging parameters such as Greeks on the valuation date are then computed using the compact scheme and Richardson extrapolation. The simulation results for European and American barrier options show that the pro-posed method gives much more accurate price and Greeks than other recent lattice methods with less computational effort.

FINITE DIFFERENCE METHOD FOR THE TWO-DIMENSIONAL BLACK-SCHOLES EQUATION WITH A HYBRID BOUNDARY CONDITION

  • HEO, YOUNGJIN;HAN, HYUNSOO;JANG, HANBYEOL;CHOI, YONGHO;KIM, JUNSEOK
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.23 no.1
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    • pp.19-30
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    • 2019
  • In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

수학과 음악

  • 김성숙
    • Journal for History of Mathematics
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    • v.15 no.2
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    • pp.93-100
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    • 2002
  • Mathematics and music play very different roles in our society. However, they are closely related to each other In the time of the ancient Greeks, they were strongly connected. This paper identifies such connection and concludes that music has mathematical characteristics.

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