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A Study on Black-Scholes Formula with Computer Simulations and Graphics

Author

Listed:
  • Yukari Shirota

Abstract

学生にとって難解と思われているブラック=ショールズ方程式であるが,視覚的にグラフィクス表現することで,理解が容易になる。本稿では,その確率的ブラウン運動を含む確率微分方程式に関するシミュレーション実験結果と代数学的に求められる理論的結果を3次元グラフィクスにより示す。確率的現象をコンピュータ上で再現することで,確率的ブラウン運動の理解が容易になり,同時に理論的に求められる正規分布を示し両者を比較することで,理論的事柄の理解を深める。また,オプションの期待値の導出過程における,期待値計算の積分計算範囲を,正規分布に従う確率変数と対数正規分布に従う確率変数に関して,両者同時にグラフィクスで視覚的に示す。本稿のグラフィクスの特長は,変数間の関係をスライダー操作によるモーションとして表現した点である。スライダーで変数を動かすことにより,複雑な関係式における他の変数への影響の理解が容易になる。

Suggested Citation

  • Yukari Shirota, 2013. "A Study on Black-Scholes Formula with Computer Simulations and Graphics," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 49(4), pages 251-260.
  • Handle: RePEc:abc:gakuep:49-4-3
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    File URL: http://www.gakushuin.ac.jp/univ/eco/gakkai/pdf_files/keizai_ronsyuu/contents/contents2013/4904/4904shirota/4904shirota.pdf
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    Cited by:

    1. Sudip Chaudhuri, 2015. "Premature Deindustrialization in India and Re thinking the Role of Government [La désindustrialisation précoce en Inde : pour un nouveau rôle du gouvernement]," Working Papers halshs-01143795, HAL.
    2. Christian Walter, 2015. "Jumps in financial modelling: pitting the Black-Scholes model refinement programme against the Mandelbrot programme [La modélisation des discontinuités boursières : le programme de Mandelbrot et le," Working Papers halshs-01146581, HAL.
    3. Lucas Chancel & Géraldine Thiry & Damien Demailly, 2014. "Les nouveaux indicateurs de prospérité : pour quoi faire ? Enseignements de six expériences nationales," Working Papers halshs-01060845, HAL.
    4. Christian Walter, 2015. "The two quantifications of the financial theory. A contribution to the critical history of financial modelling [Les deux quantifications de la théorie financière. Contribution à une histoire critiq," Working Papers halshs-01118147, HAL.
    5. Guilhem Fabre, 2015. "The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign? [La part du lion, acte 2 : Les dessous de la campagne anti-corruption en Chine]," Working Papers halshs-01143800, HAL.
    6. Géraldine Thiry & Léa Sébastien & Tom Bauler, 2014. "Ce que révèle le discours des acteurs officiels sur un « au-delà du PIB »," Working Papers halshs-01081451, HAL.
    7. Géraldine Thiry & Philippe Roman, 2014. "The Inclusive Wealth Index. A Sustainability Indicator, Really?," Working Papers halshs-01011250, HAL.

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