オプション価格理論の学説史(2)

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書誌事項

タイトル別名
  • Option Pricing Models: The Review of Literatures (2)
  • ブロンジーノ・モデル(1908)とその拡張
  • Bronzin (1908) and Its extensions

説明

This paper investigates the option pricing model by Bronzin (1908) and its extensions. His approach is different from Bachelier (1900) that is the oldest option pricing model and other option pricing models such as Black and Scholes (1973). He derived the European option pricing model by integrating the survival function　(one minus distribution function) of the underlying asset. We try to extend his basic model in the following three points. The first, it is possible to obtain the same result based on definite integral, rather than indefinite integral as done by Bronzin. Secondly, as a result, visualization of the option premium becomes possible because the premium can be represented by the area under the survival function. Thirdly, we study the way to incorporate the risk preference of the investors in the option premium. The risk adjustment can be done by moving the survival function up and down. As an example, Black and Scholes (1973) model can be obtained by sifting the survival probability curve downward by the risk premium. It corresponds to a change of the drift term from the expected return to the risk free rate.

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