European Style Derivatives

  • You-lan Zhu
  • Xiaonan Wu
  • I-Liang Chern
  • Zhi-zhong Sun
Part of the Springer Finance book series (FINANCE)


As examples, in Figs.1.1–1.7 we showed how the prices of assets vary with time t. Figure 2.1 shows the stock price of Microsoft Inc. in the period March 30, 1999, to June 8, 2000. From these figures, we can see the following: the graphs are jagged, and the size of the jags changes all the time. This means that we cannot express S as a smooth function of t, and it is difficult to predict exactly the price at time t from the price before time t. It is natural to think of the price at time t as a random variable. Now let us give a model for such a random variable.


Stock Price Asset Price Stochastic Differential Equation Option Price Wiener Process 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • You-lan Zhu
    • 1
  • Xiaonan Wu
    • 2
  • I-Liang Chern
    • 3
  • Zhi-zhong Sun
    • 4
  1. 1.Department of Mathematics & StatisticsUniversity of North CarolinaCharlotteUSA
  2. 2.Department of MathematicsHong Kong Baptist UniversityHong KongPeople’s Republic of China
  3. 3.Department of MathematicsNational Taiwan UniversityTaipeiTaiwan R.O.C.
  4. 4.Department of MathematicsSoutheast UniversityNanjingPeople’s Republic of China

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