國立清華大學 數學系

Abstract Option pricing is a problem which provides a very natural way to introduce Stochastic Calculus, a topic of Mathematics that has developed very rapidly since Black and Scholes introduced their formula, in 1971-1973. This required the use of the Ito Calculus, which itself requires a perfect understanding of Lebesgue integral, Kolmogorov filtrations, Meyer's Martingales. But one can get a very good insight of the basic ideas thanks to an idea of Sharp, an Economics Nobel Price winner that was developed by Cox, Ross, and Rubinstein. One of the first idea is to understand in what way the probability used is introduced. It provides fficient algorithms easy to understand. Note: This lecture include exercises in Scilab. Please repare your own laptop and install Scilab from https://www.scilab.org/en/download/6.0.1 in advance.