An Introduction to Stochastic Analysis
Before we can start to explain the option pricing theory of Black & Scholes it is necessary to build up a toolbox of stochastic analysis. This chapter introduces the Ito integral and the Ito formula, which constitute the foundation of stochastic analysis. The martingale property is discussed together with conditional expectation. We restrict our attention to those parts of stochastic analysis that are useful to option theory. Since we try to avoid too advanced mathematics, we shall resort to intuitive arguments rather than being mathematically stringent when presenting the theory. The more theoretically inclined reader is advised to look in [33,41] for a thorough introduction to stochastic analysis and its many applications.
KeywordsStochastic Process Brownian Motion Stock Price Stochastic Differential Equation Option Price
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