@inbook{a20728407c214b06a7e9ac2fd26fbc82,
title = "The Martingale Approach",
abstract = "The martingale approach is widely used in the literature on contingent claim analysis. Following the definition of a martingale process, we give some examples, including the Wiener process, stochastic integral, and exponential martingale. We then present the Girsanov{\textquoteright}s theorem on a change of measure. As an application, we derive the Black–Scholes formula under risk neutral measure. A brief discussion on the pricing kernel representation and the Feynman–Kac formula is also included.",
keywords = "Option Price, Quadratic Variation, Stochastic Differential Equation, Stock Price, Wiener Process",
author = "Carl Chiarella and He, {Xue Zhong} and Nikitopoulos, {Christina Sklibosios}",
note = "Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",
year = "2015",
doi = "10.1007/978-3-662-45906-5_8",
language = "English",
series = "Dynamic Modeling and Econometrics in Economics and Finance",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "157--189",
booktitle = "Dynamic Modeling and Econometrics in Economics and Finance",
}