|Abstract: ||The thesis consists of three chapters which focus on two broad topics, applying machine learning in ﬁnance (Chapters 1 and 2) and extracting implied information from options (Chapter 3).
In Chapter 1, I combine the data-driven approach from the machine learning community and economic theory from the ﬁnance community to design a deep neural network to estimate the implied volatility surface.
Chapter 2 is a second example of applying machine learning in ﬁnance. Yang et al.  proposes a gated neural network for pricing European call options. Yang et al.  is rewritten in this chapter using the general framework introduced in Chapter 1.
In Chapter 3, I provide a solution to the following question. Is there any ﬂexible implementation framework to derive the conditional risk neutral density of any arbitrary period of return and calculate corresponding statistics, namely, implied variance, implied skewness and implied kurtosis from option prices? I solve this problem by proposing a framework combining implied volatility surface and Automatic Differentiation [Rall, 1981, Neidinger, 2010, Griewank and Walther, 2008, Baydin et al., 2015].|