Financial instruments exhibit very dynamic behavior over time. Individuals dealing with them must understand the nitty-gritty details and associated risks to maximize profit. This knowledge can come in both white-box and black-box forms. As a data science practitioner, one would be more interested in the former. Deterministic models of financial instruments are often unproductive as they fail to capture hidden factors and the resulting uncertainty that may lead to potential business losses. Conversely, stochastic methods, particularly time-dependent stochastic processes, are far more effective in this regard.

Stochastic finance encompasses techniques for modeling financial instruments through stochastic processes. It goes beyond theory, focusing on designing and implementing these models in a programming language, particularly Python. The two main objectives are forecasting an instrument's future behavior and capturing uncertainty (i.e., risks), as these help investors manage their budgets effectively. Modeling the underlying stochastic process is a standard part of the solution in both cases.

Stochastic Finance is rooted in Probability and Statistics. A solid understanding of probability, statistical estimation theory, and simulations is necessary as prerequisites. Individuals with weaker statistical backgrounds will find the lectures on Probability, Simulation, and stochastic processes in the course beneficial, as most of these foundational topics are thoroughly covered using Python code. Topics like density estimation from characteristic functions should capture learners' interest. Therefore, this course serves as a primer for learning applied statistics from a financial theory perspective, as indicated by the subtitle.

In this course, you will learn:

i. Finance & basic interest theory, computation of returns

ii. Python templates for Monte Carlo simulation

iii. Fundamentals of stochastic processes and how to apply Monte Carlo simulation to generate paths

iv. Stochastic differential equation foundations and diffusion models, accompanied by an MLE-based parameter estimation framework in Python.

v. The jump model template, supported by Ito’s Lemma and the Merton model, emphasizes parameter estimation through a density recovery method based on the characteristic function, as well as the corresponding Python implementation.