Notes
Machine Learning
Basics of Reinforcement Learning
This tutorial provides an introduction to the fundamentals of reinforcement learning. The main reference is the video lecture series by Sergey Levine.
Quantitative Finance
Solution Manual to Stochastic Calculus for Finance II
Stochastic Calculus for Finance II is one of the most accessible books in mathematical finance. The prerequisites for understanding the material include familiarity with graduate-level probability theory and a solid knowledge of mathematical analysis. Here, I have compiled the solutions I prepared for the exercises in this book.
Exotic Options
Exotic options, a category of derivative securities, feature complex structures and unique payoff mechanisms that differ from standard options like European and American options. The document provides some details on the pricing of barrier options (e.g., up & out), lookback options, and Asian options based on geometric Brownian motion assets.
Feynman-Kac Theorem
Feynman-Kac Theorem states that the price of a derivative can be represented as the solution to a certain PDE. The document provides some concrete examples on how Feynman-Kac Theorem can be used for pricing derivatives.
The Dupire Formula
Dupire's formula is a fundamental result in quantitative finance that provides a framework for modeling the local volatility of an asset. It relates the local volatility of an underlying asset to the prices of European call and put options across different strikes and maturities. The document provides a proof of this formula.
Implied Volatility
Implied volatility reflects the market's forecast of a security's price fluctuation over a specific period. It is derived from the market price of an option and represents the volatility that, when input into the Black-Scholes model, yields the observed market price. The page includes Python code that calculates IV for index options using a combination of bisection and Newton root finding.