## GARCH Estimation

This post details GARCH(1,1) model and its estimation manually in Python, compared to using libraries and in Stata. For GJR-GARCH(1,1), see my documentation on frds.io.

This post details GARCH(1,1) model and its estimation manually in Python, compared to using libraries and in Stata. For GJR-GARCH(1,1), see my documentation on frds.io.

A measure of market impact cost from Kyle (1985), which can be interpreted as the cost of demanding a certain amount of liquidity over a given time period.

A simple test for the random walk hypothesis of prices and efficient market.

This note briefly explains what's the **minimum variance hedge ratio** and how
to derive it in a cross hedge, where the asset to be hedged is not the same as
underlying asset.

Suppose today the stock price is \(S\) and in one year time, the stock price could be either \(S_1\) or \(S_2\). You hold an European call option on this stock with an exercise price of \(X=S\), where \(S_1<X<S_2\) for simplicity. So you'll exercise the call when the stock price turns out to be \(S_2\) and leave it unexercised if \(S_1\).

This note is just to show that the different variants of Black-Scholes formula in textbook and tutorial solutions are in fact the same.

Beta is a measure of market risk. This post tries to explain the unlevered and levered betas.

An accumulator is a financial derivative that is sometimes known as "*I kill you later*". This post attempts to explain how it is structured and price it via Monte Carlo simulations in Python.