# Teaching Notes¶

## 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.

## Kyle's Lambda

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.

## Variance Ratio Test - Lo and MacKinlay (1988)

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

## Minimum Variance Hedge Ratio

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.

## Call Option Value from Two Approaches

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 $$S_1$$.

## Reconciliation of Black-Scholes Variants

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 - Unlevered and Levered

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

## Accumulator Option Pricing

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.