# Teaching NotesΒΆ

## Translog Cost Function Estimation

This post focuses on the translog cost function. I discuss the linear homogeneity constraint, the technique to impose the constraint, and its estimation via

• Ordinary Least Square (OLS)
• Stochastic Frontier Analysis (SFA)

Code examples are provided, too.

## Translog Production and Cost Functions

In this post, I'll carefully explain the derivation of cost function from a CES production function, as well as the derivation of translog (transcendental logarithmic) production and cost functions.

flowchart TB
subgraph Production
A[Production Function] -. approximation .-> D(Translog Production Function)
end
subgraph Cost
B[Cost Function] -. approximation .-> C(Translog Cost Function)
end
A == Conversion via Duality ==> B

Before I start, the graph above illustrate the relations. Specifically, we can derive the cost function from a CES production function via the duality theorem. Translog production and translog cost functions are approximations to the production and corresponding cost function, respectively, via Taylor expansion.

## GARCH-Constant Conditional Correlation (CCC)

This post details a multivariate GARCH Constant Conditional Correlation (CCC) model. It was somewhat surprising that I didn't find a good Python implementation of GARCH-CCC, so I wrote my own, see documentation on frds.io. It performs very well, often generates (marginally) better estimates than in Stata based on log-likelihood.

## 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.

## 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.