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

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.

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.

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 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
\(S_1\).

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.