Notes: Ait-Sahalia and Jacod (2010)

Some words...

1. Introduction In this post, I summarize the econometric method introduced in Analyzing the Spectrum of Asset Returns (JEL 2011) by Yacine Ait-Sahalia and Jean Jacod. From an economic perspective, Delbaen and Schachermayer (1994) (Theorem $1.1$) … [Continue reading]

Notes: Kristensen and Mele (2011)

Percentage errors from approximating option prices...

1. Introduction In this post, I work through Adding and Subtracting Black Scholes, JFE (2011) by Antonio Mele and Dennis Kristensen. This paper develops a method for approximating the price of an asset where no closed form expression exists. In the … [Continue reading]

The Buckingham Pi Theorem

Frame from slow motion footage of the Trinity nuclear test with distance measurement at the bottom showing the blast radius.

1. Introduction In this post I outline the Buckingham $\pi$ Theorem which shows how to use dimensional analysis to compute answers to seemingly intractable physical problems. For instance, in $1950$ Geoffrey Taylor used the theorem to work out the … [Continue reading]

Notes: Glosten and Milgrom (1985)

x-axis: Price of risky asset. Panel (a): Value function for the high (red) and low (blue) type informed trader. Panel (b): Bid (red) and ask (blue) prices for the risky asset. Panel (c): Between trade price drift.

1. Introduction In this post, I replicate the main results from Glosten and Milgrom (1985) using the setup outlined in Back and Baruch (2003). I begin in Section $2$ by laying out the continuous time asset pricing framework. I consider the behavior … [Continue reading]