These past two months I’ve found out exactly how hard it is to write a project proposal in Math and Stats. My ideas focused on detection schemes similar to my thesis, but had elements of market microstructure. I hope you take a look!

LSE Statistics Proposal:

It’s about detecting adverse selection events, and learning about how the order book changes when a private signal makes it to informed traders.

LSE Mathematics Proposal:

It’s about also detecting adverse selection events, but emphasizing the use of queuing theory, learning the mathematics behind the thresholds and constraints faced by investors when they cause these changes.

Originally published January 19, 2021

Hi, this is very overdue but I thought I should upload my old stochastic optimization project. I did it as the final rpoject for the course stochastic optimization by computer simulation MATH 795-61 at the graduate center. The course (website) was taught by Prof. Felisa Vasquez-Abad and the it gave a statistical footing on the underpinnings of machine learning.

The project was about calibrating the parameters from the Heston stochastic volatility to a time series of closing option prices. The work uses stochastic optimization to minimize the MSE between the observed option prices and the simulated option prices.

I should make a demo on github but the project paper is great on its own.

github link

Originally published: September 25, 2020

Hello all,

Putting out the current draft of my thesis beamer just in case anyone wants to check it out. Still working on a useful application, and incorporating CUSUM statistics for spreads but this work some cool insights.

Ivan

Abstract:

In this thesis, our objective is to study the relationship between transaction price and volume in the BTC/USD Coinbase exchange. In the second chapter, we develop a consecutive CUSUM algorithm to detect instantaneous changes in the arrival rate of market orders. We begin by estimating a baseline rate using the assumption of a local time-homogeneous compound Poisson process. Our observations lead us to reject the plausibility of a time-homogeneous compound Poisson model on a more global scale by using a chi-squared test. We thus proceed to use CUSUM-based alarms to detect consecutive upward and downward changes in the arrival rate of market orders. In the third chapter we identify active periods from the number of consecutive upward CUSUM alarms, leading to the classification of active versus inactive periods. Finally we use One-Way ANOVA to assess the level effect on price swings for periods classified as containing at least two or three consecutive CUSUM up alarms. We show that in these active periods, price swings are significantly larger.

Link: A Study of CUSUM Statistics on Bitcoin Transactions

Originally published: July 23, 2020

In this blog post I talk a little about Markov Processes as a foundation for the traditional BSM-OPM derivation. Since RMarkdown API is depreciated,  I can’t post the RMarkdown notebook directly on wordpress. I kindly ask you to check it out on github.

.pdf version:

Markov Processes – Foundations of Stochastic Finance

Originally published January 17, 2019

In this blog post I start the series every way to derive BSM-OPM. Here I demonstrate the easiest most intuitive way. Since RMarkdown API is depreciated,  I can’t post the RMarkdown notebook directly on wordpress. I kindly ask you to check it out on github. I basically cover Alexei Krouglov’s derivation.

.pdf version:

Intuitive Probabilistic Derivation of Black Scholes – Option Pricing Formula

Originally published: November 20, 2018

Today’s synthesis is a semisynthesis of (+)-Chromazonarol and (+)-Yuhazunone. These preps start a natural sesquiterpene fragrance Sclareolide. I haven’t developed the intuition yet, but clever functional group interconversion and novel synthetic techniques are the drivers behind remarkable semisyntheses.

Baran showcases the prep of a “Borono-Sclareolide” to access a wide range of Meroterpenoids.  A scalable semisynthesis from (+)-Sclareol to get to (+)-8-O-Acetylchromazonarol and (+)-8-O-Acetylyahazunone. A Li, Csuk, and Li collaboration cut’s Baran’s 7 step prep down to 5 (6 if you count) the Acetyl deprotection. Li, Csuk, and Li improve on Baran’s work by having the core finished in 3 steps compared to Baran’s 6 steps. In addition, Li, Csuk, and Li’s synthesis doesn’t hinge on a Alcohol directed hydroboration to set a stereocenter which resolves one of Baran’s issues. Wu also resolves this issue through a palladium cross coupling but given this groups goals of creating a divergent synthesis, they could not afford to save steps by sacrificing the functionality of the 1,4 benzoquinone.

Originally published: September 18, 2018