Advanced Securities Pricing with Monte Carlo Simulations

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Securities Pricing

There are a variety of methods used to price securities. I would argue that this topic is as much an art as it is a science. This article discusses the advantages of using simulations (mainly in the form of stochastic inputs) for pricing financial instruments. If you are unfamiliar with securities pricing I would suggest this progression of articles…

Martingales and Markov Processes

  • A gentle introduction to stochastic processes

Geometric Brownian Motion

  • The primary stochastic process used in the Black-Scholes model

Stochastic Integrals

  • The evaluation of stochastic integrals for deriving the Black-Scholes model

Deriving the Black-Scholes Model

  • Deriving the infamous…

Python and Black-Scholes Pricing for Dynamic Hedges

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Option Portfolios

Equities that have a very straightforward exposure to idiosyncratic and systematic risk. Options, on the other hand, have exposure to not only the underlying asset, but also interest rates, time, and volatility. These exposures are inputs to the Black-Scholes option pricing model(see Deriving the Black-Scholes Model). Since these inputs affect the value of the…

Quantitative Research in Derivatives Pricing

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How Trading Desks Do It

The pricing of financial derivatives becomes increasingly complex with respect to the complexity of the instruments being priced. It is not uncommon for a trading desk to assume some underlying model (say a Heston model, for the sake of this example) and fit the model parameters to a market volatility surface to derive an exotic price. Though fitting model parameters may sound ambiguous, the process is relatively straightforward. Using one of the various minimization techniques available (e.g. least-squares) the several parameters of the Heston model (V0, kappa, theta, omega, and rho — if these don’t ring a bell see Stochastic…

A Curated Selection of Books by Topic

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This list comprises books that I have found helpful on my journey in quantitative finance. This list is by no means exhaustive, but I can personally vouch for the usefulness of each of these books as I have read them myself.

Note: I am in no way affiliated with the sale of any book on this list



Calculus: Early Transcendentals

Linear Algebra Done Right

Diffusions, Markov Processes and Martingales: Volume 2, Ito Calculus


Machine Learning: An Applied Mathematics Introduction

Mathematics for Machine Learning

Applied Econometric Time Series

Artificial Intelligence & Machine Learning

Entry Level

Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython

Python Data…

Hands-on Tutorials

A Quickstart Guide to Generative Machine Learning with Code

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Generative machine learning can be helpful in a variety of contexts. One, for example, is when some closed-form or quasi-closed-form solution is available but computationally expensive. In this case, a neural network may provide a timely solution with an acceptable degree of accuracy. Nevertheless, to train such a network, data must be aggregated and in most cases can be scarce. A great example can be found in the setting of pricing exotic options. I’ll leave a link to the SSRN paper if you wish to learn more about this specific example…

A solution to this problem can be found in…

With Real Strategies Developed by Quantitative Research

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Quantitative Research

Backtesting quantitative research prior to implementation in a live trading environment (see Algorithmic Trading with Python or Dynamic Algorithmic Trading Systems) is as essential as it is the fruit of a quantitative researcher’s labor. It’s critical to note that the outcome of a backtest is directly related to the quality of research (which is often reflected by the quality of data). In this article, I want to discuss one of my previous major research efforts in analyzing trading signals from Twitter. …

Researching Algorithmic Trading Signals

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Quantitative Research

In my previous articles, I have discussed at length the development of algorithmic trading systems in a variety of programming languages. Solutions to the intricacies of these systems (architecture, connection, persistence, trade execution, reporting, etc…) can all be found in my previous articles. I have yet to provide a specific example of a trading signal. It should be quite obvious why one may be unable to find academic (or any) literature on this particular topic: it’s lucrative. Trading signals are difficult to research and after identification, there are few reasons to make the findings public. The aim of this article…

A Fast Track Guide to Downloading Twitter Data using Python

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Twitter data is widely used in the world of natural language processing. This article is meant to give you everything you need to get started downloading and working with Twitter data right now.

Twitter’s Developer API

To use Tweepy you need to apply for developer access to receive the necessary keys and authentication tokens.

After applying for, and being granted developer access head over to the developer portal and create a new app.

Algorithmic Trading System Design Patterns

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Efficiency and reusability is critical, especially when building systems that trade multiple securities. I have discussed development using Interactive Broker’s Java and Python API in the past:

I would suggest reading those articles first if you are unfamiliar with Interactive Broker’s API. In this article, I want to further the notion of algorithmic trading by exhibiting a system design pattern that allows for ease of extension to multiple securities.

Establishing a Controller

EClient and EWrapper Classes

The EWrapper class is responsible for receiving data from the server that is requested by the EClient class. More intuitively, we can think…

Roman Paolucci

Quantitative Finance, Mathematics, Artificial Intelligence and Computer Science

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