https://github.com/daleroberts/math-finance-cheat-sheet

Mathematical finance cheat sheet.
https://github.com/daleroberts/math-finance-cheat-sheet

finance mathematics probability

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Mathematical finance cheat sheet.

• Host: GitHub
• URL: https://github.com/daleroberts/math-finance-cheat-sheet
• Owner: daleroberts
• License: gpl-3.0
• Created: 2014-05-02T00:19:01.000Z (over 10 years ago)
• Default Branch: master
• Last Pushed: 2019-08-30T02:32:38.000Z (over 5 years ago)
• Last Synced: 2024-10-15T18:44:57.407Z (2 months ago)
• Topics: finance, mathematics, probability
• Language: TeX
• Homepage:
• Size: 2.61 MB
• Stars: 228
• Watchers: 15
• Forks: 31
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Mathematical Finance Cheat Sheet

A one page cheat sheet (double-sided) on some of the main tools and models used in Mathematical Finance. A 'Brownian Motion only' version can be found in this [branch](https://github.com/daleroberts/math-finance-cheat-sheet/tree/bm-only/). Download the [PDF](https://rawgithub.com/daleroberts/math-finance-cheat-sheet/master/math-finance-cheat-sheet.pdf), here is a thumbnail:

![thumbnail](https://rawgithub.com/daleroberts/math-finance-cheat-sheet/master/thumb.png)

This cheat sheet is aimed for students and derivative-pricing quants that are interviewing. In fact, this is what I give my undergraduate students for their final exam. It has a stronger focus on interest-rate derivative results since most "Black Scholes" results are easily derived from scratch. Explicit pricing formulas (e.g., bonds or options under the Vasicek or CIR model) are not given as I typically assume they can also be derived as well (and they make fine exam questions).

## Contents

  * Normal random variables: univariate and multivariate case. Moment generating function.

  * Gaussian shift theorem

  * How to correlate Brownian motions

  * How to identify a martingale from SDE representation

  * Novikov's condition

  * Stochastic integrals (on BM version)

  * Itô's formula in one-dimensional case

  * The product rule

  * The Radon-Nikodym derivative

  * Cameron-Martin-Girsanov Theorem and its Converse

  * Martingale Representation Theorem

  * Multidimensional Diffusions, Quadration Covariation, and Multi-dimensional Itô's Formulas

  * The Stochastic Exponential

  * Solving Linear Ordinary Differential Equations

  * Solving Linear Stochastic Differential Equations

  * Fundamental Theorem of Asset Pricing

  * Market Price of Risk

  * Black's Model

  * Conversion between Forward Rates, Short Rates, Yields, and Bond Prices

  * Short-Rate and No-Arbitrage Models

  * Bond Pricing for Affine Models

  * The Heath-Jarrow-Morton Framework

  * The LIBOR Market Model

  

 

## Contributions

Contributions to this cheat sheet will generally be accepted if they fit within the philosophy that everything fits to a double-sided A4 page.