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. Download the PDF, here is a thumbnail:

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.