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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:

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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.


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