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