1. | Start with a hypothetical problem |
2. | Present and discuss the mathematics needed to solve the problem |
3. | Apply the mathematics to solve the problem |
Proprietary Valuation Models:
Schurman RO1C Model - Discounts for Reliance on One CustomerCommentary on the Valuation Models of Others:
Butler Pinkerton Total Beta Model - PDFThe Dividend Discount Model:
The Dividend Discount Model (DDM) DerivationThe Capital Asset Pricing Model:
Part I - The Derivation of the CAPM - A Single Source of UncertaintyBrownian Motion:
Part I - The Scaled Random WalkThe Mathematics of Vanilla Stock Option Valuation:
Part I - An Introduction to the Valuation ProcessThe Mathematics of Exotic Stock Option Valuation:
Part I - The Reflection Principle For Brownian MotionModeling Events:
The Binomial DistributionThe Yield Curve:
The Spot Rate CurveBond Pricing:
The Short Rate ProcessModeling Bond Prices in Continuous-Time:
Risk-Free Bond Price, Duration and ConvexityLoan Guarantees (BVR Presentation):
Loan Guarantees - Part I: The Two State Guarantee ModelModeling and Pricing for Events (BVR Presentation):
Part I - Annualized Cash FlowModeling The Business Cycle:
Part I - Cyclical RevenueReturn Models and Mean Reversion (BVR Presentation):
Part I - Discrete-Time Return Model Excluding Mean ReversionPortfolio Value Equations (BVR Presentation):
Normally-Distributed Asset ValuesRisk-Neutral Pricing:
Finding the ArbitrageDerivative Pricing in Incomplete Markets:
Pricing Redundant Assets in a Complete MarketModeling Dividends and Other Distributions:
Part I - The Effect Of Dividends On Future Asset PriceCapitalizing Research and Development Expenditures:
Part I - Product Capitalized R&D in Discrete-TimeThe Schurman Parabola:
A Mean-Reverting Revenue ModelThe Newton-Raphson Method of Solving Nonlinear Equations:
Solving Univariate Non-Linear Equations - Derivation and ApplicationSolving Differential Equations in Finance and Economics:
The Integrating Factor Technique - Part IMathematical Series:
Polylogarithms of Order ZeroThe Exponential Integral:
The Exponential Integral - Derivation and SolutionThe Incomplete Gamma Function:
The Incomplete Gamma Function - Derivation and SolutionSome Fun Math Stuff:
Integration By Parts - Part I: The Mathematics And A Simple ExampleThe Practitioners Toolbox:
Valuation in Discrete and Continuous TimeThe Monte Carlo Toolbox:
Pulling Two Correlated Normally-Distributed Random Variates - Part I: Gaussian CopulaProbability and Statistics:
The Calculus of the Normal DistributionPublished Articles:
Valuing Loan Guarantees