Risk Neutral Pricing and Financial Mathematics: A Primer provides a foundation to financial mathematics for those whose undergraduate quantitative preparation does not extend beyond calculus, statistics, and linear math. It covers a broad range of foundation topics related to financial modeling, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, and term structure models, along with related valuation and hedging techniques. The joint effort of two authors with a combined 70 years of academic and practitionere

Includes index.

Front Cover; Risk Neutral Pricing and Financial Mathematics; Copyright Page; Dedication; Contents; About the Authors; Preface; 1 Preliminaries and Review; 1.1 Financial Models; 1.2 Financial Securities and Instruments; 1.3 Review of Matrices and Matrix Arithmetic; 1.3.1 Matrix Arithmetic; 1.3.1.1 Matrix Arithmetic Properties; 1.3.1.2 The Inverse Matrix; Illustration: The Gauss-Jordan Method; Illustration: Solving Systems of Equations; 1.3.2 Vector Spaces, Spanning, and Linear Dependence; 1.3.2.1 Linear Dependence and Linear Independence; Illustrations: Linear Dependence and Independence 1.3.2.2 Spanning the Vector Space and the BasisIllustration: Spanning the Vector Space and the Basis; 1.4 Review of Differential Calculus; 1.4.1 Essential Rules for Calculating Derivatives; 1.4.1.1 The Power Rule; 1.4.1.2 The Sum Rule; 1.4.1.3 The Chain Rule; 1.4.1.4 Product and Quotient Rules; 1.4.1.5 Exponential and Log Function Rules; 1.4.2 The Differential; Illustration: The Differential and the Error; 1.4.3 Partial Derivatives; 1.4.3.1 The Chain Rule for Two Independent Variables; 1.4.4 Taylor Polynomials and Expansions; 1.4.5 Optimization and the Method of Lagrange Multipliers Illustration: Lagrange Optimization1.5 Review of Integral Calculus; 1.5.1 Antiderivatives; 1.5.2 Definite Integrals; 1.5.2.1 Reimann Sums; 1.5.3 Change of Variables Technique to Evaluate Integrals; Illustration: Change of Variables Technique for the Indefinite Integral; 1.5.3.1 Change of Variables Technique for the Definite Integral; 1.6 Exercises; Notes; 2 Probability and Risk; 2.1 Uncertainty in Finance; 2.2 Sets and Measures; 2.2.1 Sets; Illustration: Toss of Two Dice; 2.2.1.1 Finite, Countable, and Uncountable Sets; 2.2.2 Measurable Spaces and Measures; 2.3 Probability Spaces 2.3.1 Physical and Risk-Neutral ProbabilitiesIllustration: Probability Space; 2.3.2 Random Variables; Illustration: Discrete Random Variables; 2.4 Statistics and Metrics; 2.4.1 Metrics in Discrete Spaces; 2.4.1.1 Expected Value, Variance, and Standard Deviation; Illustration; 2.4.1.2 Co-movement Statistics; 2.4.2 Metrics in Continuous Spaces; Illustration: Distributions in a Continuous Space; 2.4.2.1 Expected Value and Variance; 2.5 Conditional Probability; Illustration: Drawing a Spade; 2.5.1 Bayes Theorem; Illustration: Detecting Illegal Insider Trading; 2.5.2 Independent Random Variables Illustration2.5.2.1 Multiple Random Variables; 2.6 Distributions and Probability Density Functions; 2.6.1 The Binomial Random Variable; Illustration: Coin Tossing; Illustration: DK Trades; 2.6.2 The Uniform Random Variable; Illustration: Uniform Random Variable; 2.6.3 The Normal Random Variable; 2.6.3.1 Calculating Cumulative Normal Density; 2.6.3.2 Linear Combinations of Independent Normal Random Variables; 2.6.4 The Lognormal Random Variable; 2.6.4.1 The Expected Value of the Lognormal Distribution; Illustration: Risky Securities; 2.6.5 The Poisson Random Variable