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wickerhauser m introducing financial mathematics theory 2022

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Textbook in PDF format Introducing Financial Mathematics: Theory, Binomial Models, and Applications seeks to replace existing books with a rigorous stand-alone text that covers fewer examples in greater detail with more proofs. The book uses the fundamental theorem of asset pricing as an introduction to linear algebra and convex analysis. It also provides example computer programs, mainly Octave/MATLAB functions but also spreadsheets and Macsyma scripts, with which students may experiment on real data.The text's unique coverage is in its contemporary combination of discrete and continuous models to compute implied volatility and fit models to market data. The goal is to bridge the large gaps among nonmathematical finance texts, purely theoretical economics texts, and specific software-focused engineering texts. Preface Basics Assets and Portfolios Stocks and Bonds Foreign Exchange Derivatives Riskless Return Interest Rates and Present Value Payoff and Profit Graphs Payoff Graphs for Forward Contracts Payoff and Profit Graphs for Options Payoff and Profit Graphs for Contingent Options Arbitrage Random Variables and Stochastic Processes Deterministic Arbitrages Arbitrage and Expected Value No Arbitrage and Its Consequences Hedging Martingales and Fair Prices No-Arbitrage Price Equalities No-Arbitrage Inequalities Exercises Further Reading Continuous Models Some Facts from Probability Theory Understanding Brownian Motion The Black-Scholes Formula Option Pricing Historical Note Black-Scholes Greeks Implementation Numerical Differentiation Interpolation Regression Exercises Further Reading Discrete Models One-Step, Two-State Models Risk Neutral Probabilities Pricing Derivatives by Hedging Pricing Foreign Exchange Derivatives by Hedging Zero-Coupon Bonds of Different Maturity One-Step, Multistate Models Multistep Binomial Models Recombining Models Generalized Backward Induction Pricing Arrow-Debreu Securities Jamshidian’s Forward Induction Formula Zero-Coupon Bonds and Interest Rate Constraints The Cox-Ross-Rubinstein Model Arrow-Debreu Decomposition in CRR Limit of CRR as N → ∞ CRR Greeks Exercises Further Reading Exotic Options Recombining Binomial Tree Prices European-Style Options in CRR American-Style Options in CRR Binary Options in CRR Compound Options in CRR Chooser Options in CRR Forward Start Options in CRR Barrier Options Booster Options Path Dependent Prices Efficient Data Structures Paths in Recombining Trees Path Dependent Arrow-Debreu Securities Asian-Style Options Floating Strike Options Lookback Options Ladder Options Exercises Further Reading Forwards and Futures Discrete Models for Forwards No-Arbitrage Forwards Values Binomial Models for Forwards Prices Discrete Models for Futures Binomial Models for Futures Prices No-Arbitrage Futures Values Margin Calls and Defaults Exercises Further Reading Dividends and Interest Stocks with Dividends Effects on Forwards Effects on American Call Options Dividends as Cash Flows Interest Rates Zero-Coupon Bonds Coupon Bonds Cash Flow Swaps Benchmarks Exercises Further Reading Implied Volatility The Inverse Problem for Volatility Implied Volatility Surfaces Implied Binomial Trees Path Independent Probabilities Jackwerth’s Generalization Rubinstein’s One-Two-Three Algorithm Exercises Further Reading Fundamental Theorems Finite Financial Models Arbitrage and Positivity Fundamental Theorems of Asset Pricing Applications of the Fundamental Theorems Hedges Complete Markets Incomplete Markets Cones, Convexity, and Duals Open and Closed Sets Dual Cones and Double Duals Proofs of the Fundamental Theorems Farkas’s Lemma Hyperplane Separation Exercises Further Reading Project Suggestions Index

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wickerhauser m introducing financial mathematics theory 2022

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