Amber Habib is a professor at the Mathematical Sciences Foundation, New Delhi. He obtained his Masters in mathematics from IIT Kanpur and his PhD from the University of California, Berkeley. His research interests are in representation theory and harmonic analysis. He is also deeply involved in making mathematics education more interesting and fulfilling through special topics, projects, and an appreciation of the myriad links of mathematics with other disciplines.

1 Basic Concepts 1.1 Arbitrage 1.2 Return and Interest 1.3 The Time Value of Money 1.4 Bonds, Shares and Indices 1.5 Models and Assumptions 2 Deterministic Cash Flows 2.1 Net Present Value 2.2 Internal Rate of Return 2.3 A Comparison of IRR and NPV 2.4 Bonds: Price and Yield 2.5 Clean and Dirty Price 2.6 Price –Yield Curves 2.7 Duration 2.8 Term Structure of Interest Rates 2.9 Immunisation 2.10 Convexity 2.11 Callable Bonds 3 Random Cash Flows 3.1 Random Returns 3.2 Portfolio Diagrams and Efficiency 3.3 Feasible Set 3.4 Markowitz Model 3.5 Capital Asset PricingModel 3.6 Diversification 3.7 CAPM as a Pricing Formula 3.8 Numerical Techniques 4 Forwards and Futures 4.1 Forwards and Futures 4.2 Forward and Futures Price 4.3 Value of a Futures Contract 4.4 Method of Replicating Portfolios 4.5 Hedging with Futures 4.6 Currency Futures 4.7 Stock Index Futures 5 Stock Price Models 5.1 LognormalModel 5.2 Geometric BrownianMotion 5.3 Suitability of GBM for Stock Prices 5.4 Binomial Tree Model 6 Options 6.1 Call Options 6.2 Put Options 6.3 Put–Call Parity 6.4 Binomial Options PricingModel 6.5 Pricing American Options 6.6 Factors Influencing Option Premiums 6.7 Options on Assets with Dividends 6.8 Dynamic Hedging 6.9 Risk-Neutral Valuation 7 The Black–Scholes Model 7.1 Risk-Neutral Valuation 7.2 The Black–Scholes Formula 7.3 Options on Futures 7.4 Options on Assets with Dividends 7.5 Black–Scholes and BOPM 7.6 Implied Volatility 7.7 Dynamic Hedging 7.8 The Greeks 7.9 The Black–Scholes PDE 7.10 Speculating with Options 8 Value at Risk 8.1 Definition of VaR 8.2 Linear Model 8.3 QuadraticModel 8.4 Monte Carlo Simulation 8.5 The Martingale Appendix A: Calculus A.1 One Variable Calculus A.2 Partial Derivatives A.3 LagrangeMultipliers Method A.4 Differentiating under the Integral Sign A.5 Double Integrals Appendix B: Probability and Statistics B.1 Basic Probability B.2 Random Variables B.3 Cumulative Distribution Function B.4 Binomial Random Variable B.5 Normal Random Variable B.6 Expectation and Variance B.7 Lognormal Random Variable B.8 Cauchy Random Variable B.9 Bivariate Distributions B.10 Conditional Probability B.11 Independence B.12 Multivariate Distributions B.13 Covariance Matrix B.14 Linear Regression and Least Squares B.15 Random Sampling B.16 Sample Mean, Variance and Covariance B.17 Central Limit Theorem B.18 Stable Distributions B.19 Data Fitting B.20 Monte Carlo Simulation Appendix C: Solutions to Selected Exercises Bibliography Index